# Multitask Deep Learning for Accurate Risk Stratification and Prediction of
Next Steps for Coronary CT Angiography Patients

Juan Lu  Mohammed Bennamoun Senior Member, IEEE  Jonathon Stewart  Jason K.
Eshraghian Member, IEEE  Yanbin Liu  Benjamin Chow  Frank M. Sanfilippo and
Girish Dwivedi Manuscript submitted on 21 April. This project was supported by
the Western Australian Health Translation Network’s Health Service
Translational Research project grant, and the funding source had no
involvement in the study.J. L. is with the Medical school and Harry Perkins
Institute of Medical Research and School of Computer Science and Software
Engineering, the University of Western Australia, Perth, WA 6009 Australia,
(e-mail: juan.lu@uwa.edu.au).M. B. is with the School of Computer Science and
Software Engineering, the University of Western Australia, Perth, WA 6009
Australia (e-mail: mohammed.bennamoun@uwa.edu.au).J. S. is with the Medical
School and Harry Perkins Institute of Medical Research, the University of
Western Australia, Perth, WA, 6009 (e-mail: jonathon.stewart@uwa.edu.au).J. E.
was with School of Computer Science and Software Engineering, the University
of Western Australia Perth, WA, 6009 Australia. He is now with the Department
of Electrical and Computer Engineering, University of California, Santa Cruz,
CA, 95064 USA (e-mail: jeshragh@ucsc.edu).Y. L. is with the School of
Computing, Australian National University, Canberra, ACT 2601 Australia
(e-mail: csyanbin@gmail.com).B. C. is with the Division of Cardiology and
Departments of Medicine, University of Ottawa Heart Institute, Ottawa, ON K1Y
4W7 (e-mail: bchow@ottawaheart.ca).F. S. is with the School of Population and
Global Health, the University of Western Australia, Perth, WA 6009 Australia
(e-mail: frank.sanfilippo@uwa.edu.au).G. D. is with the Medical School and
Harry Perkins Institute of Medical Research, the University of Western
Australia. He is also with the Department of Cardiology, Fiona Stanley
Hospital, Perth, WA, 6154 (e-mail: girish.dwivedi@perkins.uwa.edu.au).

###### Abstract

Diagnostic investigation has an important role in risk stratification and
clinical decision making of patients with suspected and documented Coronary
Artery Disease (CAD). However, the majority of existing tools are primarily
focused on the selection of gatekeeper tests, whereas only a handful of
systems contain information regarding the downstream testing or treatment. We
propose a multi-task deep learning model to support risk stratification and
down-stream test selection for patients undergoing Coronary Computed
Tomography Angiography (CCTA). The analysis included 14,021 patients who
underwent CCTA between 2006 and 2017. Our novel multitask deep learning
framework extends the state-of-the art Perceiver model to deal with real-world
CCTA report data. Our model achieved an Area Under the receiver operating
characteristic Curve (AUC) of 0.76 in CAD risk stratification, and 0.72 AUC in
predicting downstream tests.

Our proposed deep learning model can accurately estimate the likelihood of CAD
and provide recommended downstream tests based on prior CCTA data. In clinical
practice, the utilization of such an approach could bring a paradigm shift in
risk stratification and downstream management. Despite significant progress
using deep learning models for tabular data, they do not outperform gradient
boosting decision trees, and further research is required in this area.
However, neural networks appear to benefit more readily from multi-task
learning than tree-based models. This could offset the shortcomings of using
single task learning approach when working with tabular data.

multitask learning, deep learning, coronary artery disease, diagnostic test,
gradient boosting decision tree, perceiver, coronary computed tomography

##  1 Introduction

Coronary Artery Disease (CAD) is one of the leading causes of death around the
globe [1]. It accounts for millions of death annually and is a huge global
economic burden [2]. Therefore, providing precise diagnostic tests and
prevention support can have a substantial influence on reducing CAD-related
mortality and save billions for the economy [3].

Coronary Computed Tomography Angiography (CCTA) has evolved as an accurate
method for the non-invasive evaluation of CAD, and to direct subsequent
treatment [4]. It provides anatomical information on the severity of stenosis.
Invasive Coronary Angiography (ICA) and revascularization may be carried out
after the CCTA for patients with obstructive coronary artery stenosis [5].
However, the recent PROMISE trail111The PROMISE (Prospective Multicenter
Imaging Study for Evaluation of Chest Pain) is a large-scale study that was
conducted to evaluate the use of non-invasive tests, such as CCTA and stress
tests, in the diagnosis and management of patients with stable chest pain. The
study was designed to compare the diagnostic accuracy and clinical outcomes of
these non-invasive tests with those of the traditional invasive test, Invasive
Coronary Angiography (ICA) revealed that CCTA-guided treatment resulted in
more ICAs and revascularizations without improving clinical outcomes compared
to functional testing [6]. Functional tests such as exercise stress
electrocardiography (EST), single-photon emission computerized tomography
(SPECT), and positron emission tomography (PET) evaluate the degree of blood
flow restriction (or ischemia) to the heart muscle due to blockages in the
coronary arteries. It has been shown that the integration of functional tests
with CCTA test will identify patients who would benefit most from further
invasive investigation and revascularization [7].

