# Multi-indication evidence synthesis in oncology health technology assessment

Janharpreet Singh  Biostatistics Research Group, Department of Population
Health Sciences, University of Leicester, Leicester, UK  Sumayya Anwer  Centre
for Reviews and Dissemination, University of York, York, UK  Stephen Palmer
Centre for Health Economics, University of York, York, UK  Pedro Saramago
Centre for Health Economics, University of York, York, UK  Anne Thomas
Leicester Cancer Research Centre, University of Leicester, Leicester, UK
Sofia Dias  Centre for Reviews and Dissemination, University of York, York, UK
Marta Soares  Centre for Health Economics, University of York, York, UK
Sylwia Bujkiewicz  Biostatistics Research Group, Department of Population
Health Sciences, University of Leicester, Leicester, UK

###### Abstract

Background: Multi-indication cancer drugs receive licensing extensions to
include additional indications, as trial evidence on treatment effectiveness
accumulates. We investigate how sharing information across indications can
strengthen the inferences supporting Health Technology Assessment (HTA).

Methods: We applied meta-analytic methods to randomised trial data on
bevacizumab, to share information across oncology indications on the treatment
effect on overall survival (OS) or progression-free survival (PFS), and on the
surrogate relationship between effects on PFS and OS. Common or random
indication-level parameters were used to facilitate information sharing and
the further flexibility of mixture models was also explored.

Results: Treatment effects on OS lacked precision when pooling data available
at present-day within each indication separately, particularly for indications
with few trials. There was no suggestion of heterogeneity across indications.

Sharing information across indications provided more precise inferences on
treatment effects, and on surrogacy parameters, with the strength of sharing
depending on the model. When a surrogate relationship was used to predict OS
treatment effects, uncertainty was only reduced with sharing imposed on PFS
effects in addition to surrogacy parameters.

Corresponding analyses using the earlier, sparser (within and across
indications) evidence available for particular HTAs showed that sharing on
both surrogacy and PFS effects did not notably reduce uncertainty in OS
predictions. Limited heterogeneity across indications meant that the added
flexibility of mixture models was unnecessary.

Conclusions: Meta-analysis methods can be usefully applied to share
information on treatment effectiveness across indications in an HTA context,
to increase the precision of target indication estimates. Sharing on surrogate
relationships requires caution, as meaningful precision gains will likely
require larger bodies of evidence and clear support for surrogacy from other
indications.

Keywords: Meta-analysis, health technology assessment, oncology, surrogate
endpoints, mixture models, multi-indication drugs

##  1 Introduction

In health technology assessment (HTA) of cancer drugs, evidence on a relative
treatment effect on overall survival (OS) supports assessments of the clinical
and economic value of a drug, relative to a comparator, for a patient
population defined by a particular indication (e.g., tumour type and stage of
disease). As HTA agencies seek to make a reimbursement decision soon after a
drug is licensed, to ensure timely patient access to treatment, the evidence
on treatment effectiveness may be limited. Regulatory agencies increasingly
make accelerated licensing decisions based on a single trial, and often a
treatment effect measured on a surrogate endpoint; for example progression-
free survival (PFS) as a surrogate endpoint to OS [1]. This can result in
large uncertainty in effect estimates on OS, or effect estimates available for
PFS alone, at the time the HTA is conducted.

Some cancer drugs are, however, trialled across multiple indications over
time. When the results in a new indication are reported, the drug’s license
may be extended to this new indication [2]. Despite this accumulation of
evidence over time, HTAs typically restrict their scope to consider evidence
within a single target indication. Alternatively, sharing information across
indications could strengthen the evidence base supporting decision-making on a
new indication. The National Institute for Health and Care Excellence (NICE)
in England and Wales has identified the development of evidence synthesis
methods for multi-indication HTA of cancer drugs as a key priority [3].

Explicit evidence synthesis models exist that share information across
evidence sets [4] by defining relationships between parameters corresponding
to the different sets of evidence. These relationships can be functional,
hierarchical, multivariate, or based on a prior distribution in a Bayesian
framework. For example, network meta-analysis, which allows for sharing of
information across treatment comparisons, has become an established method to
inform treatment effect estimates in HTA [5]. Similarly, multivariate meta-
analysis for sharing information across multiple outcomes, has been proposed
to help validate a supposed surrogate endpoint as a good predictor of clinical
benefit by modelling a surrogate relationship between the treatment effects on
a surrogate endpoint (e.g PFS) and a final clinical outcome (e.g OS) [6, 7,
3].

Sharing of information has been previously applied in the multi-indication
context. Panoramic meta-analysis [8, 9], and models for the analysis of basket
trials of histology independent oncology drugs [10, 11], have used
hierarchical models assuming full exchangeability (similarity) across
indications where indication-level parameters vary according to a common
distribution. In these models, the data determine the strength of sharing.
However, more flexible models may be required to support decision making. For
example, models that do not presume full exchangeability, and models which
allow clinical opinion to regulate the degree of sharing where there is
uncertainty regarding the plausibility of sharing across particular
indications due to clinical factors.

Mixture models implement a sharing component and a component assuming
independence, with the contribution of each component being regulated by a
probability parameter. This probability can either be pre-specified, estimated
from the data, or informed by a prior distribution to incorporate external
information. The simplest mixture model consists of a weighted mixture of two
components: an informative prior distribution (sharing component), and a vague
prior distribution [12]. Extensions include a model where the sharing
component consists of a common parameter across strata [13], and a model where
the sharing component consists of a hierarchical relationship across strata
[14]. The latter model has been termed a partial exchangeability model and was
originally proposed for the analysis of indication strata within an individual
study.

Mixture models have been applied in other contexts of evidence synthesis, but
have not been formally evaluated for use in the multi-indication context.
Notably, Papanikos et al shared information on surrogate relationships
(between treatment effects on surrogate and final outcomes) across treatment
classes by assuming either full, or partial, exchangeability for the class-
level surrogacy parameters [15]. They found that the models for sharing
information can provide a reduction in uncertainty compared to a subgroup
analysis, particularly where data are limited within classes, and that the
partial exchangeability model can identify differences in surrogate
relationships between classes to regulate the level of sharing.

Applying mixture models to perform a multi-indication meta-analysis could
allow sharing of information across similar indications whilst avoiding
sharing from extreme indications, providing more robust inference in cases
where the plausibility of full exchangeability across indications is
uncertain. These models could also allow for the inclusion of external
information on the mixture probability representing the plausibility of
sharing across indications. Furthermore, such models can be implemented to
share either on treatment effects on OS as a single final endpoint, or on the
surrogate relationships between treatment effects on PFS and OS to predict an
effect on OS for a particular indication.

In this paper, we demonstrate the application of mixture models to multi-
indication meta-analysis in oncology, to enable sharing on individual
endpoints and on a surrogate relationship, where a predicted treatment effect
on OS is the key estimate of interest. We use the example of bevacizumab, one
of the earliest multi-indication oncology drugs, which has been trialled
across multiple cancer indications and been the subject of several NICE
technology appraisals (TAs).

In the remainder of this paper, we describe the data set for the bevacizumab
case study (Section 2), introduce the meta-analysis models implemented to
share information across indications (Section 3), present the results from
applying the models to the case study data (Section 4) and discuss our
findings (Section 5).

##  2 Case study: bevacizumab

Bevacizumab is an angiogenesis inhibitor which is used as a targeted therapy
for different solid tumours and has become the standard-of-care treatment for
several advanced cancers [2]. It has received multiple licensing extensions
from the European Medicines Agency, such that it is currently approved as a
treatment for seven cancer indications. In the UK, it has been the subject of
11 NICE TAs across seven cancer indications.

The evidence base for bevacizumab was established by performing a literature
search to identify randomised controlled trial (RCT) evidence across its
licensed indications in the advanced or metastatic cancer setting: breast
cancer (BC), cervical cancer (CC), colorectal cancer (CRC), glioblastoma
(GBM), non-small cell lung cancer (NSCLC), ovarian fallopian tube, and primary
peritoneal (OFTPP) cancer, and renal cell carcinoma (RCC). Evidence sources
included NICE TAs, Cochrane Reviews, and the ClinicalTrials.gov database. The
scope was restricted to phase II/III trials where the treatment effect of
bevacizumab as a monotherapy could be isolated.

Figure 1 shows the development of RCT evidence on the relative effectiveness
of bevacizumab from 1997 to 2023, and the time point(s) at which these trials
reported results. A total of 41 RCTs across seven cancer indications were
identified. Most of these trials compared the addition of bevacizumab to
backbone therapy, typically chemotherapy. All 41 trials reported effect
estimates for PFS, and 36 reported effect estimates for OS.

Over the time period considered, bevacizumab was the subject of seven NICE TAs
across four cancer indications. The appraisal time points are indicated in
Figure 1 with vertical dashed lines. For our analyses, we will focus on the
evidence available at present day and at two appraisal time points, an earlier
time point with limited evidence and a later time point with more abundant
evidence. The first appraisal is TA178, appraising the use of bevacizumab in
RCC [16]. At the time of this appraisal, there were three completed trials in
the target indication (three reporting effect estimates for PFS and two for
OS), and an additional 14 trials across three other indications (14 reporting
effect estimates for PFS and 11 for OS). The second appraisal is TA285 in
ovarian cancer [17]. By the time of this appraisal, there were four trials in
this indication (all reporting effect estimates for both PFS and OS), and an
additional 28 trials across six other indications (28 reporting effect
estimates for PFS, and 23 for OS). We focus on these time points to
demonstrate the methods in contrasting scenarios in terms of the availability
of evidence.

Figure 1: Plot summarises the accumulation of data on overall survival (OS)
(circles) and progression-free survival (PFS) (crosses) from randomised
controlled trials assessing bevacizumab within each cancer indication
(labelled on far right) between 1997 and 2023. Vertical dashed lines indicate
time points corresponding to particular technology appraisals (TAs) by the
National Institute for Health and Care Excellence. NSCLC - Non-small cell lung
cancer.

Figure 2 presents the final log hazard ratio (HR) estimates, on PFS (left) and
OS (right), reported by trials across all cancer indications. The estimates
are ordered by OS effect size (largest to smallest) within each indication.
The majority of trials show a significantly favourable effect of bevacizumab
on PFS and this is consistent both within and across indications. There is
more uncertainty around effect estimates on OS, where point estimates indicate
a favourable effect of bevacizumab but statistical significance is achieved in
only seven trials. For the indications with relatively more trials (CRC, NSCLC
and OFTPP), there is evidence of between-studies heterogeneity in PFS
estimates (demonstrated by non-overlapping confidence intervals), although
this is more difficult to establish on OS. The data show that larger effect
estimates on PFS correspond to larger effect estimates on OS, particularly for
CRC, NSCLC, and OFTPP cancer, which is suggestive of a potential surrogate
relationship between these outcomes.

Figure 2: Forest plot summarising log-transformed hazard ratio estimates on
progression-free survival (PFS) and overall survival (OS) from randomised
controlled trials assessing bevacizumab across cancer indications. Estimates
are ordered by OS effect size within each cancer indication. BEV -
bevacizumab. NSCLC - Non-small cell lung cancer. OFTPP - Ovarian, fallopian
tube and primary peritoneal. A list of full treatment names is provided in
Appendix B.1.

##  3 Methods

In this section, we define the models used to perform the multi-indication
meta-analysis (3.1) and detail their implementation (3.2). All models are
defined in a Bayesian framework and are implemented using Markov chain Monte
Carlo (MCMC) simulation. We describe the models in two parts. The first part
relates to the within-indication model components (Section 3.1.1). In this
part, we synthesise treatment effects on OS (univariate models) or,
alternatively, on surrogate relationships between treatment effects on PFS and
OS (bivariate models). Both approaches synthesise data on the log HR scale.
The second part relates to the between-indications component of the models
(Section 3.1.2). We consider five alternative approaches to facilitate
different levels of sharing of information across indications on the
indication-specific parameters. We apply each of the five sharing approaches
to both the univariate and bivariate models. We also consider how to interpret
parameters in the context of HTA decision-making and how to predict a
treatment effect on OS, the key parameter of interest, using the bivariate
models (Section 3.1.3).

###  3.1 Models for multi-indication meta-analysis

####  3.1.1 Within-indication component: within-study and between-studies
models

Modelling approaches considered at the within-indication level use standard
meta-analytic specifications for the within-study (likelihood) and the
between-studies models.

The univariate models use a standard contrast-based meta-analytic approach
assuming the normal-normal hierarchical (random effects) model as described by
Sutton and Abrams [18]. This assumes that the relative treatment effects,
$Y_{ij}$ (in study $i$ within indication $j$), are normally-distributed, with
associated standard errors $\sigma_{ij}^{2}$ (assumed known), and mean defined
by the true treatment effects $\delta_{ij}$,

$Y_{ij}\sim N(\delta_{ij},\sigma_{ij}^{2}).$ (1)

At the between-studies level, the true treatment effects are assumed to be
exchangeable across studies within each indication,

$\delta_{ij}\sim N(d_{j},\tau_{j}^{2}),$ (2)

where $d_{j}$ is the pooled effect for indication $j$ and $\tau_{j}$ is the
associated (within-indication) between-studies standard deviation. A weakly
informative half-Normal prior distribution is placed on the between-studies
standard deviation parameters, $\tau_{j}\sim|N(0,0.5^{2})|$, as recommended by
Rover et al [19], which are assumed to be independent across indications in
all analyses. For the purpose of multi-indication meta-analysis, we seek to
share information on the pooled effects, $d_{j}$.

The bivariate modelling approach uses the formulation by Daniels and Hughes
[7] to examine a linear surrogate relationship between the treatment effects
on the surrogate endpoint and on the final clinical outcome within each
indication. We assume that, in each study $i$ and indication $j$, data on the
effects are available (e.g., as log HR estimates) on a surrogate endpoint,
$Y_{1ij}$, and a final outcome, $Y_{2ij}$, with associated standard errors
$\sigma^{2}_{1ij}$ and $\sigma^{2}_{2ij}$, respectively, and within-study
correlation $\rho_{wij}$. At the within-study level, the correlated observed
effects are assumed to follow a bivariate normal distribution,

$\displaystyle\begin{pmatrix}Y_{1ij}\\\ Y_{2ij}\end{pmatrix}\sim
N\left(\begin{pmatrix}\delta_{1ij}\\\
\delta_{2ij}\end{pmatrix},\begin{pmatrix}\sigma_{1ij}^{2}&\sigma_{1ij}\sigma_{2ij}\rho_{wij}\\\
\sigma_{1ij}\sigma_{2ij}\rho_{wij}&\sigma_{2ij}^{2}\end{pmatrix}\right)$ (3)

where $\delta_{1ij}$ and $\delta_{2ij}$ are the correlated true effects on the
surrogate endpoint and final clinical outcome, respectively. The within-study
correlation between the effects on the two outcomes is rarely reported, but
can be informed by external data or assigned a prior distribution. We use a
vague uniform prior distribution in our implementation $\rho_{wij}\sim
U(-1,1)$.

At the between-studies level, the true effects on the final outcome,
$\delta_{2ij}$, are assumed to have a linear relationship with the true
effects on the surrogate endpoint $\delta_{1ij}$,

$\delta_{2ij}\sim
N\left(\lambda_{0j}+\lambda_{1j}\delta_{1ij},\psi^{2}_{j}\right)$ (4)

where $\lambda_{0j}$ and $\lambda_{1j}$ represent the intercept and slope
respectively, and $\psi^{2}_{j}$ is the variance of the true effects on the
final outcome conditional on the true effects on the surrogate endpoint
(conditional variance) within indication $j$.

These parameters can be used to assess the strength of the surrogate
relationship using the criteria proposed by Daniels and Hughes [7]; where a
null effect on the surrogate endpoint should imply a null effect on the final
outcome ($\lambda_{0j}=0$), the slope should indicate an association between
the endpoints ($\lambda_{1j}\neq 0$), and the conditional variance measures to
what extent the treatment effect on the final outcome can be predicted from
the effect on the surrogate endpoint (with $\psi_{j}^{2}=0$ corresponding to
perfect predictions). Vague normal prior distributions are placed on the true
effects corresponding to the surrogate endpoint, $\delta_{1ij}\sim
N\left(0,10^{2}\right)$, which are assumed to be independent across studies.
For the purpose of multi-indication meta-analysis, we seek to share
information on the intercept ($\lambda_{0j}$), slope ($\lambda_{1j}$), and
conditional variance parameters ($\psi^{2}_{j}$), across indications.

####  3.1.2 Between-indications component

We apply five distinct between-indications models making different assumptions
about the relationships between indication-specific parameters, and therefore,
implying different degrees of sharing of information across indications. To
allow generalisability to both univariate and bivariate modelling approaches,
we henceforth denote the indication-level parameters by the vector
$\boldsymbol{\theta}_{j}$. Note that, in the bivariate approach, the following
five models share information for each of the three surrogacy parameters
(intercept, slope and conditional variance), but the sharing relationships are
implemented independently for each parameter such that the level of sharing
could differ between the parameters.

##### Independent parameters (IP) model

Here, independent prior distributions are placed on the
$\boldsymbol{\theta}_{j}$ ,

$\boldsymbol{\theta}_{j}\sim P().$ (5)

When modelling data on a treatment effect (univariate model), we use a vague
normal prior distribution for each indication, $P(d_{j})=N(0,10^{2})$. When
considering parameters of a surrogate relationship (bivariate model), the
vague prior distributions used for each of the parameters are;
$P(\lambda_{0j})=N(0,10^{2})$, $P(\lambda_{1j})=N(0,10^{2})$ and
$P(\psi_{j})=|N(0,0.5^{2})|$.