Figure 1: Study Framework. A multitask deep learning neural network was
implemented with patients’ information (demographics, vital sign, medications,
comorbidity history, and coronary computed tomography angiography test
readings) jointly predict risk of coronary artery disease and down-streaming
investigations or treatments.

It is common in clinical practice to use a validated pretest probability model
for predicting the probability of CAD to inform the choice of diagnostic test.
Most existing tools primarily focus on identifying the gatekeeper test (i.e.,
a diagnostic test or screening tool that is used to determine whether a
patient should be referred for further testing or treatment), while only a few
provide information on follow up testing or treatment options [8, 9].
Meanwhile, it has been observed that the overuse of diagnostic imaging is on
the rise in clinical practices causing a significant stress on health budget
and fundings [10]. As a result, current guidelines emphasize the importance of
using risk stratification tools and pre-test probability assessment tools
(i.e., to assess the likelihood of disease) prior to initiation of downstream
testing. However, their lack of general applicability has been identified as a
limitation. Multiple studies have shown that these risk assessment models
perform sub-optimally in certain groups of patients [11, 5]. Patients have
varying underlying conditions that require personalized approach. Furthermore,
differences in derivation (variations in the way these models are developed,
such as the use of different imaging modalities, cut-off values for defining
CAD risk, and data processing techniques) often occur and may further limit
the effectiveness of these tools. Machine learning models are ideally suited
for addressing these challenges. It could suggest an optimized probability
based on the most recent locally relevant data as input. Therefore, our aim
was to develop a machine learning model, using the CCTA diagnostic test
reports of patients as input. These data are collected as tabular data.

As a subfield of machine learning, deep neural networks has achieved dazzling
success in a wide variety of areas, such as computer vision and natural
language processing using transformer-based architecture [12, 13]. For tabular
data, tree-based machine learning or ensemble models are reported as the best
algorithms [14, 15, 16], as these models have been found to be effective in
delivering good performance with less training time and are easily
explainable. However, tree-based models can be sensitive to small changes in
the input and have limitations when dealing with limited labeled data when
advanced semi-supervised learning techniques are used and in handling high
dimensional data [17, 18]. Conversely, deep learning models have their own
strengths, such as the ability to handle both single-task and multi-task
learning of image or text inputs, or multi-modal input, including tabular data
[19]. In this paper, we sought to apply deep learning to construct a multi-
task learning model on tabular data.

It is logical to assume that the downstream diagnosis of each patient is
primarily based on their CAD risk, so it makes a very strong case to consider
the CAD risk and downstream diagnosis together. In this scenario, multi-task
learning [20] is a viable solution as it allows to exploit useful information
from these two related learning tasks.

Multitask learning, which is a promising field in deep learning, aims to
improve the accuracy of learning each task by leveraging the useful
information shared across multiple tasks. It has been empirically and
theoretically demonstrated that learning multiple tasks can result in better
performance than learning them individually [21]. In this research, we aimed
to introduce a multi-task deep learning model for identifying patients who may
benefit from invasive coronary investigation and revascularization. Our multi-
task deep learning model was designed to learn from patient demographics,
clinical history, and CCTA test readings, in order to predict patients’ risk
of CAD and their down-streaming investigations and treatment options.

The contributions of this paper are summarized as following:

  * •

The introduction of TabPerceiver, a simple and less computationally expensive
transformer-based deep learning model that can handle multi-modal data.

  * •

The multi-task TabPerceiver model automatically associates downstream
diagnosis and treatment with patient CAD risk.

  * •

Demonstrating that TabPerceiver achieved better performance than gradient
boosting decision trees but there is no universally superior solution between
GBDT and deep learning models for tabular data.