In the IP model, the indication-level parameters are informed by direct
(within-indication) evidence only and there is no sharing of information
across indications. This model provides a reference to compare the treatment
effect estimates from other models where sharing is allowed.

##### Common parameter (CP) model

Here, we assume a common overall treatment effect parameter,
$\boldsymbol{\theta}$, which pools the indication-specific parameter values,

$\boldsymbol{\theta}_{j}=\boldsymbol{\theta}.$ (6)

A vague prior distribution $\boldsymbol{\theta}\sim P()$ is then assigned to
this parameter.

The CP model implements the maximum sharing of information, serving as a polar
opposite reference to the IP model, enabling an assessment of the assumption
of equal effects between indications.

##### Mixed common and independent parameters (MCIP) model

Here, a mixture of common and independent parameters (MCIP) is assumed. This
is facilitated by a mixture indicator variable, $c_{j}$, which follows a
Bernoulli distribution. In each iteration of the MCMC simulation, this
variable is either equal to 1, in which case the $\boldsymbol{\theta}_{j}$ are
assumed equivalent, or is equal to 0, in which case $\boldsymbol{\theta}_{j}$
are assumed independent,

$\displaystyle\boldsymbol{\theta}_{j}=\begin{cases}\boldsymbol{\theta},\quad&c_{j}=1\\\
\boldsymbol{\theta}_{j}\sim P(),\quad&c_{j}=0\end{cases}$ (7) $\displaystyle
c_{j}\sim Bernoulli(p_{j}).$

The mixture hyper-parameter, $p_{j}$, is assigned a vague beta prior
distribution, $p_{j}\sim\beta(1,1)$ to reflect uncertainty in its values. The
posterior mean of the mixture indicator, $c_{j}$, represents the mixture
probability quantifying the level of mixing.

The MCIP model combines the IP and CP models, providing additional flexibility
for the data to determine, for each indication, the plausibility of the IP and
CP assumptions. Note that, in this model, the overall pooled parameter,
$\boldsymbol{\theta}$, does not represent a common effect across all
indications in the data set, but rather a common effect conditional on such a
common effect existing. For example, an indication with data that is extreme
in relation to those of other indications will be estimated to have a small
mixture probability value and, for this reason, will make only a negligible
contribution to the overall pooled parameter estimate.

##### Random parameters (RP) model

Here, the indication-level parameters are assumed to be fully exchangeable
(also termed random), and vary according to a common distribution,

$\boldsymbol{\theta}_{j}|\boldsymbol{\eta}_{j}\sim F(\boldsymbol{\eta}_{j}).$
(8)

The exchangeability distribution is typically defined as normal. For the
univariate between-indications model, it is defined as

$d_{j}|m_{d},\tau_{d}\sim F(m_{d},\tau_{d})=N(m_{d},\tau_{d}^{2}),$ (9)

where $m_{d}$ is the overall pooled effect and $\tau_{d}$ is the between-
indications standard deviation. A vague normal prior distribution is placed on
the pooled parameter $m_{d}\sim N(0,10^{2})$, and a weakly-informative half-
normal prior distribution is placed on the standard deviation parameter
$\tau_{d}\sim|N(0,0.5^{2})|$.

For the bivariate between-indications model, the exchangeability distributions
are given by,

$\displaystyle\lambda_{0j}|\beta_{0},\xi_{0}\sim
F(\beta_{0},\xi_{0})=N(\beta_{0},\xi_{0}^{2})$ (10)
$\displaystyle\lambda_{1j}|\beta_{1},\xi_{1}\sim
F(\beta_{1},\xi_{1})=N(\beta_{1},\xi_{1}^{2})$ $\displaystyle\psi_{j}|h\sim
F(h)=|N(0,h)|$

where $\beta_{0}$ and $\beta_{1}$ are the overall pooled intercept and slope
parameters, respectively, $\xi_{0}$ and $\xi_{1}$ are the associated between-
indications standard deviation parameters, and $h$ is the between-indications
variance of the conditional variances. The overall pooled intercept and slope
parameters can be assigned a vague normal prior distribution
$\beta_{0},\beta_{1}\sim N(0,10^{2})$, and a weakly-informative half-normal
prior distribution can be placed on the between-indications standard deviation
parameters $\xi_{0},\xi_{1}\sim|N(0,0.5^{2})|$. Finally, a vague gamma prior
distribution can be placed on the between-indications variance parameter for
the conditional variances $h\sim\Gamma(1,0.01)$.

The RP model assumes full exchangeability, and the data determines the level
of sharing via the parameters of the common distribution. The between-
indications standard deviation parameters quantify the level of heterogeneity
between the indication-level effect estimates. Smaller standard deviation
values suggest that the effect estimates are expected to be more similar
across indications (with results of the RP model approximating those of the CP
model), and larger values suggest that the effect estimates differ
significantly from each other (with results of the RP model approximating
those of the IP model). Within this model, indication-specific effects are
shrunk towards the overall mean effect. The degree of shrinkage depends on the
data. An extreme but imprecise IP model effect is likely to be significantly
shrunken in the RP model towards the overall mean, whilst retaining large
uncertainty. A less extreme and imprecise IP model effect may become more
precise under the RP model, but with the point estimate not significantly
changed.

##### Mixed random and independent parameters (MRIP) model

Here, a mixture of random and independent parameters (MRIP) is assumed

$\displaystyle\boldsymbol{\theta}_{j}\sim\begin{cases}F(\boldsymbol{\eta}_{j}),\quad&c_{j}=1\\\
P(),\quad&c_{j}=0\end{cases}$ (11) $\displaystyle c_{j}\sim Bernoulli(p_{j})$

where $c_{j}$ and $p_{j}$ are the mixture indicator and mixture hyper-
parameter variables, respectively, and have the same interpretation as in the
MCIP model. Here, $F(\boldsymbol{\eta}_{j})$ represents the exchangeability
distribution which is the same as in the RP model (Equations 9 and 10), and
$P()$ is the set of vague prior distributions which are the same as those
defined for the IP model.

The MRIP model provides additional flexibility in relation to the RP model for
the data to determine, for each indication, the plausibility of the RP
assumption via the mixture indicator. In a similar way to the MCIP model, the
parameters describing the exchangeability distribution in the MRIP model do
not represent a common distribution across all indications in the data set.
Instead, they represent a common distribution across indications where a
common distribution is deemed to exist (as determined by the data).

Within this model, $\boldsymbol{\theta}_{j}$ represents the indication-
specific estimate which is a weighted-average (i.e., weighted by the mixture
probability) of the exchangeable and independent components. For the
univariate model, $d_{j}$ is the indication-specific treatment effect estimate
which is informed by sharing information across indications (via the
exchangeability distribution), where the degree of sharing is regulated by the
mixture probability.

####  3.1.3 Obtaining estimates of a treatment effect on overall survival (OS)

In this section, we will consider two points which must be addressed when
using the models described above to predict treatment effects in the context
of HTA. Firstly, how to obtain indication-specific parameter estimates from
each of the sharing models (from the between-indications component). Secondly,
how to obtain predictions of a treatment effect on OS from the bivariate
models.

Considering the between-indications component, the indication-level parameters
in the IP model draw only from the indication-specific evidence. Because
sharing is not allowed, this model does not produce a summary estimate across
all indications, or an estimate for a new indication. All remaining models
impose sharing across indications and so the indication-specific estimates are
influenced by both direct (within-indication) and indirect (between-
indications) evidence. In the CP model, the overall pooled estimate reflects
the expected value (for the effect on a single endpoint or on a surrogacy
parameter) in all of the observed indications (which are assumed equal). For
the univariate models, this overall pooled estimate represents both the
treatment effect across all indications and the effect for a new indication
(since these are assumed to be equivalent).

From the RP model, appropriate estimates for observed indications are the
shrunken estimates $\boldsymbol{\theta}_{j}$. For a new indication, an
estimate can be predicted by sampling from the predictive distribution. For
example, for the univariate RP and MRIP models, the predictive distribution
would be given by $d_{pred}\sim N(m_{d},\tau_{d}^{2})$. In the HTA context,
policy decisions are made for a population and the estimates used to inform
decision-making must take heterogeneity in the treatment effects into
consideration. As such, the mean of the common distribution in the RP model
could lead to overprecise estimates of treatment effect and the predictive
distribution is recommended as a basis for decision-making [20].

For the MCIP and MRIP models, indication-specific estimates are based on the
mixture probability, the estimate from the sharing component (respectively, CP
and RP) and the independent component estimate. For a new indication, a
mixture probability needs to be specified separately to allow for predictions
from the sharing component and from an independent component (which, in the
absence of evidence, could be drawn from a vague prior distribution). Where
the new indication is considered perfectly exchangeable with the indications
deemed similar by the model (i.e. mixture probability equal to one)
predictions from only the sharing component of these models can be used.

Different approaches can be used to obtain predictions of a treatment effect
on OS in a target indication using the bivariate models, i.e. utilising
indication-level parameter estimates obtained from the between-indications
component of the above models for sharing of information on the intercept
($\lambda_{0j}$), slope ($\lambda_{1j}$), and conditional variance
($\psi_{j}^{2}$) parameters (see Equation (4) in Section 3.1.1).

Note that, under the formulation by Daniels and Hughes, the bivariate models
assume independent parameters for the surrogate endpoint (PFS) effect at the
study-level. Consequently, the surrogate relationship estimated by the
bivariate model needs to be applied to an indication-specific effect estimate
for PFS to predict an effect on OS. Decisions over the sharing of information
on this indication-specific PFS effect estimate can differ from those on the
bivariate model into which it is entered. We implemented two options. The
first enters the indication-level PFS estimate from the univariate IP model
into the indication-specific surrogate relationships estimated by each of the
bivariate sharing models (CP, MCIP, RP, MRIP). In this case, the predicted
effect on OS will be based on sharing information on the surrogate
relationships but not on the effects on PFS across indications. The second
approach involves matching the between-indications relationship to share on
both effects on PFS and surrogacy parameters (i.e., the PFS effect estimate
from the CP univariate model is entered into the surrogate relationship
estimated by the CP bivariate model, etc.). Formulae for obtaining a predicted
treatment effect on OS from an effect estimate on PFS are described in
Appendix D.

###  3.2 Model implementation

####  3.2.1 Application to case study

The proposed methods will be initially applied to data on bevacizumab
available at present day (see Figure 2), across all indications. Given that
bevacizumab was one of the earliest multi-indication oncology drugs, this
analysis will examine a well developed evidence base (as well developed as can
be expected in HTA). Results from the present day analysis will represent a
benchmark with which to compare the results from the more policy-relevant
analyses at (earlier) appraisal time points, where less evidence had
accumulated across indications. The analyses at two particular appraisal time
points (TA178 in RCC, and TA285 in OFTPP cancer) assume we want to estimate
effects for the target indication in those appraisals, using the multi-
indication data available at the time of each appraisal (see figures in
Appendix C for a summary of each data set). These analyses will illustrate
whether efficient estimates of key parameters of interest for HTA decision-
making can still be obtained with less developed evidence bases, by sharing
information across indications.

####  3.2.2 Software

All models were implemented in OpenBUGS, via the R2OpenBUGS package (version
3.2.1) [21] in R (version 4.1.3) [22], using MCMC sampling to estimate
Bayesian posterior distributions for model parameters. Each implementation
consisted of three MCMC chains, where 20,000 iterations were used as an
initial burn-in period for each chain. Posterior estimates were based on
80,000 samples per chain, and checked for sensitivity to changes in initial
values. The effective sample size and $\hat{R}$ statistics were used to assess
non-convergence of chains [23].

####  3.2.3 Assessment of fit and model choice

The deviance information criterion (DIC) provides a measure of how well a
model fits a data set, whilst penalising model complexity in terms of the
number of parameters, where lower values are preferred. This measure, along
with the residual deviance, are useful for comparing different models when
applied to the same data set [24]. In our application, we use the residual
deviance and DIC to select between the multi-indication meta-analysis models
(IP, CP, MCIP, RP, MRIP), for the univariate and bivariate models separately,
at each analysis time point. We use a difference of three units in DIC to
represent a meaningful difference in model fit between two models, as
recommended by Spiegelhalter et al [24]. Where the difference is less than
three units in DIC, the simplest model in terms of the number of effective
parameters is selected.

##  4 Results

We report the results from applying the multi-indication meta-analysis methods
described in Section 3, for sharing of information either on treatment effects
on an individual endpoint or on a surrogate relationship between effects on
two endpoints, to the data available at the following three time points (see
Figure 1 for an illustration of trial data with respect to these time points);
present day, TA178 (RCC), and TA285 (OFTPP cancer).

###  4.1 Present day analyses

Figure 3 illustrates the results of the analyses of data available at present
day. It presents the median and 95% credible interval (CrI) for the treatment
effect estimates corresponding to each indication, grouped by the between-
indications model. The columns denoted as ‘PFS’ and ‘OS’ include the estimates
from the application of the univariate models to synthesise effects on PFS and
OS, respectively. The predicted effects on OS obtained from the application of
the bivariate models are included in the columns identified as ‘OS - Predicted
(IP)’ and ‘OS - Predicted (Matched)’. We will describe the results from the
univariate and bivariate models in turn.

Figure 3: Treatment effect estimates (on the log hazard ratio scale) from
multi-indication meta-analysis of data available at present day. For the CP
model, the indication-level estimates are all equivalent to the ’All
indications’ estimate, on the PFS, OS, and OS - Predicted (Matched) outcomes.
PFS - progression-free survival, OS - overall survival, IP - independent
parameters, CP - common parameter, MCIP - mixed common and independent
parameters, RP - random parameters, MRIP - mixed random and independent
parameters, CRC - colorectal cancer, BC - breast cancer, NSCLC - non-small
cell lung cancer, RCC - renal cell carcinoma, CC - cervical cancer, GBM -
glioblastoma, OFTPP - ovarian, fallopian tube, and primary peritoneal.

####  4.1.1 Results from univariate analyses of treatment effects on
individual endpoints

In line with the trial-level results (presented in Figure 2), univariate
synthesis of treatment effects on PFS suggests bevacizumab to be beneficial
across the majority of indications, with no evidence of heterogeneity in the
effects across indications. Where within-indication evidence (IP model) is
insufficient for the treatment effect estimates to be statistically meaningful
(e.g. for CC and GBM), sharing of information across all indications increases
the precision of the estimates leading to CrIs that do not include the null
effect (CP, MCIP, RP, MRIP models).

A positive treatment effect on OS is also apparent from within-indication
evidence (IP model) for those indications with more data, e.g., CRC (nine
trials) and BC (ten trials), but data are too limited to make conclusions for
the other indications. Thus, there is no suggestion from these data that
sharing on OS is inappropriate.

Estimates from the CP model, which assumes equality of the treatment effects
and provides maximal sharing across indications, suggest that a meaningful
positive effect can be expected on both outcomes. The RP model, which allows
for variability in effects across indications, provides indication-specific
estimates that are more similar to each other compared to those from the IP
model (i.e. they are shrunken towards the overall mean), but retain wider
uncertainty for the indications with sparser data (e.g., CC or GBM). Notably,
the point estimate of the PFS effect for BC has not been substantially
shrunken (due to the higher level of evidence for this indication and
discrepancy with the point estimates from the other indications).

The estimates obtained from the mixture models are in close agreement with
those from the corresponding non-mixture sharing model (i.e., MCIP with CP,
MRIP with RP), and the mixture probabilities are approximately equal to one
for most indications (see Table 1 for the mixture probability estimates).
These results add plausibility for sharing across indications in this case
study as the data are relatively consistent. The discrepancy in the point
estimate for the PFS effect in BC is accounted for by the MCIP model, by
attributing this indication a lower mixture probability (mean 0.96, standard
deviation 0.19) compared to the other indications (see Table 1). There is no
meaningful difference in the goodness-of-fit between the different models for
the synthesis of treatment effects on both OS and PFS, as the DIC values
(presented in Appendix A.1.3) differ by less than 3 units. This suggests that
whilst any model could be considered appropriate, the application of the
simpler CP model is most efficient in describing these data.

Table 1: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), from the application of univariate models to data on overall survival (OS), and progression-free survival (PFS), at present-day.  Model | Indication | Probability | Informative | Vague
---|---|---|---|---
OS |  |  |  |
MCIP | BC | 1.00 (0.05) | -0.12 (-0.17, -0.06) | -0.10 (-61.80, 61.70)
MCIP | CC | 0.99 (0.11) | -0.12 (-0.17, -0.06) | -0.21 (-61.70, 61.85)
MCIP | CRC | 0.99 (0.08) | -0.12 (-0.17, -0.06) | -0.14 (-62.23, 61.94)
MCIP | GBM | 0.99 (0.08) | -0.12 (-0.17, -0.06) | 0.02 (-62.00, 61.71)
MCIP | NSCLC | 1.00 (0.06) | -0.12 (-0.17, -0.06) | -0.13 (-61.95, 62.01)
MCIP | OFTPP | 1.00 (0.07) | -0.12 (-0.17, -0.06) | -0.04 (-61.79, 61.94)
MCIP | RCC | 1.00 (0.07) | -0.12 (-0.17, -0.06) | -0.07 (-61.84, 61.94)
MRIP | BC | 1.00 (0.07) | -0.12 (-0.19, -0.04) | -0.06 (-61.65, 61.84)
MRIP | CC | 0.99 (0.11) | -0.13 (-0.30, 0.01) | -0.11 (-61.83, 61.82)
MRIP | CRC | 0.99 (0.07) | -0.14 (-0.25, -0.06) | -0.18 (-61.92, 61.69)
MRIP | GBM | 0.99 (0.08) | -0.10 (-0.21, 0.03) | -0.02 (-61.72, 61.67)
MRIP | NSCLC | 1.00 (0.06) | -0.12 (-0.23, -0.02) | -0.07 (-62.01, 62.20)
MRIP | OFTPP | 1.00 (0.06) | -0.10 (-0.18, -0.01) | -0.08 (-61.97, 61.95)
MRIP | RCC | 0.99 (0.07) | -0.13 (-0.25, -0.01) | -0.08 (-61.95, 61.64)
PFS |  |  |  |
MCIP | BC | 0.96 (0.19) | -0.37 (-0.46, -0.30) | -0.29 (-61.28, 61.39)
MCIP | CC | 0.99 (0.09) | -0.37 (-0.46, -0.30) | -0.16 (-61.79, 61.67)
MCIP | CRC | 0.99 (0.08) | -0.37 (-0.46, -0.30) | -0.34 (-61.80, 61.82)
MCIP | GBM | 0.99 (0.08) | -0.37 (-0.46, -0.30) | -0.30 (-62.12, 61.94)
MCIP | NSCLC | 1.00 (0.06) | -0.37 (-0.46, -0.30) | -0.21 (-61.69, 62.19)
MCIP | OFTPP | 1.00 (0.06) | -0.37 (-0.46, -0.30) | -0.01 (-62.14, 62.23)
MCIP | RCC | 0.99 (0.10) | -0.37 (-0.46, -0.30) | -0.29 (-61.95, 61.70)
MRIP | BC | 0.99 (0.11) | -0.32 (-0.43, -0.24) | -0.28 (-61.82, 61.36)
MRIP | CC | 0.99 (0.10) | -0.39 (-0.61, -0.20) | -0.19 (-61.71, 61.70)
MRIP | CRC | 0.99 (0.08) | -0.42 (-0.58, -0.30) | -0.36 (-61.73, 62.01)
MRIP | GBM | 0.99 (0.09) | -0.41 (-0.60, -0.25) | -0.14 (-61.79, 62.11)
MRIP | NSCLC | 0.99 (0.08) | -0.40 (-0.57, -0.25) | -0.28 (-61.94, 61.63)
MRIP | OFTPP | 0.99 (0.07) | -0.40 (-0.57, -0.25) | -0.17 (-61.67, 62.03)
MRIP | RCC | 0.99 (0.09) | -0.42 (-0.61, -0.28) | -0.31 (-61.39, 62.16)

####  4.1.2 Results of surrogate endpoint evaluation

Before interpreting the results from using the bivariate models to predict a
treatment effect on OS in Section 4.1.3, we focus on the inferences obtained
for the parameters describing the surrogate relationship (i.e., intercept,
slope, and conditional variance parameters) between treatments effects on PFS
and OS. Figure 4 depicts the median and 95% CrI estimates for these parameters
based on the present day data set, where each column corresponds to a
particular parameter and each row includes the indication-specific estimate.
The estimates are grouped by the between-indications model. Further results of
this analysis can be found in Appendix A.1.4, and Appendix A.4 presents the
results from a cross validation procedure used to evaluate the surrogate
relationship in more detail [6]. Note that the intercept parameter is
estimated on the same scale as a treatment effect on the final outcome (OS),
and can be interpreted as a log HR. The slope parameter quantifies how the
effect on the final outcome, OS, varies with respect to the effect on the
surrogate endpoint, PFS, and as such can be interpreted as a ratio of log HRs.

The results from applying the IP model show that the surrogacy parameters are
estimated with large uncertainty in indications with limited data; RCC (two
trials), CC (one trial), and GBM (three trials). Consequently, it is difficult
to determine whether the surrogacy criteria (described in Section 3.1.1) are
satisfied for these indications by considering the within-indication evidence
alone. Across all indications, CrIs for intercepts contain the value zero (as
desired according to the surrogacy criteria). The CrIs for the slope parameter
for CRC and NSCLC (indications with data on both PFS and OS effects from 6,067
patients across nine trials, and 3,034 patients across six trials,
respectively) do not include zero. This suggests a positive association
between the treatment effects on the two outcomes within these indications,
where a larger effect on PFS is associated with a larger effect in OS, and is
indicative of a strong surrogate relationship. However, the CrIs corresponding
to the slope parameter for BC and OFTPP cancer include zero, despite the
availability of a similar level of data (from 4,459 patients across ten trials
in BC, and 4,345 patients across seven trials in OFTPP cancer). This absence
of evidence does not imply that surrogacy does not hold within these
indications, but encourages caution in the interpretation of the results from
the less flexible sharing models, particularly those assuming common or
exchangeable surrogacy parameters across all indications (CP and RP).

The conditional variance estimates were relatively large for RCC, CC and GBM
(compared to other indications), reflecting the sparse evidence for
determining surrogacy in these indications. Out of the remaining indications
(BC, NSCLC, OFTPP cancer and CRC), CRC presents the smallest conditional
variance estimate with the narrowest CrI, due to the higher level of evidence
for the existence of a surrogate relationship (with precise estimates for all
three surrogacy parameters). The higher uncertainty in NSCLC and OFTPP cancer
estimates (in relation to CRC) may be due to the relatively small number of
studies; six and seven studies, respectively. In contrast, the higher
uncertainty in BC estimates (in relation to CRC), where the number of studies
was ten, is indicative of a weaker surrogate relationship within this
indication. The point estimates of the conditional variance parameter
corresponding to BC, NSCLC and OFTPP cancer all appear to be larger compared
to the point estimate for CRC, but this may be due to the higher uncertainty
in these indications and a positively-skewed distribution for this parameter.

Indication-specific estimates from the sharing models are more precise
compared to those from the IP model. For instance, the slope parameter
estimates (including CrIs) are positive in across indications for all sharing
models. An exception to this are the conditional variance estimates from
applying the mixture models (MCIP and MRIP), which still show relatively large
uncertainty for the indications with sparser data: RCC, CC, and GBM. Mixture
probabilities for the intercept and slope parameters are all approximately
equal to one (see Appendix A.1.6), but range between 0.57 and 0.82 for the
conditional variance parameter, assuming lowest values in CC and GBM.

In terms of goodness-of-fit (see Appendix A.1.5), the mixture models have
notably smaller DIC values compared to the non-mixture models, with the lowest
DIC value for the MRIP model. In this application, the added flexibility of
the mixture models (i.e. the ability to regulate the degree of sharing for
each indication) is likely to be more suitable for sharing on the conditional
variance parameter as the corresponding mixture probabilities are lower and
more variable. This indicates a lack of support from the data for the
assumptions of equivalence or exchangeability across indications on this
parameter.

Figure 4: Multi-indication meta-analysis of surrogacy parameters using the
data available at present day. For the CP model, the indication-level
estimates are all equivalent to the ’All indications’ estimate. IP -
independent parameters, CP - common parameter, MCIP - mixed common and
independent parameters, RP - random parameters, MRIP - mixed random and
independent parameters, CRC - colorectal cancer, BC - breast cancer, NSCLC -
non-small cell lung cancer, RCC - renal cell carcinoma, CC - cervical cancer,
GBM - glioblastoma, OFTPP - ovarian, fallopian tube, and primary peritoneal.

####  4.1.3 Predicted effects on overall survival (OS) using surrogate
relationships

The predicted treatment effects on OS obtained from the bivariate models for
each indication are depicted in Figure 3, in columns ‘OS - Predicted (IP)’ and
‘OS - Predicted (Matched)’ (see Section 3.1.3 for a description of how these
are obtained).

The predicted OS effects estimated by the bivariate IP model are consistent
with the pooled OS effects estimated by the univariate IP model, albeit with
slightly larger uncertainty (see Table A3 in Appendix A.1.2 for specific
numerical values). The predicted OS effects estimated by the bivariate models
which allow for sharing of information on the surrogacy parameters (but
without sharing on the PFS effect) are only slightly more precise compared to
estimates from the bivariate IP model, even when implementing a CP assumption.
This demonstrates the limited impact of sharing on the surrogate relationship
alone (when not sharing on the PFS effect). It is only when sharing on both
the PFS effect and the surrogate relationship (OS - Predicted (Matched)
column) that notable precision gains are obtained in relation to not sharing.
This suggests that sharing on the PFS effect, to obtain a more precise pooled
estimate, is particularly important in predicting the corresponding OS effect
using the bivariate models.

Considering the matched bivariate models, which allow for sharing on both the
PFS effect and the surrogate relationship (by matching the sharing assumption
made on the two sets of parameters), the predicted estimates from the
bivariate CP model show the lowest uncertainty, which is to be expected as
this model allows maximal sharing. These estimates are consistent with the
pooled OS estimates from the univariate CP model. The predicted estimates from
the bivariate MCIP model show wider uncertainty than CP model estimates. The
bivariate RP and MRIP models present more variation in the point estimates
across all indications, all being in line with the IP model but shrunken
towards the overall mean value. The shrinkage is greater for indications other
than CRC and BC.

The level of uncertainty in the OS effect estimates predicted by the matched
bivariate sharing models is similar to the uncertainty in the pooled OS
effects estimated by the univariate sharing models. However, there are some
differences in the estimates between the univariate and bivariate approaches.
For instance, the bivariate approach leads to higher variation in point
estimates across indications. Furthermore, predictions for a new indication
made by the hierarchical sharing models (RP and MRIP) have larger uncertainty
in the bivariate context. For CC, for which data were only available from a
single trial, the RP model CrIs include the null effect when sharing across
indications on OS alone, but not when predicting the OS effect by sharing on
both the PFS effect and the surrogacy parameters (see CrI in OS - Predicted
(Matched) column).

###  4.2 Appraisal specific analyses

Figure 5 depicts the results obtained from perfoming multi-indication meta-
analyses using the data that were available on PFS and OS at the time of two
NICE TAs; TA178 for RCC (panel ‘a’ in Figure 5), and TA285 for OFTPP cancer
(panel ‘b’). Further results, including numerical estimates, are presented in
Appendix A.2.1 and Appendix A.3.1) respectively. Broadly, the point estimates
obtained from the different models are consistent with one another within the
target indication, and there is large overlap in the CrIs for the effects on
both PFS and OS. The estimates from the sharing models (CP, MCIP, RP, MRIP)
show improved precision compared to the IP model, which does not allow for
sharing across indications.

The results from the TA time point analyses show a similar trend to those
obtained from the analysis of present day data, in terms of the benefit of
sharing across indications for gaining precision in effect estimates. However,
less evidence had accumulated at these earlier time points and so the
corresponding analyses provide less precise predicted OS effect estimates
(using both the univariate and bivariate approaches). In particular, the
predicted OS effect estimates obtained from the bivariate models are
noticeably more imprecise compared to the pooled estimates from the univariate
models. This remains the case even when sharing is imposed on both the PFS
effect and the surrogate relationship, which contrasts with the results from
the present day analysis, suggesting that predictions based on the bivariate
models are unlikely to strengthen estimates in realistic appraisal contexts.

Figure 5: Multi-indication meta-analysis of data available at the time of: a)
TA178 (target indication: renal cell carcinoma (RCC)), and b) TA285 (target
indication: ovarian, fallopian tube, and primary peritoneal (OFTPP) cancer).
PFS - progression-free survival, OS - overall survival, IP - independent
parameters, CP - common parameter, MCIP - mixed common and independent
parameters, RP - random parameters, MRIP - mixed random and independent
parameters, RCC - renal cell carcinoma, OFTPP - ovarian, fallopian tube, and
primary peritoneal.

##  5 Discussion

In this paper, we explored alternative meta-analysis models for the synthesis
of evidence on treatment effects on an individual endpoint, or on a surrogate
relationship between treatment effects on a surrogate endpoint and a final
clinical outcome, across multiple indications in oncology. We demonstrated the
methods using data on treatment effects of bevacizumab on PFS and OS from
trials across multiple cancer indications, by applying them to all data
available at present day and, in the context of HTA, to data that had
accumulated at time points corresponding to two NICE TAs of bevacizumab; for
renal and ovarian cancers.

Bevacizumab is one of the first examples of a targeted multi-indication cancer
drug, and therefore it’s evidence base is relatively well developed at present
day. Such evidence still shows considerable uncertainty in the OS effect
estimates within the majority of the indications for which bevacizumab is
licensed, but does not show any noticeable heterogeneity in effects across
indications (see Figure 2). This suggests that a case study on bevacizumab is
appropriate to explore whether sharing information across indications has the
potential to strengthen indication-specific evidence, for inference in the HTA
context.

Our case study showed that the application of methods for sharing information
across indications can lead to more precise inferences on treatment effects,
and on the parameters describing a surrogate relationship. This gain in
precision was more noticeable for indications with limited evidence. Although
the OS effects predicted using the surrogacy parameters were consistent with
the pooled OS effects (from sharing across indications on OS effects alone),
they only showed meaningful gains in precision when sharing was imposed on the
PFS effects in addition to the surrogacy parameters. Corresponding analyses
using the earlier, sparser (within and across indications) evidence available
at particular HTA appraisal points showed that sharing on surrogacy
parameters, even when also sharing on PFS effects, did not notably reduce
uncertainty in predicted OS effects. These findings highlight that uncertainty
in the surrogacy parameter estimates may be due to limited evidence or the
lack of a clear surrogate relationship within the broader evidence base (i.e.,
within other indications), and this must be considered when determining
whether sharing across indications on these parameters is appropriate.

There were differences in the support provided by the indication-level
evidence for surrogacy between indications with higher levels of evidence. For
example, the evidence suggested a surrogate relationship within CRC (nine
trials); with small, precise estimates for the intercept and conditional
variance parameters, and a precise non-zero estimate for the slope parameter.
Such estimates are indicative of surrogacy, although there are no clear cut
rules to infer this statistically. Despite there being a similar level of
evidence in BC (ten trials), there was higher uncertainty in the slope and
conditional variance parameters which implies that surrogacy may not hold
within this indication. Thus, the surrogacy parameter estimates based on
sharing information from BC may be deemed overly precise, even for the mixture
models which provide greater flexibility to regulate the level of sharing from
a particular indication. However, it can be argued that as long as these
results are not used to judge the strength of the surrogate relationship
within BC alone, this sharing can be implemented to improve our predictions of
the effect on the final outcome in particular indications. We performed a
sensitivity analysis by applying the sharing models to the present day data
after removing trials in BC but did not see a notable difference in the
surrogacy parameter estimates in the remaining indications (see Appendix
A.7.1).

The predicted OS effect estimate was more greatly influenced by the precision
of the corresponding PFS effect estimate, which was entered into the bivariate
model to make the prediction, than the surrogacy parameter estimates
themselves. This suggests that applying a bivariate model to predict an OS
effect may only be applicable where there is strong evidence on the PFS
effect. In a HTA context, the feasibility of predicting the OS effect for a
particular indication will depend on the level of evidence available on PFS
within that indication and across other indications from which sharing is
deemed plausible. Further research is required to explore the conditions under
which sharing on surrogate relationships strengthens predictions of OS
effects. We expect that this is likely to require that at least one indication
in the broader, multi-indication, evidence base has a meaningful level of
evidence (in terms of data on treatment effects on both the surrogate endpoint
and the final outcome) and shows support for surrogacy.

In this work, we explored a range of models imposing different levels of
information sharing, including no sharing across indications, models with
increasing levels of flexibility in the strength of sharing, to assuming an
equal, common, effect across all indications. These models fit the data
similarly when sharing on each endpoint individually (univariate models),
adding to the plausibility of sharing across all indications, and suggesting
that the added flexibility of the models with higher parametrisations was not
required. However, the application of the more flexible sharing (mixture)
models requires important methodological considerations when sharing on
surrogate relationships (bivariate models). For instance, the mixture
probabilities were much lower for the conditional variance parameter, compared
to the intercept and slope parameters, cautioning against sharing on this
parameter. This may also explain why the mixture models provided a better fit
to these data compared to the non-mixture models which make more rigid
assumptions regarding sharing. We performed a sensitivity analysis where the
sharing models were implemented with the assumption of independent conditional
variance parameters (i.e., sharing on the intercept and slope parameters
only), but did not see a notable difference in results (see Appendix A.6.1). A
better understanding of the scenarios where the mixture models offer a benefit
over the non-mixture models, for example, where data from a particular
indication are more extreme relative to the other indications, would be
provided by a simulation study. Some of such scenarios for sharing information
on surrogate relationships across treatment classes have been explored by
Papanikos et al [15]. A simulation study could also provide a systematic
assessment of the models’ performance (i.e., when they are prone to bias, or
over/under coverage, with respect to a known true effect).

To illustrate and explore the sharing methods in a multi-indication evidence
synthesis context, in our case study, we considered it appropriate to focus
the synthesis on aggregate trial-level data on a treatment effect for a
survival outcome, represented by a log HR on either PFS or OS. However, future
research on multi-indication meta-analyses should extend the methodological
framework to account for scenarios where the log HR is not representative of
the true effect; for example, where there is evidence of non-proportional
hazards between trial arms.