##  2 Methods

###  2.1 Study Data

We used a substantial dataset acquired from the University of Ottawa Heart
Institute, Canada. In the total cohort, 20,683 CCTA test reports were
identified in the period between 2006 to 2017. The date of their first CCTA
test was defined as $t_{0}$. The timeline is presented in Fig. 2. We excluded
patients whose tests were cancelled or whose CCTA readings were missing.
Additionally, we excluded duplicate reports for the same patients and kept
records from experienced senior readers. Our cohort was further restricted to
include patients who had CCTA as their primary test, and had not undergone
revascularization or other tests (ICA, SPECT, PET, EST) within 1 year before
$t_{0}$. More specifically, we included patients with i) CCTA as their initial
test, ii) underwent at least one of the SPECT, PET, EST, ICA or
revascularizations (percutaneous coronary intervention (PCI) and coronary
artery bypass graft surgery (CABG)) within one year after $t_{0}$, and iii)
had a second test interpretation available. This resulted in the selection of
a cohort of 884 patients as showed in Fig. 3. All reported results were
obtained from a held-out test set that was not used to train or tune the
model.

Figure 2: Timeline of cohort selection and output definition. We identified
patients who had CCTA, and $t_{0}$ is the date of their index CCTA. Patients
who have undergone previous tests or treatments within 1 year before $t_{0}$
are excluded. The eligible down-streaming tests should be conducted within 1
year after $t_{0}$. Patients with no follow-up records are excluded since
their outcomes are unknown.

Figure 3: Cohort selection based on patients’ CCTA test report availability
and investigation journey.

###  2.2 Predictors

Each patient entry included demographic information (age, sex, weight, and
height), clinical information (heart rate, blood pressure, and reasons for
test), pretest probability of CAD (Diamond & Forrester) [22], significant
cardiovascular risk factors (family history, smoking status, diabetes
mellitus, hypertension, hyperlipidemia, and history of CAD), medications
(aspirin, beta-blockers, calcium channel blockers, statins, and metformin) and
CCTA segment stenosis readings. All of this information was included as input
to our models.

###  2.3 Pre-processing

We removed features that had more than 50% missing values and imputed the
remaining missing values in 22 features with maximum missing rate of 8.8%
using multivariate imputation [23]. All the other input features were used to
estimate the missing values in a round-robin fashion.

###  2.4 Outcomes

We linked the diagnostic tests and revascularization data for each individual
patient using the available data. The downstream tests or treatments were
those performed within one year after their CCTA tests. We separated the down
streaming test or treatments into two groups: functional testing (including
EST, SPECT and PET) vs. invasive tests and/or revascularization (including
ICA, PCI and CABG). This makes the downstream tests or treatments prediction
to be a binary classification task.

The risk of CAD for patients was determined by the readings of the follow-up
tests as shown in Fig. 4. The risk of patients was classified into three
groups: low, intermediate and high risk. Then the risk prediction task becomes
a classification task with multiple classes. Based on the tests and data
availability, the risks of CAD were defined differently for each test.

The results of the test were used to determine the risk for patients who had
EST after their CCTA. The Summed Difference Score (SDS) was used to determine
the risk of CAD for patients who received SPECT and PET [24]. This was
determined by test findings for patients who had ICA. Patients who were
scheduled for revascularisation were determined to be at high risk.

Figure 4: Output labeling. The test conclusions were utilised to determine the
risk of CAD for patients who had EST following their CCTA.The Summed
Difference Score (SDS) was used to determine the risk of CAD for patients who
received SPECT and PET.[24] This was determined by test findings for patients
who had ICA. Patients who were assigned for revascularisation were determined
to be high risks. Predefined fields included: scar, ischemia, LAD, RCA, LCX,
RCALCX, TID, DilatedLV.
LAD, left anterior descending artery; RCA, right coronary artery; LCX, left
circumflex artery; TID, transient ischemic dilation; LV, left ventricular;
ICA, invasive coronary angiography; PCI, percutaneous coronary intervention;
CABG, coronary artery bypass graft surgery

###  2.5 Statistical analysis and metrics for performance measure

The discriminant power of the risk prediction and downstream test or treatment
recommendation tasks was evaluated using the area under the receiver operating
characteristic curve (AU-ROC) with a 95% confidence interval (CI). We also
reported sensitivity (recall), specificity, precision (positive predictive
value) and negative predictive value. The calibration was evaluated using the
Brier score, which calculates the difference between the estimated and
observed results. We evaluated the performance of GBDT, multi-layer perceptron
(MLP) and TabPerciever in performing single task learning, and also assessed
the performance of the multi-task TabPerceiver. We then compared the
performance of different models using a paired sample T-test and reported the
corresponding p-value. The group difference was compared using the chi-square
test for categorical variables. One-way ANOVA was used to compare the means of
continuous variables across distinct risk groups, whereas the T-test was used
to compare down-streaming diagnostic tests or treatments. We regarded the
performance difference to be statistically significant if there was no overlap
between 95% CIs and the p-value was less than 0.05.

###  2.6 The architecture of TabPerceiver

We have extended the architecture of Perceiver-IO [25] and Tab-transformer
[26] to create the Tab-Perceiver. Perceiver-IO is an advanced artificial
intelligence architecture that can handle arbitrary inputs and outputs. It can
produce various outputs, such as language and video, and is built on the same
building blocks as the original Perceiver [27]. It is computationally
efficient and can handle large inputs and outputs than the standard self-
attention Transformer [28]. We constructed separate embeddings for categorical
and continuous features implementing different algorithms. The categorical and
continuous embeddings were then fed into perceiver encoders individually.
Perceiver encoder is a stack of cross-attention modules that transfer the
input embedding to a latent vector, with a latent Transformer [29] converting
one latent vector to another latent vector. The latent transformer consists of
a multi-head self-attention layer. The perceiver decoder is constructed in a
similar manner to the encoder. Both encoder and decoder take in two inputs.
The first input is used as the input to the key and value network of the
cross-attention module, while the second is used as the input to the query
network. The architecture of TabPerceiver is shown in Fig. 5.

Figure 5: The TabPerceiver architecture. It uses a cross-attention module to
project the input embeddings to a fixed-dimensional latent bottleneck and then
processing it using a stack of Transformer-style self-attention blocks in the
latent space. The latent indices $N$ and latent dimension $I$ are hyper-
parameters and independent from the number of input features $M$ and $C$. $D$
is the dimension of embedding. The encoder iteratively attends to the input by
alternating cross-attention and latent self-attention blocks. The decoder
takes the concatenated output of encoder as input to its key ($K$) and value
($V$) networks, and the model output was the input to its query ($Q$) network.

Let $(x,y)$ denote a feature-target pair, where
$x\equiv\\{x_{cat},x_{num}\\}$.

$x_{num}\in\mathbb{R}^{C}$ denotes all of the $C$ continuous features. Let
$x_{cat}\equiv\\{x_{1},x_{2},\cdots,x_{M}\\}$ with each $x_{i}$ being a
categorical feature, for $i\in\\{1,\cdots,M\\}$. We embedded each of the
$x_{i}$ categorical features into a parametric embedding of dimension $D$
using feed-forward network with a learnable embedding layer. Let
$e_{\phi_{i}}(x_{i})\in\mathbb{R}^{c}$ for $i\in\\{1,\cdots,M\\}$ be the
embedding of the $x_{i}$ feature, and
$E_{\phi}(x_{cat})=\\{e_{\phi_{1}}(x_{1}),\cdots,e_{\phi_{M}}(x_{M})\\}$ be
the set of embeddings for all the categorical features.

Next, these parametric embeddings $E_{\phi}(x_{cat})$ are input to the
perceiver encoder. The perceiver encoder alternatively employed the cross-
attention and the Transformer (self-attention) modules. Both cross-attention
and self-attention modules are organised around the use of query-key-value
(QKV) attention. QKV attention applies three networks - the query, key, and
value networks, which are typically MLPs. To each element of
$E_{\phi_{i}}(x_{cat})$, producing three vectors that preserve the index
dimensionality $M$.

To understand how this works in self-attention, it is import to first note
that for $Q\in\mathbb{R}^{M}{}^{\times}{}^{D}$,
$K\in\mathbb{R}^{M}{}^{\times}{}^{D}$, and
$V\in\mathbb{R}^{M}{}^{\times}{}^{D}$, (where $D$ is the dimension of
embedding) the complexity of the QKV attention operation - essentially,
$softmax(QK^{T})V$ \- is $\mathcal{O}(M^{2})$, as it involves two matrix
multiplications with matrices of dimension $M$. In cross-attention, while $K$
and $V$ are projections of the input, $Q$ is a projection of a learned latent
array with index dimension $N$, where the latent’s dimension $N$ is a hyper-
parameter. Consequently, the cross-attention operation has complexity
$\mathcal{O}(MN)$.

The output of the cross-attention module takes the shape of the
$e_{\phi_{i}}(x_{i})$ to the $Q$ network. Hence, the cross-attention layer
introduces a bottleneck. We can then further analyze this bottleneck in depth
by utilizing multi-head self-attention module in the latent space, and the
this comes at the cost of $\mathcal{O}(N^{2})$. This results in an
architecture with complexity $\mathcal{O}(MN+LN^{2})$, where $L$ represents
the number of layers of self-attention module in perceiver encoder. The
introduction of $N$ decouples the input size from the depth of self-attention
module, allowing for more flexibility in terms of the input size and depth of
the model. For large-scale data with high dimension $M$, $N<<M$, helps to
reduce the complexity of the model. This allows for construction of deep
networks with a lower cost. $N>M$ is also acceptable for small-scale tabular
data with selected input features. It contributes to the expansion of input
for subsequent layers.