Meta-analytic methods can be usefully applied to share information across
indications to obtain more precise treatment effect estimates on an endpoint
of interest. Such an approach is also applicable when using a bivariate model
to predict an effect on a final outcome based on the effect on a surrogate
endpoint, where sharing across indications can provide precision gains for
both the effect on the surrogate endpoint and the parameters quantifying the
surrogate relationship. Mixture models may be more appropriate when sharing on
a surrogate relationship, where greater flexibility is required to regulate
the degree of sharing on the conditional variance parameter. The findings from
this case study on bevacizumab are likely to be generalisable to other multi-
indication health technologies. For decision-making in a HTA context, these
methods can be beneficial where there is limited evidence on the final outcome
within the target indication, and sufficient evidence has accumulated across
the other indications to demonstrate the existence of a surrogate
relationship. However, the plausibility of any sharing assumptions should be
carefully validated with clinical experts, where possible.

##  6 Acknowledgements

This research was funded by the Medical Research Council, Better Methods
Better Research panel [MRC MR/W021102/1]. SB and JS were also supported by
Leicester NIHR Biomedical Research Centre (BRC). The views expressed are those
of the author(s) and not necessarily those of the NIHR or the Department of
Health and Social Care.

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##  Appendix A Additional results

###  A.1 Present day

####  A.1.1 Pooled OS and PFS estimates

Table A1: Mean and 95% credible interval estimates from applying univariate multi-indication meta-analysis models to data available at present-day on treatment effects on overall survival (log hazard ratio scale). Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | -0.19 (-0.33, -0.07) | -0.12 (-0.17, -0.07) | -0.12 (-0.18, -0.06) | -0.15 (-0.25, -0.07) | -0.15 (-0.25, -0.06)
RCC | -0.15 (-0.65, 0.35) | -0.12 (-0.17, -0.07) | -0.12 (-0.18, -0.06) | -0.13 (-0.25, -0.01) | -0.13 (-0.25, -0.01)
BC | -0.11 (-0.22, 0.00) | -0.12 (-0.17, -0.07) | -0.12 (-0.17, -0.06) | -0.12 (-0.19, -0.04) | -0.12 (-0.19, -0.04)
NSCLC | -0.14 (-0.34, 0.08) | -0.12 (-0.17, -0.07) | -0.12 (-0.18, -0.06) | -0.13 (-0.23, -0.02) | -0.13 (-0.23, -0.02)
OFTPP | -0.07 (-0.19, 0.04) | -0.12 (-0.17, -0.07) | -0.12 (-0.17, -0.06) | -0.10 (-0.18, -0.01) | -0.10 (-0.18, -0.01)
CC | -0.26 (-1.35, 0.83) | -0.12 (-0.17, -0.07) | -0.12 (-0.18, -0.06) | -0.13 (-0.30, 0.01) | -0.13 (-0.31, 0.01)
GBM | -0.03 (-0.36, 0.32) | -0.12 (-0.17, -0.07) | -0.12 (-0.18, -0.06) | -0.10 (-0.21, 0.03) | -0.10 (-0.21, 0.04)
All Indications |  | -0.12 (-0.17, -0.07) | -0.12 (-0.17, -0.06) | -0.12 (-0.20, -0.04) | -0.12 (-0.20, -0.04)
New Indication |  |  |  | -0.12 (-0.29, 0.05) | -0.12 (-0.29, 0.04)
Table A2: Mean and 95% credible interval estimates from applying univariate multi-indication meta-analysis models to data available at present-day on treatment effects on progression-free survival (log hazard ratio scale). Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | -0.47 (-0.67, -0.30) | -0.37 (-0.45, -0.30) | -0.38 (-0.47, -0.30) | -0.43 (-0.58, -0.30) | -0.43 (-0.58, -0.31)
RCC | -0.53 (-1.01, -0.15) | -0.37 (-0.45, -0.30) | -0.38 (-0.47, -0.30) | -0.43 (-0.61, -0.28) | -0.43 (-0.62, -0.28)
BC | -0.29 (-0.38, -0.21) | -0.37 (-0.45, -0.30) | -0.37 (-0.45, -0.29) | -0.32 (-0.42, -0.24) | -0.32 (-0.42, -0.24)
NSCLC | -0.42 (-0.73, -0.11) | -0.37 (-0.45, -0.30) | -0.37 (-0.46, -0.30) | -0.40 (-0.58, -0.25) | -0.40 (-0.57, -0.25)
OFTPP | -0.41 (-0.71, -0.11) | -0.37 (-0.45, -0.30) | -0.37 (-0.46, -0.30) | -0.40 (-0.57, -0.25) | -0.40 (-0.57, -0.25)
CC | -0.38 (-1.48, 0.70) | -0.37 (-0.45, -0.30) | -0.37 (-0.47, -0.30) | -0.39 (-0.61, -0.20) | -0.39 (-0.61, -0.20)
GBM | -0.46 (-0.94, 0.01) | -0.37 (-0.45, -0.30) | -0.38 (-0.47, -0.30) | -0.41 (-0.60, -0.25) | -0.41 (-0.60, -0.25)
All Indications |  | -0.37 (-0.45, -0.30) | -0.37 (-0.46, -0.30) | -0.40 (-0.53, -0.29) | -0.40 (-0.53, -0.29)
New Indication |  |  |  | -0.40 (-0.67, -0.15) | -0.40 (-0.66, -0.16)

####  A.1.2 Predicted OS estimates

Table A3: Mean and 95% credible interval estimates for predicted effects on overall survival (log hazard ratio scale), from entering the progression-free survival effect estimate from the univariate independent parameters (IP) model into the surrogacy models, using data available at present-day. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | -0.22 ( -0.36, -0.09) | -0.17 ( -0.25, -0.07) | -0.17 ( -0.26, -0.08) | -0.20 ( -0.31, -0.09) | -0.20 ( -0.31, -0.09)
RCC | -0.07 ( -9.76, 10.42) | -0.21 ( -5.06, 4.07) | -0.20 ( -4.86, 3.96) | -0.15 ( -4.55, 4.22) | -0.15 ( -4.87, 4.57)
BC | -0.09 ( -0.23, 0.05) | -0.12 ( -0.26, 0.00) | -0.12 ( -0.26, 0.00) | -0.10 ( -0.24, 0.03) | -0.10 ( -0.24, 0.03)
NSCLC | -0.14 ( -0.38, 0.11) | -0.11 ( -0.26, 0.06) | -0.11 ( -0.27, 0.06) | -0.13 ( -0.30, 0.06) | -0.13 ( -0.31, 0.06)
OFTPP | -0.08 ( -0.23, 0.09) | -0.07 ( -0.19, 0.06) | -0.07 ( -0.19, 0.06) | -0.07 ( -0.20, 0.06) | -0.07 ( -0.20, 0.06)
CC | -0.22 (-33.56, 32.95) | -0.21 ( -7.74, 7.33) | -0.21 ( -8.22, 7.80) | -0.26 ( -9.94, 9.24) | -0.26 (-10.45, 9.71)
GBM | -0.02 ( -0.94, 0.91) | 0.00 ( -0.62, 0.60) | 0.00 ( -0.60, 0.59) | -0.01 ( -0.63, 0.61) | -0.01 ( -0.63, 0.62)
Table A4: Mean and 95% credible interval estimates for the predicted effect on overall survival (log hazard ratio scale), from entering the progression-free survival effect estimate from each univariate model into the corresponding surrogacy model, using data available at present-day. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | -0.22 ( -0.36, -0.09) | -0.11 ( -0.16, -0.06) | -0.12 ( -0.19, -0.07) | -0.19 ( -0.29, -0.10) | -0.19 ( -0.29, -0.10)
RCC | -0.07 ( -9.76, 10.42) | -0.11 ( -0.16, -0.06) | -0.12 ( -0.18, -0.06) | -0.14 ( -0.27, -0.02) | -0.14 ( -0.28, -0.01)
BC | -0.09 ( -0.23, 0.05) | -0.11 ( -0.16, -0.06) | -0.11 ( -0.17, -0.06) | -0.09 ( -0.17, -0.01) | -0.09 ( -0.18, -0.01)
NSCLC | -0.14 ( -0.38, 0.11) | -0.11 ( -0.16, -0.06) | -0.11 ( -0.17, -0.06) | -0.14 ( -0.25, -0.04) | -0.14 ( -0.26, -0.03)
OFTPP | -0.08 ( -0.23, 0.09) | -0.11 ( -0.16, -0.06) | -0.11 ( -0.17, -0.05) | -0.09 ( -0.18, 0.00) | -0.09 ( -0.18, 0.01)
CC | -0.22 (-33.56, 32.95) | -0.11 ( -0.16, -0.06) | -0.11 ( -0.24, -0.04) | -0.17 ( -0.37, -0.01) | -0.16 ( -0.40, 0.03)
GBM | -0.02 ( -0.94, 0.91) | -0.11 ( -0.16, -0.06) | -0.12 ( -0.17, -0.04) | -0.07 ( -0.19, 0.05) | -0.07 ( -0.21, 0.06)
All Indications |  | -0.11 ( -0.16, -0.06) | -0.12 ( -0.17, -0.06) | -0.13 ( -0.23, -0.03) | -0.13 ( -0.23, -0.03)
New Indication |  |  |  | -0.13 ( -0.38, 0.09) | -0.13 ( -0.38, 0.10)

####  A.1.3 Deviance information criterion (DIC)

Table A5: Residual deviance, deviance, number of effective parameters, and deviance information criterian (DIC) from the application of univariate models to data on overall survival at present-day. *Based on 38 data points. Model | Residual deviance | Deviance | $p_{D}$ | DIC
---|---|---|---|---
IP | 33.58 | -39.04 | 20.26 | -18.78
CP | 33.80 | -38.82 | 17.06 | -21.76
MCIP | 33.79 | -38.83 | 17.10 | -21.73
RP | 33.38 | -39.24 | 17.87 | -21.37
MRIP | 33.42 | -37.81 | 17.89 | -19.92
Table A6: Residual deviance, deviance, number of effective parameters, and deviance information criterian (DIC) from the application of univariate models to data on progression-free survival at present-day. *Based on 43 data points. Model | Residual deviance | Deviance | $p_{D}$ | DIC
---|---|---|---|---
IP | 42.48 | -44.76 | 29.17 | -15.59
CP | 45.28 | -41.97 | 28.96 | -13.00
MCIP | 45.19 | -42.05 | 28.93 | -13.13
RP | 43.44 | -43.80 | 28.35 | -15.45
MRIP | 43.48 | -42.38 | 28.28 | -14.10

####  A.1.4 Surrogacy parameter estimates

Table A7: Median and 95% credible interval estimates for the intercept parameter in the surrogacy models using data available at present-day. N - number of trials per indication. Indication | N | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---|---
CRC | 9 | 0.05 ( -0.11, 0.21) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.13) | 0.04 ( -0.06, 0.12) | 0.03 ( -0.07, 0.13)
RCC | 2 | 0.05 (-12.75, 15.19) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.13) | 0.05 ( -0.07, 0.16) | 0.05 ( -0.08, 0.17)
BC | 10 | 0.04 ( -0.33, 0.45) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.13) | 0.05 ( -0.06, 0.14) | 0.04 ( -0.06, 0.14)
NSCLC | 6 | 0.10 ( -0.18, 0.38) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.13) | 0.05 ( -0.06, 0.15) | 0.05 ( -0.06, 0.15)
OFTPP | 7 | 0.02 ( -0.18, 0.28) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.13) | 0.05 ( -0.04, 0.15) | 0.05 ( -0.05, 0.15)
CC | 1 | -0.40 (-22.89, 23.86) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.05, 0.14) | 0.03 ( -0.12, 0.14) | 0.03 ( -0.13, 0.16)
GBM | 3 | 0.11 ( -1.52, 1.64) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.13) | 0.07 ( -0.04, 0.21) | 0.06 ( -0.05, 0.21)
Overall | 38 |  | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.13) | 0.05 ( -0.05, 0.14) | 0.05 ( -0.05, 0.14)
Table A8: Median and 95% credible interval estimates for the slope parameter in the surrogacy models using data available at present-day. N - number of trials per indication. Indication | N | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---|---
CRC | 9 | 0.59 ( 0.24, 0.91) | 0.42 ( 0.23, 0.61) | 0.43 ( 0.22, 0.66) | 0.53 ( 0.29, 0.74) | 0.52 ( 0.28, 0.74)
RCC | 2 | 0.44 (-28.08, 34.37) | 0.42 ( 0.23, 0.61) | 0.42 ( 0.22, 0.63) | 0.43 ( 0.14, 0.72) | 0.43 ( 0.12, 0.73)
BC | 10 | 0.40 ( -0.55, 1.60) | 0.42 ( 0.23, 0.61) | 0.42 ( 0.22, 0.63) | 0.42 ( 0.15, 0.70) | 0.42 ( 0.15, 0.69)
NSCLC | 6 | 0.58 ( 0.02, 1.12) | 0.42 ( 0.23, 0.61) | 0.42 ( 0.22, 0.63) | 0.48 ( 0.23, 0.70) | 0.47 ( 0.22, 0.71)
OFTPP | 7 | 0.24 ( -0.20, 0.75) | 0.42 ( 0.23, 0.61) | 0.41 ( 0.21, 0.63) | 0.34 ( 0.10, 0.57) | 0.34 ( 0.09, 0.58)
CC | 1 | -0.47 (-54.65, 59.38) | 0.42 ( 0.23, 0.61) | 0.42 ( 0.21, 0.75) | 0.49 ( 0.16, 0.92) | 0.47 ( 0.09, 0.98)
GBM | 3 | 0.30 ( -3.14, 3.47) | 0.42 ( 0.23, 0.61) | 0.42 ( 0.20, 0.63) | 0.34 ( 0.03, 0.60) | 0.35 ( 0.01, 0.63)
Overall | 38 |  | 0.42 ( 0.23, 0.61) | 0.42 ( 0.22, 0.63) | 0.43 ( 0.20, 0.66) | 0.43 ( 0.19, 0.66)
Table A9: Median and 95% credible interval estimates for the conditonal variance parameter in the surrogacy models using data available at present-day. N - number of trials per indication. Indication | N | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---|---
CRC | 9 | 0.05 (0.00, 0.17) | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.13) | 0.04 (0.00, 0.11) | 0.04 (0.00, 0.13)
RCC | 2 | 0.26 (0.01, 1.02) | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.26) | 0.04 (0.00, 0.15) | 0.05 (0.00, 0.33)
BC | 10 | 0.07 (0.00, 0.26) | 0.05 (0.00, 0.11) | 0.04 (0.00, 0.14) | 0.04 (0.00, 0.13) | 0.04 (0.00, 0.16)
NSCLC | 6 | 0.08 (0.00, 0.34) | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.15) | 0.04 (0.00, 0.14) | 0.05 (0.00, 0.17)
OFTPP | 7 | 0.06 (0.00, 0.30) | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.19) | 0.04 (0.00, 0.14) | 0.04 (0.00, 0.18)
CC | 1 | 0.34 (0.02, 1.12) | 0.05 (0.00, 0.11) | 0.07 (0.01, 0.75) | 0.05 (0.00, 0.19) | 0.08 (0.00, 0.74)
GBM | 3 | 0.23 (0.02, 0.91) | 0.05 (0.00, 0.11) | 0.08 (0.01, 0.48) | 0.05 (0.00, 0.18) | 0.07 (0.00, 0.39)
Overall | 38 |  | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.13) |  |

####  A.1.5 Deviance information criterion (DIC)

Table A10: Residual deviance, deviance, number of effective parameters, and deviance information criterian (DIC) from the application of surrogacy models to data at present-day. *Based on 38 data points. Model | Residual deviance | Deviance | $p_{D}$ | DIC
---|---|---|---|---
IP | 70.95 | -127.59 | 48.75 | -78.84
CP | 72.75 | -118.81 | 39.52 | -79.29
MCIP | 72.35 | -115.95 | 41.27 | -74.68
RP | 71.92 | -122.36 | 42.80 | -79.56
MRIP | 71.61 | -114.92 | 43.01 | -71.91