The bottleneck may impede the network’s ability to acquire detailed
information from the input. To mitigate this impact, the perceiver encoder
could be structured with multiple cross-attend layers that enable the latent
vector to extract information from the input in an iterative manner, which
helps to gather more detailed information from the input. Given that there is
no ordering of the categorical features in tabular data, positional encoding
is not applied. We denote the sequence of cross-attend layers as a function
$f_{\theta}$. The function $f_{\theta}$ operates on parametric categorical
embeddings $\\{e_{\phi_{1}}(x_{1}),\cdots,e_{\phi_{M}}(x_{M})\\}$ and returns
the corresponding latent vector with shape $N\times I$, where the latent’s
channel $I$ is another hyper-parameter.

Concurrently, continuous features were first encoded using piece-wise linear
encoding [30]. Let $x_{num}\equiv\\{x_{1},x_{2},\cdots,x_{C}\\}$ with each
$x_{j}$ being a continuous feature, for $j\in\\{1,\cdots,C\\}$. For each
$x_{j}$, we split its value range into the disjoint set of $T$ bins according
to their empirical quantiles, denoted as $B_{1},\cdots,B_{T}$.

$B_{t}=[b_{t-1},b_{t})\,,$ (1)

where $b_{t}$ is calculated using the empirical quantile function. Trivial
bins of zero size are removed. Then we allocated one trainable embedding
$e_{t}$ for each bin $B_{t}$ and aggregated the embeddings of its bins with
$v_{t}$ as weights, plus bias $v_{0}$. The embedding for each continuous
feature $x_{j}$ can thus be denoted as:

$e_{t}=\begin{cases}0,&x<b_{t_{1}},t>1\\\ 1,&x\geq b_{t},t<T\\\
\frac{x-b_{t}-1}{b_{t}-b_{t-1}},&\text{otherwise}\end{cases}\,,$ (2)
$e_{\varphi_{j}}(x_{j})=v_{0}+\sum_{t=1}^{T}e_{t}\cdot v_{t}\,,$ (3)

and where
$E_{\varphi}(x_{cont})=\\{e_{\varphi_{1}}(x_{1}),\cdots,e_{\varphi_{C}}(x_{C})\\}$
is the set of embeddings for all the continuous features. The latent vector of
categorical features are then flattened and concatenated with the latent
vector of continuous features to form a vector of dimension $2NI$. This vector
is one of the input to perceiver decoder. We denote the decoder as a function
$g$, and it also operates on the target $y$. Let $H$ be the cross-entropy for
classification tasks. We minimize the following loss function
$\mathcal{L}(x,y)$ to learn all the TabPerceiver parameters. The TabPerceiver
parameters include $\phi$ for column embedding, $\theta$ for cross-attend
layers.

$\mathcal{L}(x,y)\equiv
H(g(f_{\theta}(E_{\phi}(x_{cat}),f_{\theta}(E_{\varphi}(x_{num})),y))\,.$ (4)

As an alternative to decoder, we investigated the use of MLP in the
architecture. After undergoing embedding and perceiver encoder, the
concatenated latent output of categorical and continuous embeddings can simply
be passed through an MLP denoted as $k_{\psi}$ to predict the target $y$. The
equation (4) can be updated as below, if the MLP with $\psi$ for the top layer
were used after the encoder.

$\mathcal{L}(x,y)\equiv
H(k_{\psi}(f_{\theta}(E_{\phi}(x_{cat})),f_{\theta}(E_{\varphi}(x_{num}))),y)\,.$
(5)

Hard and soft parameter sharing are two prevalent techniques for performing
multitask learning in deep neural networks. Hard parameter sharing maintains
task-specific output layers while sharing the hidden layers between all tasks.
Soft parameter sharing preserves individual hidden layers for each task. [31]
In our multitask TabPerceiver, we opted for the hard parameter sharing
strategy, where we shared the hidden layers between all tasks, but kept task-
specific output layers. We had two tasks during the learning, risk and
downstream tests or treatments prediction, denoted
$y^{t}\in\mathbb{R}^{N},t\in\\{1,2\\}$. We employed one decoder for each task,
and then we applied uncertainty to weight the loss [32], where the weight
$w_{i}$ for each task is a learnable parameter. Then the equation for multi-
task TabPerceiver would form as:

$\mathcal{L}(x,y)\equiv\sum\limits_{i=1}^{T}w_{i}\mathcal{L}(x,y^{i})\,.$ (6)

###  2.7 Feature selection

Feature ranking in GBDT was obtained by computing Shapley Additive Explanation
values (SHAP) [33]. We then selected the top ranked features and fitted them
in the GBDT. We conducted an ablation study to assess the importance of
different features in TabPerceiver (demographics, clinical information,
comorbidity history, medications, CCTA scan readings) by alternatively
removing each of these features. We also experimented with the selected
features in GBDT on the TabPerceiver model. The detailed feature and their
selection results can be found in Appendix section "List of available and
selected features".

###  2.8 Hyper-parameter tuning

Bayesian optimization [34] was used to tune the model hyper-parameters for all
the experimental models, including learning rates, batch size, bins count for
continuous feature encoding, number of heads, cross-attend layers and latent
dimension in TabPerceiver. We also tuned the number of estimators, number of
leaves, maximum depth, minimum data in each leaf, maximum bin and subsample in
GBDT. All the models were tuned on the validation set, and the optimal hyper-
parameter setting for ML-TabPerceiver is listed in the Appendix section "Model
hyper-parameters".

##  3 Results

###  3.1 Patient characteristic

Out of the 894 patients in the cohort, 475 (53.7%) were determined to be high
risk, 225 (25.5%) were found to be low risk, and around one-fifth of the
patients, 184 (20.8%), were defined as intermediate risk. Of the total number
of patients, 239 (27%) received functional testing as a downstream diagnostic
test, while the remaining 645 (73%) received invasive testing or
revascularization. The mean age was 59.0 years (SD 10.8) and 65.6% were male
(Table 1). Both hyperlipidemia (61.8%) and hypertension (56.3%) were prominent
risk factors, whilst diabetes mellitus was presented in 16.2% of the
population and 16.9% were current smokers. The mean baseline heart rate was 67
(SD 11.9), mean Agatston score was 361.3 (SD 551.4), and the mean baseline
systolic and diastolic blood pressure were 137 (SD 19.7) and 79 (SD 10.4),
respectively. As showed in Fig. 6, the CAD risks of patients are highly
correlated with their down-streaming tests. Most of patients at high risks of
CAD had invasive tests or treatments after their CCTA.

Table 1: Patient characteristics Patient characteristics |  n(%) unless otherwise specified |  p-value (CAD risk) |  p-value (down-stream tests)
---|---|---|---
Age, mean (SD), years |  59.0 (10.8) |  $<$ 0.05 |  $<$ 0.05
Male |  580 (65.6) |  0.49 |  0.32
Height (cm), mean (SD) |  170.0 (10.5) |  0.98 |  0.14
Weight (kg), mean (SD) |  85.3 (18.4) |  0.66 |  0.45
Baseline HR (bpm), mean (SD) |  67 (11.9) |  $<$ 0.05 |  0.08
Baseline Systolic BP (mmHg), mean (SD) |  137.0 (19.7) |  0.07 |  0.41
Baseline Diastolic BP (mmHg), mean (SD) |  79 (10.4) |  0.34 |  0.52
Agatston, mean (SD) |  361.3 (551.4) |  $<$ 0.05 |  $<$ 0.05
Probability of CAD, mean (SD) |  35.6 (31.2) |  $<$ 0.05 |  $<$ 0.05
Family history of CAD |  450 (50.9) |  0.38 |  0.29
Hypertension |  498 (56.3) |  $<$ 0.05 |  $<$ 0.05
Hyperlipidemia |  546 (61.8) |  0.37 |  0.10
Diabetes mellitus |  143 (16.2) |  $<$ 0.05 |  0.07
Smoking |  149 (16.9) |  0.45 |  $<$ 0.05
Test for chest pain reason |  501 (56.7) |  $<$ 0.05 |  $<$ 0.05
Test for equivocal reason |  66 (7.5) |  0.09 |  0.81
Dyspnea |  547 (61.9) |  0.15 |  $<$ 0.05
Palpitations |  414 (46.8) |  $<$ 0.05 |  0.44
Syncope |  280 (31.7) |  0.18 |  0.83
Aspirin |  514 (58.1) |  $<$ 0.05 |  $<$ 0.05
ACE inhibitors |  240 (27.1) |  $<$ 0.05 |  $<$ 0.05
Beta-blockers |  390 (44.1) |  $<$ 0.05 |  $<$ 0.05
Calcium Channel Blockers |  132 (14.9) |  0.24 |  $<$ 0.05
Diuretics |  157 (17.8) |  0.57 |  0.06
Statins |  458 (51.8) |  0.10 |  0.07
CAD, coronary artery disease; SD, standard deviation; HR, heart rate; BP,
blood pressure; ACE, angiotensin-converting enzyme
Figure 6: Task profile. CAD risk and down-streaming tests are visualized
separately using kernalized Principal Component Analysis with 2 principal
components. Classes are separated by colors. Each point is a patient entry.