####  A.1.6 Mixture probabilities

Table A11: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), for the intercept parameter from the application of surrogacy models to data at present-day.  Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | BC | 1.00 (0.04) | 0.04 (-0.04, 0.13) | 0.14 (-61.89, 61.86)
MCIP | CC | 0.98 (0.14) | 0.04 (-0.04, 0.13) | 0.04 (-61.76, 61.83)
MCIP | CRC | 0.99 (0.07) | 0.04 (-0.04, 0.13) | -0.03 (-62.00, 61.82)
MCIP | GBM | 0.99 (0.11) | 0.04 (-0.04, 0.13) | 0.13 (-61.82, 62.14)
MCIP | NSCLC | 1.00 (0.04) | 0.04 (-0.04, 0.13) | -0.08 (-61.91, 61.88)
MCIP | OFTPP | 1.00 (0.05) | 0.04 (-0.04, 0.13) | 0.11 (-62.11, 62.06)
MCIP | RCC | 1.00 (0.05) | 0.04 (-0.04, 0.13) | 0.11 (-62.02, 62.11)
MRIP | BC | 1.00 (0.04) | 0.04 (-0.06, 0.14) | 0.04 (-61.87, 61.87)
MRIP | CC | 0.99 (0.10) | 0.03 (-0.12, 0.16) | -0.07 (-62.06, 61.74)
MRIP | CRC | 1.00 (0.05) | 0.03 (-0.07, 0.13) | 0.02 (-61.95, 61.82)
MRIP | GBM | 0.99 (0.09) | 0.06 (-0.05, 0.21) | 0.10 (-61.85, 61.38)
MRIP | NSCLC | 1.00 (0.06) | 0.05 (-0.06, 0.15) | 0.02 (-61.94, 62.08)
MRIP | OFTPP | 1.00 (0.06) | 0.05 (-0.05, 0.15) | 0.09 (-61.78, 61.94)
MRIP | RCC | 1.00 (0.06) | 0.05 (-0.08, 0.17) | 0.02 (-62.08, 61.97)
Table A12: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), for the slope parameter from the application of surrogacy models to data at present-day.  Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | BC | 1.00 (0.06) | 0.42 ( 0.22, 0.63) | 0.17 (-62.07, 62.29)
MCIP | CC | 0.96 (0.20) | 0.42 ( 0.22, 0.63) | 0.61 (-61.25, 61.56)
MCIP | CRC | 0.92 (0.26) | 0.42 ( 0.22, 0.63) | 0.54 (-60.83, 60.93)
MCIP | GBM | 0.98 (0.14) | 0.42 ( 0.22, 0.63) | 0.18 (-61.74, 61.74)
MCIP | NSCLC | 0.99 (0.08) | 0.42 ( 0.22, 0.63) | 0.32 (-61.88, 61.93)
MCIP | OFTPP | 0.98 (0.15) | 0.42 ( 0.22, 0.63) | 0.23 (-61.61, 61.29)
MCIP | RCC | 1.00 (0.07) | 0.42 ( 0.22, 0.63) | 0.17 (-62.14, 62.01)
MRIP | BC | 0.99 (0.08) | 0.42 ( 0.15, 0.69) | 0.26 (-61.93, 62.03)
MRIP | CC | 0.97 (0.17) | 0.47 ( 0.11, 0.91) | 0.53 (-61.42, 61.47)
MRIP | CRC | 0.98 (0.14) | 0.52 ( 0.27, 0.74) | 0.47 (-61.77, 61.85)
MRIP | GBM | 0.98 (0.12) | 0.35 ( 0.02, 0.63) | 0.15 (-61.60, 61.96)
MRIP | NSCLC | 0.99 (0.09) | 0.47 ( 0.22, 0.71) | 0.21 (-62.07, 61.96)
MRIP | OFTPP | 0.99 (0.12) | 0.34 ( 0.10, 0.59) | 0.20 (-61.65, 61.76)
MRIP | RCC | 0.99 (0.10) | 0.43 ( 0.12, 0.73) | 0.22 (-61.70, 61.56)
Table A13: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), for the conditional variance parameter from the application of surrogacy models to data at present-day.  Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | BC | 0.82 (0.38) | 0.05 ( 0.00, 0.13) | 0.26 ( 0.01, 1.08)
MCIP | CC | 0.58 (0.49) | 0.05 ( 0.00, 0.13) | 0.28 ( 0.01, 1.06)
MCIP | CRC | 0.82 (0.38) | 0.05 ( 0.00, 0.13) | 0.25 ( 0.01, 1.08)
MCIP | GBM | 0.57 (0.50) | 0.05 ( 0.00, 0.13) | 0.24 ( 0.02, 1.02)
MCIP | NSCLC | 0.81 (0.39) | 0.05 ( 0.00, 0.13) | 0.25 ( 0.01, 1.08)
MCIP | OFTPP | 0.78 (0.41) | 0.05 ( 0.00, 0.13) | 0.25 ( 0.01, 1.07)
MCIP | RCC | 0.78 (0.41) | 0.05 ( 0.00, 0.13) | 0.26 ( 0.01, 1.07)
MRIP | BC | 0.79 (0.40) | 0.04 ( 0.00, 0.16) | 0.24 ( 0.01, 1.08)
MRIP | CC | 0.60 (0.49) | 0.05 ( 0.00, 0.22) | 0.29 ( 0.01, 1.06)
MRIP | CRC | 0.82 (0.39) | 0.04 ( 0.00, 0.15) | 0.25 ( 0.01, 1.08)
MRIP | GBM | 0.68 (0.46) | 0.06 ( 0.00, 0.21) | 0.24 ( 0.01, 1.05)
MRIP | NSCLC | 0.79 (0.41) | 0.04 ( 0.00, 0.17) | 0.24 ( 0.01, 1.07)
MRIP | OFTPP | 0.80 (0.40) | 0.04 ( 0.00, 0.17) | 0.25 ( 0.01, 1.07)
MRIP | RCC | 0.75 (0.43) | 0.04 ( 0.00, 0.19) | 0.25 ( 0.01, 1.06)

###  A.2 TA178 (renal)

####  A.2.1 Pooled OS and PFS estimates

Table A14: Median and 95% credible interval estimates from the application of univariate models to effects on overall survival (log hazard ratio scale) using data available at the time of NICE TA178. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | -0.23 (-0.41, -0.06) | -0.16 (-0.25, -0.06) | -0.16 (-0.25, -0.06) | -0.19 (-0.33, -0.06) | -0.19 (-0.33, -0.06)
BC | -0.10 (-0.29, 0.10) | -0.16 (-0.25, -0.06) | -0.16 (-0.25, -0.06) | -0.13 (-0.26, 0.02) | -0.13 (-0.26, 0.01)
NSCLC | -0.11 (-0.73, 0.52) | -0.16 (-0.25, -0.06) | -0.16 (-0.25, -0.06) | -0.14 (-0.37, 0.10) | -0.14 (-0.35, 0.08)
RCC | -0.15 (-0.65, 0.35) | -0.16 (-0.25, -0.06) | -0.16 (-0.25, -0.06) | -0.15 (-0.34, 0.04) | -0.15 (-0.33, 0.03)
All Indications |  | -0.16 (-0.25, -0.06) | -0.16 (-0.25, -0.06) | -0.16 (-0.38, 0.08) | -0.15 (-0.34, 0.04)
New Indication |  |  |  | -0.16 (-0.61, 0.31) | -0.15 (-0.52, 0.23)
Table A15: Median and 95% credible interval estimates from the application of univariate models to effects on progression-free survival (log hazard ratio scale) using data available at the time of NICE TA178. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | -0.48 (-0.76, -0.26) | -0.40 (-0.52, -0.30) | -0.40 (-0.52, -0.29) | -0.43 (-0.65, -0.28) | -0.43 (-0.64, -0.28)
BC | -0.34 (-0.54, -0.15) | -0.40 (-0.52, -0.30) | -0.40 (-0.52, -0.29) | -0.37 (-0.53, -0.22) | -0.37 (-0.53, -0.22)
NSCLC | -0.29 (-0.91, 0.33) | -0.40 (-0.52, -0.30) | -0.40 (-0.52, -0.29) | -0.37 (-0.63, -0.09) | -0.37 (-0.62, -0.11)
RCC | -0.50 (-1.01, -0.15) | -0.40 (-0.52, -0.30) | -0.40 (-0.52, -0.29) | -0.44 (-0.70, -0.25) | -0.44 (-0.68, -0.26)
All Indications |  | -0.40 (-0.52, -0.30) | -0.40 (-0.52, -0.29) | -0.40 (-0.69, -0.13) | -0.40 (-0.64, -0.18)
New Indication |  |  |  | -0.40 (-0.98, 0.17) | -0.40 (-0.85, 0.04)

####  A.2.2 Predicted OS estimates

Table A16: Median and 95% credible interval estimates for predicted effects on overall survival (log hazard ratio scale), from entering the progression-free survival effect estimate from the univariate independent parameters (IP) model into the surrogacy models, using data available at the time of NICE TA178. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
RCC | -0.16 ( -8.63, 8.18) | -0.15 (-14.79, 14.26) | -0.16 (-16.27, 15.96) | -0.14 (-13.51, 13.31) | -0.15 (-15.45, 15.08)
Table A17: Median and 95% credible interval estimates for predicted effects on overall survival (log hazard ratio scale), from entering the progression-free survival effect estimate from each univariate model into the corresponding surrogacy model, using data available at the time of NICE TA178. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
RCC | -0.16 (-8.63, 8.18) | -0.16 (-0.59, 0.28) | -0.17 (-0.68, 0.30) | -0.12 (-0.51, 0.28) | -0.14 (-0.64, 0.32)

####  A.2.3 Deviance information criterion (DIC)

Table A18: Residual deviance, deviance, number of effective parameters, and deviance information criterian (DIC) from the application of univariate models to data on overall survival at the time of NICE TA178. *Based on 13 data points. Model | Residual deviance | Deviance | $p_{D}$ | DIC
---|---|---|---|---
IP | 11.13 | -16.92 | 8.99 | -7.92
CP | 10.92 | -17.13 | 7.56 | -9.57
MCIP | 10.94 | -17.11 | 7.59 | -9.52
RP | 10.87 | -17.18 | 8.23 | -8.95
MRIP | 10.84 | -15.82 | 8.16 | -7.66
Table A19: Residual deviance, deviance, number of effective parameters, and deviance information criterian (DIC) from the application of univariate models to data on progression-free survival at the time of NICE TA178. *Based on 17 data points. Model | Residual deviance | Deviance | $p_{D}$ | DIC
---|---|---|---|---
IP | 18.30 | -15.98 | 13.56 | -2.42
CP | 19.48 | -14.80 | 12.37 | -2.43
MCIP | 19.50 | -14.78 | 12.42 | -2.36
RP | 18.81 | -15.47 | 12.91 | -2.56
MRIP | 18.87 | -14.02 | 12.86 | -1.16

####  A.2.4 Mixture probabilities

Table A20: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), from the application of univariate models to data on overall survival at the time of NICE TA178. Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | BC | 0.99 (0.07) | -0.16 (-0.25, -0.06) | -0.08 (-61.86, 61.60)
MCIP | CRC | 0.99 (0.09) | -0.16 (-0.25, -0.06) | -0.12 (-61.93, 62.00)
MCIP | NSCLC | 0.99 (0.08) | -0.16 (-0.25, -0.06) | -0.03 (-62.07, 61.98)
MCIP | RCC | 0.99 (0.07) | -0.16 (-0.25, -0.06) | -0.02 (-61.95, 61.66)
MRIP | BC | 0.99 (0.08) | -0.13 (-0.26, 0.01) | -0.08 (-61.97, 61.69)
MRIP | CRC | 0.99 (0.08) | -0.19 (-0.33, -0.05) | -0.13 (-61.90, 61.54)
MRIP | NSCLC | 0.99 (0.09) | -0.14 (-0.35, 0.08) | -0.05 (-61.84, 61.86)
MRIP | RCC | 0.99 (0.09) | -0.15 (-0.34, 0.03) | -0.07 (-62.01, 62.01)
Table A21: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), from the application of univariate models to data on progression-free survival at the time of NICE TA178. Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | BC | 1.00 (0.07) | -0.40 (-0.52, -0.29) | -0.22 (-62.13, 61.50)
MCIP | CRC | 0.99 (0.08) | -0.40 (-0.52, -0.29) | -0.24 (-62.03, 62.10)
MCIP | NSCLC | 0.99 (0.10) | -0.40 (-0.52, -0.29) | -0.15 (-61.99, 61.80)
MCIP | RCC | 0.99 (0.09) | -0.40 (-0.52, -0.29) | -0.27 (-62.29, 61.98)
MRIP | BC | 0.99 (0.09) | -0.37 (-0.53, -0.22) | -0.14 (-61.44, 61.65)
MRIP | CRC | 0.99 (0.08) | -0.43 (-0.64, -0.28) | -0.15 (-62.20, 61.48)
MRIP | NSCLC | 0.99 (0.11) | -0.37 (-0.62, -0.11) | -0.12 (-62.08, 61.79)
MRIP | RCC | 0.99 (0.10) | -0.44 (-0.68, -0.25) | -0.41 (-61.91, 62.15)

###  A.3 TA285 (ovarian)

####  A.3.1 Pooled OS and PFS estimates

Table A22: Median and 95% credible interval estimates from the application of univariate models to effects on overall survival (log hazard ratio scale) using data available at the time of NICE TA285. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | -0.19 (-0.33, -0.07) | -0.13 (-0.20, -0.07) | -0.13 (-0.20, -0.07) | -0.16 (-0.26, -0.07) | -0.16 (-0.26, -0.07)
RCC | -0.15 (-0.65, 0.34) | -0.13 (-0.20, -0.07) | -0.13 (-0.20, -0.07) | -0.14 (-0.27, -0.01) | -0.14 (-0.27, -0.01)
BC | -0.12 (-0.31, 0.04) | -0.13 (-0.20, -0.07) | -0.13 (-0.20, -0.07) | -0.13 (-0.23, -0.02) | -0.13 (-0.23, -0.03)
NSCLC | -0.18 (-0.63, 0.25) | -0.13 (-0.20, -0.07) | -0.13 (-0.20, -0.07) | -0.14 (-0.29, -0.01) | -0.14 (-0.29, -0.01)
CC | -0.34 (-1.46, 0.78) | -0.13 (-0.20, -0.07) | -0.13 (-0.21, -0.07) | -0.14 (-0.36, 0.02) | -0.14 (-0.37, 0.02)
GBM | -0.02 (-0.62, 0.61) | -0.13 (-0.20, -0.07) | -0.13 (-0.20, -0.07) | -0.12 (-0.26, 0.06) | -0.12 (-0.26, 0.06)
OFTPP | -0.06 (-0.25, 0.12) | -0.13 (-0.20, -0.07) | -0.13 (-0.20, -0.07) | -0.11 (-0.21, 0.00) | -0.11 (-0.21, 0.01)
All Indications |  | -0.13 (-0.20, -0.07) | -0.13 (-0.20, -0.07) | -0.13 (-0.24, -0.04) | -0.13 (-0.23, -0.04)
New Indication |  |  |  | -0.13 (-0.34, 0.07) | -0.13 (-0.34, 0.06)
Table A23: Median and 95% credible interval estimates from the application of univariate models to effects on progression-free survival (log hazard ratio scale) using data available at the time of NICE TA285. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | -0.47 (-0.67, -0.30) | -0.38 (-0.47, -0.31) | -0.38 (-0.48, -0.30) | -0.42 (-0.58, -0.30) | -0.42 (-0.58, -0.30)
RCC | -0.50 (-1.01, -0.15) | -0.38 (-0.47, -0.31) | -0.38 (-0.48, -0.30) | -0.42 (-0.62, -0.28) | -0.42 (-0.62, -0.28)
BC | -0.30 (-0.42, -0.18) | -0.38 (-0.47, -0.31) | -0.38 (-0.47, -0.30) | -0.34 (-0.45, -0.23) | -0.34 (-0.45, -0.23)
NSCLC | -0.47 (-1.08, 0.11) | -0.38 (-0.47, -0.31) | -0.38 (-0.48, -0.30) | -0.40 (-0.63, -0.22) | -0.40 (-0.63, -0.22)
CC | -0.40 (-1.50, 0.69) | -0.38 (-0.47, -0.31) | -0.38 (-0.48, -0.30) | -0.39 (-0.61, -0.19) | -0.39 (-0.62, -0.19)
GBM | -0.35 (-0.93, 0.24) | -0.38 (-0.47, -0.31) | -0.38 (-0.48, -0.30) | -0.38 (-0.56, -0.21) | -0.38 (-0.56, -0.21)
OFTPP | -0.43 (-0.90, 0.02) | -0.38 (-0.47, -0.31) | -0.38 (-0.48, -0.30) | -0.40 (-0.61, -0.22) | -0.40 (-0.61, -0.23)
All Indications |  | -0.38 (-0.47, -0.31) | -0.38 (-0.48, -0.30) | -0.39 (-0.54, -0.28) | -0.39 (-0.53, -0.28)
New Indication |  |  |  | -0.39 (-0.68, -0.14) | -0.39 (-0.67, -0.15)

####  A.3.2 Predicted OS estimates

Table A24: Median and 95% credible interval estimates for predicted effects on overall survival (log hazard ratio scale), from entering the progression-free survival effect estimate from the univariate independent parameters (IP) model into the surrogacy models, using data available at the time of NICE TA285. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
OFTPP | -0.07 (-0.39, 0.27) | -0.07 (-0.48, 0.37) | -0.07 (-0.49, 0.38) | -0.06 (-0.46, 0.35) | -0.06 (-0.45, 0.33)
Table A25: Median and 95% credible interval estimates for predicted effects on overall survival (log hazard ratio scale), from entering the progression-free survival effect estimate from each univariate model into the corresponding surrogacy model, using data available at the time of NICE TA285. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
OFTPP | -0.07 (-0.39, 0.27) | -0.13 (-0.47, 0.21) | -0.13 (-0.51, 0.23) | -0.06 (-0.33, 0.18) | -0.05 (-0.31, 0.18)

####  A.3.3 Deviance information criterion (DIC)

Table A26: Residual deviance, deviance, number of effective parameters, and deviance information criterian (DIC) from the application of univariate models to data on overall survival at the time of NICE TA285. *Based on 27 data points. Model | Residual deviance | Deviance | $p_{D}$ | DIC
---|---|---|---|---
IP | 26.94 | -30.43 | 18.83 | -11.59
CP | 27.60 | -29.77 | 16.02 | -13.74
MCIP | 27.57 | -29.80 | 15.99 | -13.81
RP | 27.12 | -30.25 | 16.78 | -13.47
MRIP | 27.12 | -28.86 | 16.75 | -12.11
Table A27: Residual deviance, deviance, number of effective parameters, and deviance information criterian (DIC) from the application of univariate models to data on progression-free survival at the time of NICE TA285. *Based on 32 data points. Model | Residual deviance | Deviance | $p_{D}$ | DIC
---|---|---|---|---
IP | 33.27 | -36.97 | 24.75 | -12.22
CP | 34.90 | -35.33 | 23.90 | -11.43
MCIP | 35.03 | -35.21 | 23.89 | -11.31
RP | 34.13 | -36.11 | 23.86 | -12.25
MRIP | 34.10 | -34.75 | 23.87 | -10.88