###  3.2 Model performance using the selected features

Table 2 shows the AUC, sensitivity, specificity and brier score of the multi-
task TabPerceiver with decoder using the selected input variables comparing
the performance of single-task GBDT, MLP and TabPerceiver. GBDT outperformed
the competitors while doing the single task learning. However, multi-task
TabPerceiver showed the best discrimination and calibration capabilities among
the evaluated models in the CAD risk prediction task. It also achieved optimal
performance in predicting the downstream diagnostic tests.

Regarding the selection of MLP and decoder within the TabPerceiver
architecture, the decoder performed marginally better when used as the output
layer.

Figure 7: Ablation study with exclusion of different feature modalities by CAD
risk group and downstream tests. CAD, coronary artery disease, CP, chest pain,
info., information. Table 2: Performance comparison among different machine
learning methods

Models | Target | Performance
---|---|---
|  | AUC (95% CI) | Sensitivity | Specificity | Brier Score
GBDT | low | 0.733 (0.721, 0.747) | 0.58 | 0.83 | 0.31
medium | 0.602 (0.589, 0.616) | 0.18 | 0.81 | 0.25
high | 0.719 (0.706, 0.732) | 0.68 | 0.63 | 0.34
| invasive test | 0.730 (0.715, 0.745) | 0.64 | 0.42 | 0.34
MLP | low | 0.685 (0.665, 0.705) | 0.51 | 0.82 | 0.32
medium | 0.593 (0.577, 0.609) | 0.19 | 0.80 | 0.29
high | 0.696 (0.676, 0.716) | 0.65 | 0.57 | 0.35
| invasive test | 0.694 (0.681, 0.706) | 0.70 | 0.71 | 0.33
TabPerceiver (MLP) | low | 0.723 (0.711, 0.734) | 0.54 | 0.83 | 0.31
medium | 0.602 (0.590, 0.615) | 0.19 | 0.80 | 0.27
high | 0.713 (0.702, 0.725) | 0.68 | 0.63 | 0.34
| invasive test | 0.704 (0.693, 0.681) | 0.69 | 0.41 | 0.33
TabPerceiver (decoder) | low | 0.717 (0.705, 0.729) | 0.53 | 0.83 | 0.30
medium | 0.588 (0.574, 0.601) | 0.17 | 0.80 | 0.27
high | 0.703 (0.690, 0.715) | 0.68 | 0.62 | 0.36
| invasive test | 0.688 (0.677, 0.699) | 0.72 | 0.42 | 0.33
ML-TabPerceiver (MLP) | low | 0.723 (0.711, 0.734) | 0.54 | 0.83 | 0.31
medium | 0.602 (0.590, 0.615) | 0.19 | 0.80 | 0.27
high | 0.713 (0.702, 0.725) | 0.68 | 0.63 | 0.34
| invasive test | 0.704 (0.693, 0.681) | 0.69 | 0.41 | 0.33
ML-TabPerceiver (decoder) | low |  0.752 (0.742, 0.763) | 0.59 | 0.85 | 0.29
medium |  0.625 (0.611, 0.640) | 0.22 | 0.81 | 0.27
high |  0.754 (0.744, 0.764) | 0.70 | 0.66 | 0.31
| invasive test | 0.723 (0.711, 0.735) | 0.71 | 0.44 | 0.32

GBDT, gradient boosting decision tree; MLP, multi-layer perceptron; ML, multi-
task learning; AUC, area under the receiver operating characteristic curve;
CI, confidence interval

###  3.3 Feature Importance

Fig. 7 shows the results of the ablation study. It demonstrates that segment
readings such as stenosis and calcification degrees have a stronger impact on
model performance than other feature modalities, such as demographical
characteristics and other tests received by the patient. Multi-tasking
Tabperceiver achieved the optimized performance on the selected features from
different feature modalities. Feature ranking obtained using SHAP turned out
to be the most effective guide for feature selection in both GBDT and deep
learning models for CAD risk and down-streaming test prediction. Fig. 8 shows
the feature importance ranking by their SHAP values in the GBDT model.
Clinical information such as blood pressure and heart rate are revealed to be
important predictors for both tasks, as well as the Agatston score which
relate to the result and the confidence in the interpretation of the CCTA
test. Similar to the previous studies, age and hypertension were found to be
significant risk factors for CAD [4, 35]. CCTA segment readings and pre-test
probability also had an important role in predicting both tasks. This was also
consistent with the results of the ablation study.