####  A.3.4 Mixture probabilities

Table A28: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), from the application of univariate models to data on overall survival at the time of NICE TA285. Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | BC | 1.00 (0.06) | -0.13 (-0.20, -0.07) | -0.04 (-62.02, 61.96)
MCIP | CC | 0.99 (0.12) | -0.13 (-0.20, -0.07) | -0.26 (-61.67, 61.68)
MCIP | CRC | 0.99 (0.07) | -0.13 (-0.20, -0.07) | -0.10 (-61.92, 62.13)
MCIP | GBM | 0.99 (0.10) | -0.13 (-0.20, -0.07) | -0.03 (-61.37, 62.03)
MCIP | NSCLC | 0.99 (0.07) | -0.13 (-0.20, -0.07) | 0.03 (-62.02, 61.99)
MCIP | OFTPP | 0.99 (0.08) | -0.13 (-0.20, -0.07) | -0.04 (-61.74, 61.76)
MCIP | RCC | 0.99 (0.07) | -0.13 (-0.20, -0.07) | -0.04 (-61.78, 61.72)
MRIP | BC | 1.00 (0.06) | -0.13 (-0.23, -0.03) | -0.11 (-62.19, 61.87)
MRIP | CC | 0.99 (0.12) | -0.14 (-0.35, 0.01) | -0.21 (-61.91, 61.77)
MRIP | CRC | 0.99 (0.07) | -0.15 (-0.26, -0.07) | -0.12 (-61.81, 62.33)
MRIP | GBM | 0.99 (0.10) | -0.12 (-0.26, 0.05) | -0.01 (-61.88, 61.65)
MRIP | NSCLC | 1.00 (0.07) | -0.14 (-0.29, -0.01) | -0.16 (-62.12, 61.89)
MRIP | OFTPP | 0.99 (0.08) | -0.11 (-0.22, 0.00) | -0.07 (-62.13, 62.00)
MRIP | RCC | 1.00 (0.07) | -0.14 (-0.27, -0.01) | -0.12 (-61.84, 61.97)
Table A29: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), from the application of univariate models to data on progression-free survival at the time of NICE TA285. Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | BC | 0.98 (0.13) | -0.38 (-0.48, -0.30) | -0.28 (-61.64, 61.64)
MCIP | CC | 0.99 (0.10) | -0.38 (-0.48, -0.30) | -0.06 (-61.88, 62.08)
MCIP | CRC | 0.99 (0.08) | -0.38 (-0.48, -0.30) | -0.21 (-62.00, 61.83)
MCIP | GBM | 0.99 (0.07) | -0.38 (-0.48, -0.30) | -0.20 (-61.44, 62.06)
MCIP | NSCLC | 0.99 (0.08) | -0.38 (-0.48, -0.30) | -0.18 (-61.85, 61.95)
MCIP | OFTPP | 0.99 (0.08) | -0.38 (-0.48, -0.30) | -0.15 (-61.77, 61.92)
MCIP | RCC | 0.99 (0.10) | -0.38 (-0.48, -0.30) | -0.42 (-61.98, 62.03)
MRIP | BC | 0.99 (0.08) | -0.34 (-0.46, -0.23) | -0.15 (-62.29, 61.54)
MRIP | CC | 0.99 (0.10) | -0.39 (-0.61, -0.20) | -0.28 (-61.98, 62.06)
MRIP | CRC | 0.99 (0.08) | -0.42 (-0.57, -0.30) | -0.18 (-61.84, 62.22)
MRIP | GBM | 0.99 (0.08) | -0.38 (-0.56, -0.21) | -0.23 (-62.05, 61.88)
MRIP | NSCLC | 0.99 (0.09) | -0.40 (-0.63, -0.22) | -0.24 (-61.90, 61.95)
MRIP | OFTPP | 0.99 (0.08) | -0.40 (-0.60, -0.23) | -0.23 (-61.96, 62.09)
MRIP | RCC | 0.99 (0.09) | -0.42 (-0.61, -0.28) | -0.25 (-61.72, 62.13)

###  A.4 Surrogate endpoint cross validation

Table A30: Median and 95% credible interval estimates for the treatment effect on overall survival (log hazard ratio scale) from applying leave-one-out cross validation to evaluate surrogacy using trial-level data at present day. Trial | Observed | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---|---
Breast |  |  |  |  |  |
E2100 | -0.13 (-0.30, 0.05) | -0.22 ( -0.75, 0.30) | -0.18 (-0.43, 0.08) | -0.18 ( -0.45, 0.08) | -0.18 (-0.47, 0.10) | -0.19 ( -0.48, 0.11)
RIBBON-1 | -0.16 (-0.46, 0.13) | -0.12 ( -0.55, 0.32) | -0.11 (-0.44, 0.22) | -0.12 ( -0.45, 0.22) | -0.11 (-0.45, 0.23) | -0.11 ( -0.46, 0.24)
RIBBON-1 | 0.03 (-0.26, 0.32) | -0.12 ( -0.55, 0.32) | -0.11 (-0.44, 0.22) | -0.12 ( -0.45, 0.22) | -0.11 (-0.45, 0.23) | -0.11 ( -0.46, 0.24)
RIBBON-2 | -0.11 (-0.34, 0.13) | -0.06 ( -0.48, 0.37) | -0.06 (-0.34, 0.22) | -0.06 ( -0.35, 0.22) | -0.06 (-0.34, 0.23) | -0.06 ( -0.36, 0.24)
AVADO | 0.03 (-0.29, 0.35) | -0.09 ( -0.54, 0.36) | -0.07 (-0.42, 0.28) | -0.07 ( -0.43, 0.29) | -0.07 (-0.43, 0.29) | -0.07 ( -0.44, 0.30)
SUN 1094 | -0.60 (-1.05, -0.15) | -0.14 ( -0.67, 0.40) | -0.16 (-0.65, 0.32) | -0.17 ( -0.66, 0.32) | -0.15 (-0.63, 0.34) | -0.14 ( -0.63, 0.34)
LEA | -0.14 (-0.55, 0.27) | -0.01 ( -0.59, 0.56) | -0.04 (-0.48, 0.41) | -0.04 ( -0.48, 0.41) | -0.03 (-0.48, 0.42) | -0.03 ( -0.48, 0.42)
MERiDiAN | -0.21 (-0.50, 0.07) | -0.12 ( -0.57, 0.33) | -0.12 (-0.45, 0.21) | -0.12 ( -0.46, 0.22) | -0.11 (-0.45, 0.23) | -0.11 ( -0.46, 0.24)
TANIA | -0.04 (-0.27, 0.19) | -0.09 ( -0.51, 0.32) | -0.08 (-0.36, 0.19) | -0.08 ( -0.37, 0.20) | -0.08 (-0.37, 0.21) | -0.08 ( -0.38, 0.22)
E1105 | 0.09 (-0.50, 0.67) | -0.10 ( -0.85, 0.64) | -0.09 (-0.73, 0.55) | -0.09 ( -0.74, 0.55) | -0.09 (-0.73, 0.55) | -0.09 ( -0.74, 0.55)
Cervical |  |  |  |  |  |
GOG240 | -0.26 (-0.47, -0.05) | 0.00 ( -0.21, 0.21) | -0.12 (-0.37, 0.14) | 3.36 (-22.48, 29.19) | -0.11 (-0.46, 0.25) | -1.81 (-43.43, 39.81)
Colorectal |  |  |  |  |  |
AVF2107g | -0.42 (-0.66, -0.18) | -0.28 ( -0.65, 0.09) | -0.20 (-0.51, 0.10) | -0.20 ( -0.51, 0.10) | -0.20 (-0.51, 0.10) | -0.20 ( -0.51, 0.10)
AVF2192g | -0.24 (-0.57, 0.10) | -0.38 ( -0.84, 0.09) | -0.25 (-0.65, 0.15) | -0.25 ( -0.65, 0.15) | -0.25 (-0.65, 0.15) | -0.25 ( -0.65, 0.15)
E3200 | -0.29 (-0.46, -0.11) | -0.23 ( -0.53, 0.08) | -0.16 (-0.39, 0.07) | -0.16 ( -0.39, 0.07) | -0.16 (-0.39, 0.07) | -0.16 ( -0.39, 0.07)
NO16966 | -0.12 (-0.27, 0.04) | -0.02 ( -0.31, 0.26) | -0.03 (-0.23, 0.18) | -0.03 ( -0.23, 0.18) | -0.03 (-0.23, 0.18) | -0.03 ( -0.23, 0.18)
MAX | -0.13 (-0.38, 0.13) | -0.24 ( -0.59, 0.11) | -0.16 (-0.46, 0.14) | -0.16 ( -0.46, 0.14) | -0.16 (-0.46, 0.14) | -0.16 ( -0.46, 0.14)
HORIZON III | 0.05 (-0.10, 0.20) | -0.06 ( -0.36, 0.25) | -0.01 (-0.21, 0.20) | -0.01 ( -0.21, 0.20) | -0.01 (-0.21, 0.20) | -0.01 ( -0.21, 0.20)
ARTIST | -0.48 (-0.90, -0.06) | -0.42 ( -0.95, 0.12) | -0.29 (-0.76, 0.17) | -0.29 ( -0.76, 0.17) | -0.29 (-0.76, 0.17) | -0.29 ( -0.76, 0.17)
ML18147 | -0.19 (-0.34, -0.03) | -0.18 ( -0.46, 0.10) | -0.12 (-0.33, 0.08) | -0.12 ( -0.33, 0.08) | -0.12 (-0.33, 0.08) | -0.12 ( -0.33, 0.08)
AVEX | -0.24 (-0.56, 0.09) | -0.33 ( -0.75, 0.09) | -0.23 (-0.59, 0.14) | -0.23 ( -0.59, 0.14) | -0.23 (-0.59, 0.14) | -0.23 ( -0.59, 0.14)
Glioblastoma |  |  |  |  |  |
RTOG0825 | 0.12 (-0.07, 0.32) | 0.00 ( -0.19, 0.19) | -0.07 (-0.30, 0.16) | -0.06 ( -0.48, 0.35) | -0.03 (-0.30, 0.24) | -0.03 ( -0.45, 0.38)
AvaGlio | -0.13 (-0.27, 0.02) | 0.00 ( -0.15, 0.15) | -0.15 (-0.35, 0.06) | -0.14 ( -0.73, 0.46) | -0.04 (-0.32, 0.23) | -0.06 ( -0.54, 0.42)
EORTC26101 | -0.05 (-0.30, 0.19) | 0.00 ( -0.25, 0.25) | -0.28 (-0.57, 0.02) | -0.28 ( -0.72, 0.16) | -0.23 (-0.59, 0.13) | -0.23 ( -0.72, 0.25)
NSCLC |  |  |  |  |  |
E4599 | -0.24 (-0.39, -0.08) | -0.10 ( -0.50, 0.31) | -0.13 (-0.33, 0.08) | -0.12 ( -0.35, 0.10) | -0.12 (-0.35, 0.11) | -0.12 ( -0.37, 0.13)
AVAiL | 0.03 (-0.15, 0.21) | -0.02 ( -0.59, 0.54) | -0.03 (-0.26, 0.19) | -0.03 ( -0.29, 0.22) | -0.05 (-0.30, 0.20) | -0.05 ( -0.32, 0.22)
BEYOND | -0.39 (-0.70, -0.08) | -0.51 ( -1.48, 0.46) | -0.33 (-0.70, 0.04) | -0.35 ( -0.74, 0.05) | -0.39 (-0.82, 0.05) | -0.39 ( -0.84, 0.06)
JO25567 | -0.21 (-0.63, 0.21) | -0.29 ( -0.95, 0.37) | -0.23 (-0.70, 0.24) | -0.24 ( -0.72, 0.24) | -0.27 (-0.76, 0.23) | -0.26 ( -0.77, 0.24)
IMpower150 | 0.08 (-0.51, 0.67) | 0.02 ( -0.78, 0.81) | -0.01 (-0.64, 0.62) | -0.01 ( -0.65, 0.63) | -0.02 (-0.66, 0.63) | -0.02 ( -0.67, 0.64)
NEJ026 | 0.01 (-0.38, 0.40) | -0.06 ( -0.67, 0.55) | -0.07 (-0.50, 0.36) | -0.07 ( -0.51, 0.37) | -0.08 (-0.52, 0.36) | -0.08 ( -0.54, 0.38)
OFTPP |  |  |  |  |  |
GOG218 | -0.04 (-0.17, 0.08) | -0.04 ( -0.47, 0.39) | -0.07 (-0.26, 0.11) | -0.07 ( -0.32, 0.18) | -0.04 (-0.25, 0.18) | -0.04 ( -0.29, 0.21)
ICON7 | -0.01 (-0.16, 0.14) | 0.03 ( -0.50, 0.56) | 0.02 (-0.20, 0.23) | 0.02 ( -0.24, 0.28) | 0.04 (-0.19, 0.27) | 0.04 ( -0.22, 0.30)
OCEANS | -0.05 (-0.26, 0.16) | -0.23 ( -0.66, 0.21) | -0.29 (-0.56, -0.02) | -0.30 ( -0.58, -0.03) | -0.26 (-0.54, 0.02) | -0.26 ( -0.55, 0.03)
AURELIA | -0.16 (-0.41, 0.08) | -0.15 ( -0.67, 0.37) | -0.28 (-0.58, 0.02) | -0.28 ( -0.63, 0.06) | -0.21 (-0.53, 0.12) | -0.21 ( -0.56, 0.14)
GOG213 | -0.19 (-0.38, 0.01) | -0.07 ( -0.45, 0.32) | -0.15 (-0.39, 0.09) | -0.15 ( -0.44, 0.13) | -0.09 (-0.34, 0.16) | -0.09 ( -0.37, 0.18)
mEOC/GOG0241 | 0.39 (-0.58, 1.35) | 0.02 ( -1.05, 1.09) | 0.08 (-0.97, 1.13) | 0.09 ( -0.97, 1.14) | 0.08 (-0.94, 1.11) | 0.09 ( -0.95, 1.12)
mEOC/GOG0241 | -0.26 (-1.23, 0.71) | 0.02 ( -1.05, 1.09) | 0.08 (-0.97, 1.13) | 0.09 ( -0.97, 1.14) | 0.08 (-0.94, 1.11) | 0.09 ( -0.95, 1.12)
Renal |  |  |  |  |  |
AVOREN | -0.15 (-0.33, 0.03) | -0.06 (-11.23, 11.10) | -0.17 (-0.40, 0.07) | -0.17 ( -0.61, 0.26) | -0.18 (-0.47, 0.12) | -0.32 ( -2.83, 2.20)
CALGB-90206 | -0.15 (-0.36, 0.05) | -0.45 ( -9.19, 8.29) | -0.13 (-0.37, 0.12) | -0.13 ( -0.55, 0.29) | -0.12 (-0.41, 0.17) | -0.12 ( -0.62, 0.38)

###  A.5 Sensitivity analysis: equal mixture weights for surrogacy parameters

####  A.5.1 Surrogacy parameter estimates

Figure A1: Multi-indication meta-analysis assuming equal mixture weights for
surrogacy parameters using data available at present day. IP - independent
parameters, CP - common parameter, MCIP - mixed common and independent
parameters, RP - random parameters, MRIP - mixed random and independent
parameters, CRC - colorectal cancer, BC - breast cancer, NSCLC - non-small
cell lung cancer, RCC - renal cell carcinoma, CC - cervical cancer, GBM -
glioblastoma, OFTPP - ovarian, fallopian tube, and primary peritoneal.

Table A31: Median and 95% credible interval estimates for the intercept parameter in the surrogacy models, where mixture models assume equal mixture probabilities, using data available at present-day. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | 0.05 ( -0.11, 0.21) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.06, 0.12) | 0.03 ( -0.07, 0.12)
RCC | 0.05 (-12.75, 15.19) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.12) | 0.05 ( -0.07, 0.16) | 0.04 ( -0.07, 0.16)
BC | 0.04 ( -0.33, 0.45) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.12) | 0.05 ( -0.06, 0.14) | 0.04 ( -0.06, 0.14)
NSCLC | 0.10 ( -0.18, 0.38) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.12) | 0.05 ( -0.06, 0.15) | 0.05 ( -0.06, 0.15)
OFTPP | 0.02 ( -0.18, 0.28) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.12) | 0.05 ( -0.04, 0.15) | 0.05 ( -0.05, 0.15)
CC | -0.40 (-22.89, 23.86) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.05, 0.13) | 0.03 ( -0.12, 0.14) | 0.03 ( -0.13, 0.15)
GBM | 0.11 ( -1.52, 1.64) | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.12) | 0.07 ( -0.04, 0.21) | 0.06 ( -0.04, 0.21)
All Indications |  | 0.04 ( -0.04, 0.12) | 0.04 ( -0.04, 0.12) | 0.05 ( -0.05, 0.14) | 0.04 ( -0.05, 0.14)
Table A32: Median and 95% credible interval estimates for the slope parameter in the surrogacy models, where mixture models assume equal mixture probabilities, using data available at present-day. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | 0.59 ( 0.24, 0.91) | 0.42 ( 0.23, 0.61) | 0.41 ( 0.23, 0.60) | 0.53 ( 0.29, 0.74) | 0.52 ( 0.29, 0.73)
RCC | 0.44 (-28.08, 34.37) | 0.42 ( 0.23, 0.61) | 0.41 ( 0.23, 0.60) | 0.43 ( 0.14, 0.72) | 0.43 ( 0.13, 0.71)
BC | 0.40 ( -0.55, 1.60) | 0.42 ( 0.23, 0.61) | 0.41 ( 0.23, 0.60) | 0.42 ( 0.15, 0.70) | 0.41 ( 0.14, 0.68)
NSCLC | 0.58 ( 0.02, 1.12) | 0.42 ( 0.23, 0.61) | 0.41 ( 0.23, 0.60) | 0.48 ( 0.23, 0.70) | 0.47 ( 0.23, 0.71)
OFTPP | 0.24 ( -0.20, 0.75) | 0.42 ( 0.23, 0.61) | 0.41 ( 0.23, 0.60) | 0.34 ( 0.10, 0.57) | 0.33 ( 0.10, 0.57)
CC | -0.47 (-54.65, 59.38) | 0.42 ( 0.23, 0.61) | 0.41 ( 0.22, 0.61) | 0.49 ( 0.16, 0.92) | 0.48 ( 0.14, 0.93)
GBM | 0.30 ( -3.14, 3.47) | 0.42 ( 0.23, 0.61) | 0.41 ( 0.23, 0.60) | 0.34 ( 0.03, 0.60) | 0.33 ( 0.02, 0.60)
All Indications |  | 0.42 ( 0.23, 0.61) | 0.41 ( 0.23, 0.60) | 0.43 ( 0.20, 0.66) | 0.43 ( 0.19, 0.66)
Table A33: Median and 95% credible interval estimates for the conditonal variance parameter in the surrogacy models, where mixture models assume equal mixture probabilities, using data available at present-day. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | 0.05 (0.00, 0.17) | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.11) | 0.04 (0.00, 0.11) | 0.04 (0.00, 0.11)
RCC | 0.26 (0.01, 1.02) | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.11) | 0.04 (0.00, 0.15) | 0.04 (0.00, 0.15)
BC | 0.07 (0.00, 0.26) | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.11) | 0.04 (0.00, 0.13) | 0.04 (0.00, 0.13)
NSCLC | 0.08 (0.00, 0.34) | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.11) | 0.04 (0.00, 0.14) | 0.04 (0.00, 0.14)
OFTPP | 0.06 (0.00, 0.30) | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.11) | 0.04 (0.00, 0.14) | 0.04 (0.00, 0.14)
CC | 0.34 (0.02, 1.12) | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.19) | 0.05 (0.00, 0.21)
GBM | 0.23 (0.02, 0.91) | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.18) | 0.05 (0.00, 0.18)
All Indications |  | 0.05 (0.00, 0.11) | 0.05 (0.00, 0.11) |  |

####  A.5.2 Deviance information criterion (DIC)

Table A34: Residual deviance, deviance, number of effective parameters, and deviance information criterian (DIC) from the application of surrogacy models, including mixture models assuming equal mixture weights, to data at present-day. *Based on 38 data points. Model | Residual deviance | Deviance | $p_{D}$ | DIC
---|---|---|---|---
IP | 70.95 | -127.59 | 48.75 | -78.84
CP | 72.75 | -118.81 | 39.52 | -79.29
RP | 72.93 | -109.31 | 39.37 | -69.94
MCIP | 71.92 | -122.36 | 42.80 | -79.56
MRIP | 71.77 | -112.79 | 42.14 | -70.65

####  A.5.3 Mixture probabilities

Table A35: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), for the intercept parameter from the application of surrogacy models, assuming equal mixture probabilities across surrogacy parameters, to data at present-day.  Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | BC | 1.00 (0.00) | 0.04 (-0.04, 0.12) | -0.06 (-62.35, 62.01)
MCIP | CC | 0.99 (0.08) | 0.04 (-0.04, 0.12) | 0.06 (-61.73, 61.76)
MCIP | CRC | 1.00 (0.00) | 0.04 (-0.04, 0.12) | -0.01 (-61.93, 61.90)
MCIP | GBM | 1.00 (0.03) | 0.04 (-0.04, 0.12) | 0.04 (-62.20, 62.16)
MCIP | NSCLC | 1.00 (0.00) | 0.04 (-0.04, 0.12) | -0.01 (-61.82, 62.07)
MCIP | OFTPP | 1.00 (0.00) | 0.04 (-0.04, 0.12) | 0.02 (-62.11, 61.97)
MCIP | RCC | 1.00 (0.01) | 0.04 (-0.04, 0.12) | -0.21 (-62.35, 61.95)
MRIP | BC | 1.00 (0.00) | 0.04 (-0.06, 0.14) | 0.07 (-61.95, 61.72)
MRIP | CC | 0.99 (0.09) | 0.03 (-0.12, 0.14) | 0.00 (-61.89, 61.92)
MRIP | CRC | 1.00 (0.00) | 0.03 (-0.07, 0.12) | -0.06 (-62.06, 61.96)
MRIP | GBM | 1.00 (0.01) | 0.06 (-0.04, 0.21) | 0.20 (-61.81, 62.00)
MRIP | NSCLC | 1.00 (0.00) | 0.05 (-0.06, 0.15) | -0.02 (-62.13, 62.37)
MRIP | OFTPP | 1.00 (0.00) | 0.05 (-0.05, 0.15) | 0.02 (-61.92, 61.87)
MRIP | RCC | 1.00 (0.02) | 0.04 (-0.07, 0.16) | -0.04 (-62.16, 62.17)
Table A36: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), for the slope parameter from the application of surrogacy models, assuming equal mixture probabilities across surrogacy parameters, to data at present-day.  Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | BC | 1.00 (0.00) | 0.41 ( 0.23, 0.60) | 0.00 (-61.95, 61.94)
MCIP | CC | 0.99 (0.08) | 0.41 ( 0.23, 0.60) | -0.02 (-61.59, 62.38)
MCIP | CRC | 1.00 (0.00) | 0.41 ( 0.23, 0.60) | -0.07 (-61.79, 61.92)
MCIP | GBM | 1.00 (0.03) | 0.41 ( 0.23, 0.60) | 0.09 (-62.09, 62.04)
MCIP | NSCLC | 1.00 (0.00) | 0.41 ( 0.23, 0.60) | -0.10 (-61.96, 62.12)
MCIP | OFTPP | 1.00 (0.00) | 0.41 ( 0.23, 0.60) | 0.03 (-61.70, 61.99)
MCIP | RCC | 1.00 (0.01) | 0.41 ( 0.23, 0.60) | 0.19 (-61.86, 61.92)
MRIP | BC | 1.00 (0.00) | 0.41 ( 0.14, 0.68) | -0.14 (-61.80, 61.67)
MRIP | CC | 0.99 (0.09) | 0.48 ( 0.15, 0.91) | 0.20 (-61.87, 62.25)
MRIP | CRC | 1.00 (0.00) | 0.52 ( 0.29, 0.73) | -0.01 (-61.98, 61.99)
MRIP | GBM | 1.00 (0.01) | 0.33 ( 0.02, 0.60) | 0.19 (-61.90, 61.94)
MRIP | NSCLC | 1.00 (0.00) | 0.47 ( 0.23, 0.71) | -0.03 (-61.93, 61.92)
MRIP | OFTPP | 1.00 (0.00) | 0.33 ( 0.10, 0.57) | 0.04 (-61.99, 62.22)
MRIP | RCC | 1.00 (0.02) | 0.43 ( 0.13, 0.71) | -0.05 (-61.92, 61.53)
Table A37: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), for conditional variance parameters from the application of surrogacy models, assuming equal mixture probabilities across surrogacy parameters, to data at present-day.  Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | BC | 1.00 (0.00) | 0.05 ( 0.00, 0.11) | 0.34 ( 0.02, 1.11)
MCIP | CC | 0.99 (0.08) | 0.05 ( 0.00, 0.11) | 0.34 ( 0.02, 1.12)
MCIP | CRC | 1.00 (0.00) | 0.05 ( 0.00, 0.11) | 0.34 ( 0.02, 1.14)
MCIP | GBM | 1.00 (0.03) | 0.05 ( 0.00, 0.11) | 0.34 ( 0.02, 1.12)
MCIP | NSCLC | 1.00 (0.00) | 0.05 ( 0.00, 0.11) | 0.34 ( 0.02, 1.12)
MCIP | OFTPP | 1.00 (0.00) | 0.05 ( 0.00, 0.11) | 0.34 ( 0.02, 1.12)
MCIP | RCC | 1.00 (0.01) | 0.05 ( 0.00, 0.11) | 0.34 ( 0.02, 1.12)
MRIP | BC | 1.00 (0.00) | 0.04 ( 0.00, 0.13) | 0.34 ( 0.02, 1.12)
MRIP | CC | 0.99 (0.09) | 0.05 ( 0.00, 0.20) | 0.34 ( 0.02, 1.12)
MRIP | CRC | 1.00 (0.00) | 0.04 ( 0.00, 0.11) | 0.34 ( 0.02, 1.12)
MRIP | GBM | 1.00 (0.01) | 0.05 ( 0.00, 0.18) | 0.34 ( 0.02, 1.12)
MRIP | NSCLC | 1.00 (0.00) | 0.04 ( 0.00, 0.14) | 0.34 ( 0.02, 1.12)
MRIP | OFTPP | 1.00 (0.00) | 0.04 ( 0.00, 0.14) | 0.34 ( 0.02, 1.12)
MRIP | RCC | 1.00 (0.02) | 0.04 ( 0.00, 0.15) | 0.34 ( 0.02, 1.12)

###  A.6 Sensitivity analysis: independent conditional variance parameters

####  A.6.1 Surrogacy parameter estimates

Figure A2: Multi-indication meta-analysis of surrogacy parameters, assuming
independent conditional variance parameters, using data available at present
day. IP - independent parameters, CP - common parameter, MCIP - mixed common
and independent parameters, RP - random parameters, MRIP - mixed random and
independent parameters, CRC - colorectal cancer, BC - breast cancer, NSCLC -
non-small cell lung cancer, RCC - renal cell carcinoma, CC - cervical cancer,
GBM - glioblastoma, OFTPP - ovarian, fallopian tube, and primary peritoneal.

Table A38: Median and 95% credible interval estimates for the intercept parameter in the surrogacy models, assuming independent conditional variance parameters, using data available at present-day. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | 0.05 ( -0.11, 0.21) | 0.05 ( -0.04, 0.14) | 0.05 ( -0.04, 0.14) | 0.04 ( -0.07, 0.14) | 0.04 ( -0.07, 0.14)
RCC | 0.05 (-12.75, 15.19) | 0.05 ( -0.04, 0.14) | 0.05 ( -0.04, 0.14) | 0.05 ( -0.08, 0.19) | 0.06 ( -0.09, 0.19)
BC | 0.04 ( -0.33, 0.45) | 0.05 ( -0.04, 0.14) | 0.05 ( -0.04, 0.14) | 0.05 ( -0.06, 0.16) | 0.05 ( -0.06, 0.16)
NSCLC | 0.10 ( -0.18, 0.38) | 0.05 ( -0.04, 0.14) | 0.05 ( -0.04, 0.14) | 0.05 ( -0.06, 0.17) | 0.06 ( -0.06, 0.17)
OFTPP | 0.02 ( -0.18, 0.28) | 0.05 ( -0.04, 0.14) | 0.05 ( -0.04, 0.14) | 0.06 ( -0.05, 0.18) | 0.06 ( -0.05, 0.18)
CC | -0.40 (-22.89, 23.86) | 0.05 ( -0.04, 0.14) | 0.05 ( -0.05, 0.15) | 0.05 ( -0.12, 0.19) | 0.05 ( -0.14, 0.21)
GBM | 0.11 ( -1.52, 1.64) | 0.05 ( -0.04, 0.14) | 0.05 ( -0.04, 0.15) | 0.07 ( -0.06, 0.23) | 0.07 ( -0.06, 0.24)
All Indications |  | 0.05 ( -0.04, 0.14) | 0.05 ( -0.04, 0.14) | 0.05 ( -0.05, 0.16) | 0.06 ( -0.05, 0.16)
Table A39: Median and 95% credible interval estimates for the slope parameter in the surrogacy models assuming independent conditional variance parameters, using data available at present-day. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | 0.59 ( 0.24, 0.91) | 0.46 ( 0.23, 0.68) | 0.47 ( 0.23, 0.70) | 0.53 ( 0.28, 0.75) | 0.54 ( 0.29, 0.76)
RCC | 0.44 (-28.08, 34.37) | 0.46 ( 0.23, 0.68) | 0.47 ( 0.22, 0.69) | 0.45 ( 0.11, 0.77) | 0.46 ( 0.09, 0.79)
BC | 0.40 ( -0.55, 1.60) | 0.46 ( 0.23, 0.68) | 0.47 ( 0.22, 0.69) | 0.44 ( 0.15, 0.73) | 0.44 ( 0.15, 0.75)
NSCLC | 0.58 ( 0.02, 1.12) | 0.46 ( 0.23, 0.68) | 0.47 ( 0.22, 0.69) | 0.48 ( 0.22, 0.72) | 0.49 ( 0.21, 0.73)
OFTPP | 0.24 ( -0.20, 0.75) | 0.46 ( 0.23, 0.68) | 0.46 ( 0.21, 0.68) | 0.36 ( 0.11, 0.64) | 0.37 ( 0.10, 0.65)
CC | -0.47 (-54.65, 59.38) | 0.46 ( 0.23, 0.68) | 0.47 ( 0.20, 0.78) | 0.47 ( 0.08, 0.90) | 0.48 ( 0.02, 1.11)
GBM | 0.30 ( -3.14, 3.47) | 0.46 ( 0.23, 0.68) | 0.46 ( 0.19, 0.69) | 0.39 ( 0.02, 0.70) | 0.39 ( 0.01, 0.71)
All Indications |  | 0.46 ( 0.23, 0.68) | 0.47 ( 0.22, 0.69) | 0.45 ( 0.19, 0.70) | 0.45 ( 0.19, 0.71)
Table A40: Median and 95% credible interval estimates for the conditonal variance parameter in the surrogacy models assuming independent conditional variance parameters, using data available at present-day. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | 0.05 (0.00, 0.17) | 0.07 (0.00, 0.18) | 0.06 (0.00, 0.18) | 0.05 (0.00, 0.16) | 0.05 (0.00, 0.16)
RCC | 0.26 (0.01, 1.02) | 0.07 (0.00, 0.51) | 0.07 (0.00, 0.51) | 0.09 (0.00, 0.57) | 0.09 (0.00, 0.58)
BC | 0.07 (0.00, 0.26) | 0.06 (0.00, 0.20) | 0.06 (0.00, 0.20) | 0.06 (0.00, 0.21) | 0.06 (0.00, 0.21)
NSCLC | 0.08 (0.00, 0.34) | 0.06 (0.00, 0.23) | 0.06 (0.00, 0.23) | 0.06 (0.00, 0.25) | 0.06 (0.00, 0.25)
OFTPP | 0.06 (0.00, 0.30) | 0.10 (0.00, 0.30) | 0.10 (0.00, 0.31) | 0.07 (0.00, 0.26) | 0.07 (0.00, 0.26)
CC | 0.34 (0.02, 1.12) | 0.22 (0.01, 0.90) | 0.22 (0.01, 0.92) | 0.22 (0.01, 0.91) | 0.23 (0.01, 0.92)
GBM | 0.23 (0.02, 0.91) | 0.18 (0.02, 0.61) | 0.18 (0.02, 0.61) | 0.14 (0.01, 0.56) | 0.14 (0.01, 0.56)

####  A.6.2 Deviance information criterion (DIC)

Table A41: Residual deviance, number of effective parameters, and deviance information criterian (DIC) from the application of surrogacy models assuming independent conditional variance parameters to data at present-day. *Based on 38 data points. Model | Residual deviance | Deviance | $p_{D}$ | DIC
---|---|---|---|---
IP | 70.95 | -127.59 | 48.75 | -78.84
CP | 71.62 | -125.80 | 44.36 | -81.44
MCIP | 71.49 | -125.88 | 45.01 | -80.86
RP | 71.36 | -128.82 | 45.04 | -83.79
MRIP | 71.41 | -128.01 | 45.36 | -82.65

####  A.6.3 Mixture probabilities

Table A42: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), for the intercept parameter from the application of surrogacy models assuming independent conditional variance parameters to data at present-day.  Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | BC | 1.00 (0.03) | 0.05 (-0.04, 0.14) | 0.09 (-61.55, 62.29)
MCIP | CC | 0.98 (0.14) | 0.05 (-0.04, 0.14) | 0.03 (-61.70, 61.62)
MCIP | CRC | 0.99 (0.08) | 0.05 (-0.04, 0.14) | -0.01 (-62.29, 61.80)
MCIP | GBM | 0.99 (0.10) | 0.05 (-0.04, 0.14) | 0.15 (-62.04, 61.75)
MCIP | NSCLC | 1.00 (0.05) | 0.05 (-0.04, 0.14) | 0.03 (-62.26, 62.03)
MCIP | OFTPP | 1.00 (0.07) | 0.05 (-0.04, 0.14) | 0.09 (-61.54, 62.38)
MCIP | RCC | 1.00 (0.06) | 0.05 (-0.04, 0.14) | -0.03 (-61.98, 62.25)
MRIP | BC | 1.00 (0.05) | 0.05 (-0.06, 0.16) | -0.19 (-62.06, 61.65)
MRIP | CC | 0.98 (0.14) | 0.05 (-0.12, 0.20) | 0.05 (-61.73, 61.71)
MRIP | CRC | 1.00 (0.07) | 0.04 (-0.07, 0.14) | 0.05 (-61.91, 61.80)
MRIP | GBM | 0.99 (0.09) | 0.07 (-0.06, 0.23) | 0.13 (-61.92, 61.71)
MRIP | NSCLC | 1.00 (0.05) | 0.06 (-0.06, 0.17) | 0.06 (-62.08, 61.94)
MRIP | OFTPP | 1.00 (0.06) | 0.06 (-0.05, 0.18) | 0.01 (-61.93, 62.03)
MRIP | RCC | 0.99 (0.09) | 0.06 (-0.09, 0.19) | -0.04 (-61.95, 61.60)
Table A43: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), for the slope parameter from the application of surrogacy models assuming independent conditional variance parameters to data at present-day.  Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | BC | 1.00 (0.06) | 0.47 ( 0.22, 0.69) | 0.22 (-61.85, 61.96)
MCIP | CC | 0.96 (0.20) | 0.47 ( 0.22, 0.69) | 0.55 (-61.49, 61.38)
MCIP | CRC | 0.97 (0.17) | 0.47 ( 0.22, 0.69) | 0.52 (-61.69, 61.95)
MCIP | GBM | 0.97 (0.16) | 0.47 ( 0.22, 0.69) | 0.16 (-61.87, 61.65)
MCIP | NSCLC | 0.99 (0.07) | 0.47 ( 0.22, 0.69) | 0.21 (-61.93, 61.86)
MCIP | OFTPP | 0.97 (0.16) | 0.47 ( 0.22, 0.69) | 0.26 (-61.49, 61.18)
MCIP | RCC | 0.99 (0.09) | 0.47 ( 0.22, 0.69) | 0.21 (-61.89, 61.97)
MRIP | BC | 0.99 (0.09) | 0.44 ( 0.15, 0.75) | 0.23 (-61.95, 61.83)
MRIP | CC | 0.96 (0.20) | 0.48 ( 0.07, 0.92) | 0.52 (-61.27, 61.66)
MRIP | CRC | 0.99 (0.11) | 0.54 ( 0.28, 0.76) | 0.37 (-62.10, 61.72)
MRIP | GBM | 0.98 (0.13) | 0.39 ( 0.02, 0.71) | 0.13 (-61.26, 61.56)
MRIP | NSCLC | 0.99 (0.08) | 0.49 ( 0.21, 0.73) | 0.22 (-62.03, 61.99)
MRIP | OFTPP | 0.99 (0.11) | 0.37 ( 0.10, 0.66) | 0.23 (-61.87, 61.56)
MRIP | RCC | 0.99 (0.12) | 0.46 ( 0.10, 0.78) | 0.14 (-61.95, 61.78)

###  A.7 Sensitivity analysis: excluding data on breast cancer

####  A.7.1 Surrogacy parameter estimates

Figure A3: Multi-indication meta-analysis of surrogacy parameters using data
available at present day, excluding data from trials in breast cancer. IP -
independent parameters, CP - common parameter, MCIP - mixed common and
independent parameters, RP - random parameters, MRIP - mixed random and
independent parameters, CRC - colorectal cancer, BC - breast cancer, NSCLC -
non-small cell lung cancer, RCC - renal cell carcinoma, CC - cervical cancer,
GBM - glioblastoma, OFTPP - ovarian, fallopian tube, and primary peritoneal.

Table A44: Median and 95% credible interval estimates for the intercept parameter in the surrogacy models, using data available at present-day excluding breast cancer. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | 0.05 ( -0.11, 0.21) | 0.04 ( -0.05, 0.14) | 0.04 ( -0.05, 0.14) | 0.04 ( -0.07, 0.13) | 0.04 ( -0.07, 0.14)
RCC | -0.07 (-15.57, 14.90) | 0.04 ( -0.05, 0.14) | 0.04 ( -0.05, 0.15) | 0.05 ( -0.09, 0.19) | 0.05 ( -0.09, 0.20)
NSCLC | 0.10 ( -0.18, 0.38) | 0.04 ( -0.05, 0.14) | 0.04 ( -0.05, 0.15) | 0.05 ( -0.06, 0.16) | 0.05 ( -0.06, 0.17)
OFTPP | 0.02 ( -0.18, 0.27) | 0.04 ( -0.05, 0.14) | 0.04 ( -0.05, 0.15) | 0.05 ( -0.05, 0.17) | 0.05 ( -0.05, 0.17)
CC | 0.18 (-22.65, 23.18) | 0.04 ( -0.05, 0.14) | 0.04 ( -0.06, 0.16) | 0.03 ( -0.15, 0.16) | 0.04 ( -0.17, 0.20)
GBM | 0.11 ( -1.59, 1.79) | 0.04 ( -0.05, 0.14) | 0.04 ( -0.05, 0.16) | 0.07 ( -0.05, 0.23) | 0.07 ( -0.05, 0.25)
All Indications |  | 0.04 ( -0.05, 0.14) | 0.04 ( -0.05, 0.15) | 0.05 ( -0.06, 0.16) | 0.05 ( -0.06, 0.17)
Table A45: Median and 95% credible interval estimates for the slope parameter in the surrogacy models, using data available at present-day excluding breast cancer. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | 0.60 ( 0.24, 0.91) | 0.42 ( 0.22, 0.64) | 0.45 ( 0.23, 0.69) | 0.54 ( 0.29, 0.76) | 0.54 ( 0.30, 0.76)
RCC | 0.16 (-34.92, 34.43) | 0.42 ( 0.22, 0.64) | 0.44 ( 0.22, 0.66) | 0.44 ( 0.11, 0.76) | 0.45 ( 0.09, 0.79)
NSCLC | 0.58 ( 0.00, 1.13) | 0.42 ( 0.22, 0.64) | 0.44 ( 0.22, 0.66) | 0.49 ( 0.23, 0.73) | 0.49 ( 0.22, 0.74)
OFTPP | 0.23 ( -0.20, 0.75) | 0.42 ( 0.22, 0.64) | 0.43 ( 0.21, 0.66) | 0.34 ( 0.09, 0.59) | 0.34 ( 0.09, 0.61)
CC | 1.23 (-56.06, 57.32) | 0.42 ( 0.22, 0.64) | 0.44 ( 0.21, 0.77) | 0.51 ( 0.14, 0.99) | 0.50 ( 0.05, 1.08)
GBM | 0.31 ( -3.32, 3.79) | 0.42 ( 0.22, 0.64) | 0.43 ( 0.18, 0.66) | 0.34 ( 0.00, 0.64) | 0.35 ( -0.01, 0.68)
All Indications |  | 0.42 ( 0.22, 0.64) | 0.44 ( 0.22, 0.66) | 0.45 ( 0.18, 0.71) | 0.44 ( 0.17, 0.72)
Table A46: Median and 95% credible interval estimates for the conditonal variance parameter in the surrogacy models, using data available at present-day excluding breast cancer. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | 0.05 (0.00, 0.17) | 0.06 (0.00, 0.12) | 0.06 (0.00, 0.14) | 0.04 (0.00, 0.12) | 0.04 (0.00, 0.13)
RCC | 0.26 (0.01, 1.01) | 0.06 (0.00, 0.12) | 0.06 (0.00, 0.29) | 0.04 (0.00, 0.17) | 0.05 (0.00, 0.36)
NSCLC | 0.08 (0.00, 0.34) | 0.06 (0.00, 0.12) | 0.05 (0.00, 0.16) | 0.04 (0.00, 0.14) | 0.05 (0.00, 0.18)
OFTPP | 0.06 (0.00, 0.30) | 0.06 (0.00, 0.12) | 0.06 (0.00, 0.22) | 0.04 (0.00, 0.15) | 0.05 (0.00, 0.19)
CC | 0.34 (0.02, 1.12) | 0.06 (0.00, 0.12) | 0.08 (0.01, 0.74) | 0.05 (0.00, 0.21) | 0.09 (0.00, 0.74)
GBM | 0.23 (0.02, 0.92) | 0.06 (0.00, 0.12) | 0.09 (0.01, 0.48) | 0.06 (0.00, 0.19) | 0.07 (0.00, 0.40)
All Indications |  | 0.06 (0.00, 0.12) | 0.06 (0.00, 0.15) |  |

####  A.7.2 Deviance information criterion (DIC)

Table A47: Residual deviance, number of effective parameters, and deviance information criterian (DIC) from the application of surrogacy models to data at present-day excluding breast cancer. *Based on 28 data points. Model | Residual deviance | Deviance | $p_{D}$ | DIC
---|---|---|---|---
IP | 51.28 | -99.09 | 36.04 | -63.05
CP | 52.71 | -93.98 | 30.04 | -63.94
MCIP | 52.37 | -90.34 | 31.71 | -58.63
RP | 51.43 | -96.24 | 32.16 | -64.08
MRIP | 51.02 | -88.42 | 32.97 | -55.45

####  A.7.3 Mixture probabilities

Table A48: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), for the intercept parameter from the application of surrogacy models to data at present-day excluding breast cancer.  Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | CC | 0.98 (0.13) | 0.04 (-0.05, 0.15) | 0.03 (-61.60, 61.94)
MCIP | CRC | 0.99 (0.08) | 0.04 (-0.05, 0.15) | -0.01 (-61.56, 62.32)
MCIP | GBM | 0.98 (0.14) | 0.04 (-0.05, 0.15) | 0.15 (-61.27, 61.81)
MCIP | NSCLC | 1.00 (0.04) | 0.04 (-0.05, 0.15) | 0.07 (-62.34, 62.44)
MCIP | OFTPP | 1.00 (0.07) | 0.04 (-0.05, 0.15) | -0.02 (-62.18, 61.70)
MCIP | RCC | 1.00 (0.05) | 0.04 (-0.05, 0.15) | -0.04 (-61.93, 61.91)
MRIP | CC | 0.98 (0.13) | 0.04 (-0.15, 0.19) | -0.08 (-61.53, 61.48)
MRIP | CRC | 1.00 (0.07) | 0.04 (-0.07, 0.14) | -0.01 (-61.86, 61.92)
MRIP | GBM | 0.99 (0.09) | 0.07 (-0.06, 0.25) | 0.16 (-61.84, 62.11)
MRIP | NSCLC | 1.00 (0.06) | 0.05 (-0.06, 0.17) | 0.05 (-62.30, 61.86)
MRIP | OFTPP | 1.00 (0.05) | 0.05 (-0.05, 0.17) | -0.06 (-62.03, 62.23)
MRIP | RCC | 0.99 (0.07) | 0.05 (-0.09, 0.20) | -0.04 (-62.49, 61.87)
Table A49: Mixture probability estimates (as mean and standard deviation), and informative and vague mixture component estimates (as median and 95% credible interval), for the slope parameter from the application of surrogacy models to data at present-day excluding breast cancer.  Model | Indication | Probability | Informative | Vague
---|---|---|---|---
MCIP | CC | 0.96 (0.19) | 0.44 ( 0.22, 0.66) | 0.67 (-61.30, 61.40)
MCIP | CRC | 0.95 (0.21) | 0.44 ( 0.22, 0.66) | 0.59 (-61.19, 61.35)
MCIP | GBM | 0.97 (0.17) | 0.44 ( 0.22, 0.66) | 0.15 (-61.70, 61.26)
MCIP | NSCLC | 1.00 (0.06) | 0.44 ( 0.22, 0.66) | 0.16 (-61.63, 61.99)
MCIP | OFTPP | 0.97 (0.17) | 0.44 ( 0.22, 0.66) | 0.25 (-61.77, 61.38)
MCIP | RCC | 0.99 (0.08) | 0.44 ( 0.22, 0.66) | 0.25 (-61.80, 61.69)
MRIP | CC | 0.97 (0.18) | 0.49 ( 0.07, 1.00) | 0.52 (-61.66, 61.54)
MRIP | CRC | 0.99 (0.11) | 0.54 ( 0.29, 0.76) | 0.46 (-61.90, 61.58)
MRIP | GBM | 0.98 (0.13) | 0.36 ( 0.00, 0.68) | 0.16 (-61.65, 62.05)
MRIP | NSCLC | 0.99 (0.09) | 0.49 ( 0.22, 0.74) | 0.32 (-62.12, 61.84)
MRIP | OFTPP | 0.99 (0.12) | 0.34 ( 0.09, 0.62) | 0.25 (-61.98, 61.69)
MRIP | RCC | 0.99 (0.10) | 0.45 ( 0.10, 0.79) | 0.34 (-61.93, 61.54)

###  A.8 Sensitivity analysis: common effect across trials within each
indication

####  A.8.1 Treatment effect estimates

Figure A4: Multi-indication meta-analysis, assuming a common effect across
trials within each indication, synthesising effects on overall survival (OS)
and progression-free survival (PFS) using data available at present day. IP -
independent parameters, CP - common parameter, MCIP - mixed common and
independent parameters, RP - random parameters, MRIP - mixed random and
independent parameters, CRC - colorectal cancer, BC - breast cancer, NSCLC -
non-small cell lung cancer, RCC - renal cell carcinoma, CC - cervical cancer,
GBM - glioblastoma, OFTPP - ovarian, fallopian tube, and primary peritoneal.

Table A50: Median and 95% credible interval estimates for hazard ratios from multi-indication meta-analysis models, assuming a common effect across trials within each indication, using data on overall survival (OS) available at present-day. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | 0.85 (0.79, 0.90) | 0.89 (0.86, 0.92) | 0.89 (0.86, 0.92) | 0.87 (0.81, 0.91) | 0.87 (0.81, 0.91)
RCC | 0.86 (0.75, 0.99) | 0.89 (0.86, 0.92) | 0.89 (0.86, 0.92) | 0.88 (0.80, 0.95) | 0.88 (0.80, 0.95)
BC | 0.90 (0.82, 0.98) | 0.89 (0.86, 0.92) | 0.89 (0.86, 0.92) | 0.89 (0.84, 0.95) | 0.89 (0.84, 0.95)
NSCLC | 0.87 (0.79, 0.96) | 0.89 (0.86, 0.92) | 0.89 (0.86, 0.92) | 0.89 (0.82, 0.94) | 0.89 (0.82, 0.94)
OFTPP | 0.93 (0.87, 1.01) | 0.89 (0.86, 0.92) | 0.89 (0.86, 0.92) | 0.90 (0.86, 0.98) | 0.90 (0.86, 0.98)
CC | 0.77 (0.62, 0.95) | 0.89 (0.86, 0.92) | 0.89 (0.85, 0.92) | 0.88 (0.76, 0.95) | 0.88 (0.75, 0.95)
GBM | 0.96 (0.86, 1.07) | 0.89 (0.86, 0.92) | 0.89 (0.86, 0.92) | 0.91 (0.85, 1.00) | 0.91 (0.85, 1.00)
All Indications |  | 0.89 (0.86, 0.92) | 0.89 (0.86, 0.92) | 0.89 (0.84, 0.94) | 0.89 (0.84, 0.94)
New Indication |  |  |  | 0.89 (0.77, 1.02) | 0.89 (0.77, 1.01)
Table A51: Median and 95% credible interval estimates for hazard ratios from multi-indication meta-analysis models, assuming a common effect across trials within each indication, using data on progression-free survival (PFS) available at present-day. Indication | IP | CP | MCIP | RP | MRIP
---|---|---|---|---|---
CRC | 0.72 (0.67, 0.76) | 0.71 (0.68, 0.73) | 0.71 (0.68, 0.73) | 0.71 (0.68, 0.76) | 0.71 (0.68, 0.76)
RCC | 0.63 (0.56, 0.70) | 0.71 (0.68, 0.73) | 0.71 (0.68, 0.73) | 0.68 (0.60, 0.73) | 0.68 (0.60, 0.73)
BC | 0.75 (0.70, 0.80) | 0.71 (0.68, 0.73) | 0.71 (0.68, 0.73) | 0.73 (0.69, 0.78) | 0.73 (0.69, 0.78)
NSCLC | 0.70 (0.64, 0.76) | 0.71 (0.68, 0.73) | 0.71 (0.68, 0.73) | 0.70 (0.65, 0.75) | 0.70 (0.65, 0.75)
OFTPP | 0.73 (0.68, 0.78) | 0.71 (0.68, 0.73) | 0.71 (0.68, 0.73) | 0.72 (0.68, 0.76) | 0.72 (0.68, 0.76)
CC | 0.68 (0.55, 0.84) | 0.71 (0.68, 0.73) | 0.71 (0.68, 0.73) | 0.70 (0.62, 0.77) | 0.70 (0.62, 0.77)
GBM | 0.65 (0.59, 0.72) | 0.71 (0.68, 0.73) | 0.71 (0.68, 0.73) | 0.68 (0.62, 0.73) | 0.68 (0.62, 0.73)
All Indications |  | 0.71 (0.68, 0.73) | 0.71 (0.68, 0.73) | 0.70 (0.65, 0.74) | 0.70 (0.66, 0.74)
New Indication |  |  |  | 0.70 (0.59, 0.81) | 0.70 (0.59, 0.81)

####  A.8.2 Deviance information criterion (DIC)

Table A52: Residual deviance, deviance, number of effective parameters, and deviance information criterian (DIC) from the application of univariate models, assuming a common effect within indications, to data on overall survival at present-day. *Based on 38 data points. Model | Residual deviance | Deviance | $p_{D}$ | DIC
---|---|---|---|---
IP | 48.25 | -34.07 | 7.01 | -27.06
CP | 50.19 | -32.13 | 1.01 | -31.12
MCIP | 50.17 | -32.16 | 1.05 | -31.10
RP | 48.14 | -34.19 | 3.75 | -30.44
MRIP | 48.13 | -32.81 | 4.05 | -28.76