##  4 Discussion

Coronary artery disease is a commonly encountered disease associated with
significant morbidity, mortality, and high medical costs. It has been common
in clinical practice to deploy a validated pretest probability model for CAD
to guide the diagnostic test selection. The majority of existing tools
primarily focus on the selection of gatekeeper tests, whereas only a handful
of systems contain information on downstream testing or treatment [8, 9].
Hence, there is a need for models that are based on clinical observations,
which can predict the need for downstream tests or treatments in order to
identify patients who are at high risk and would benefit from invasive
diagnostic tests or revascularization. This study used patient clinical
characteristics and CCTA segment readings to predict the risk of CAD and
selection of downstream tests or treatments. We employed a transformer-based
tabular deep learning model as a novel optimized analytical approach to create
clinical decision support models. Our results show that the developed multi-
task TabPerceiver model is effective in predicting the risk of CAD and the
selection of downstream tests or treatments. Additionally, we found that the
model has appropriate calibration (the predicted probabilities of outcome
reflect true probabilities of the outcome).

Figure 8: Feature importance for predicting risk of CAD (a) and down-streaming
diagnostic test (b). Blood pressure, age, hypertension and segment readings
are ranked as the top important features for predicting patients’ risk of CAD.
Agatston score is the most determinative feature for down-streaming test
selection. Other important features include blood pressure, segment readings,
beta-blocker and chest pain trigger. CT, computed tomography, HR, heart rate,
FamilyHx, family history, P3, calcified level of distal right coronary, S7,
stenosis level of mid left anterior descending artery, P11, calcified level of
proximal left circumflex artery, P2, calcified level of mid right coronary
artery, MA, milliampere-seconds, P6, calcified level of proximal left anterior
descending artery, S6, stenosis level of proximal left anterior desending
artery, CP, chest pain; DLP, dose length product; P2, calcified level of mid
right coronary artery; ProbCAD, pre-test probability of CAD (Diamond &
Forrester); BPDias, diastolic blood pressure; P1, calcified level of proximal
right coronary artery; P10, calcified level of the second diagonal artery;
ACE, angiotensin converting enzyme inhibitors; S8, stenosis level of distal
left anterior descending artery; BPSys, systolic blood pressure

The use of the ML model in a clinical setting could streamline the
identification of patients who may benefit from invasive diagnostic evaluation
and revascularization, reducing the need for time-consuming routine clinical
steps. Meanwhile, the overuse of diagnostic imaging modalities is a major
issue causing significant stress on the health budget [36, 10]. To address
this, there has been an increased focus on the application of risk
stratification and pre-test probability assessment prior to initiation of
downstream testing [11, 5]. Despite this, multiple studies have demonstrated
that these risk assessment models performed sub-optimally in certain cohorts
[37, 38]. In recent years, various models have been validated in multiple
external populations, with a trend towards a decline in discriminative
capacity [39, 4]. Indeed, differences in derivation (utilization of various
imaging modalities as well as different cut-off values for the definition of
CAD risk, adoption of various data processing methodologies), model complexity
and inconsistent external validation limit their usefulness in clinical
practice. In an ever-changing environment where populations are longitudinally
evolving due to changes in dietary habits, environmental exposures, advances
in science and technology, it is essential to have models that adapt over
time. To address this need, machine learning has been increasingly used in the
cardiovascular field. Machine learning involves algorithms that are
specifically designed to identify relationships between data that go beyond
the traditional linear statistical approaches.

Moreover, machine learning leverages the growing accessibility of
computational power and storage space to rapidly produce meaningful results
based on complex input data. Furthermore, machine learning has proven itself
to be a powerful tool for diagnosing coronary artery disease [40]. We further
demonstrate the robustness of TabPerceiver on noisy data, in comparison to the
baseline MLP. We evaluated these two scenarios on categorical and continuous
features to specifically demonstrate the robustness of contextual embeddings
from the Perceiver encoder layers.

In our multitask learning framework, the Perceiver encoder was devised to
represent task-specific features. The model with common-task neurons, which
comprised approximately 20% of the perceiver layer, achieved the best
performance. The introduction of common-task layers into the perceiver layer
can assist in learning the shared complementary information for different
tasks. These findings demonstrate that multitask learning can enhance the
prediction performance of the correlated tasks. Additionally, it has the
advantage of improving data efficiency and reducing over-fitting through
shared representations. This can be attributed to the fact that prediction
with the associated task can reduce model overfitting and the impact of noisy
information from the heterogeneous tumor by learning related and complementary
features.

The deep feature/prediction from multiple tasks in the TabPerceiver was fused
using three information fusion strategies. The results indicate the
effectiveness of the methods compared to the GBDT. The experimental results
show the superior performance of our multitask-learning-based model over
single-task learning.

Feature concatenation may enhancethe combination of complementary features
while also replicating information from various sources of categorical and
continuous features.

The limited sample size and input seem to hinder the predictive performance of
all the models for patients with moderate(medium) risk of CAD. This is
consistent with prior findings that current information remains limited for
clinicians to accurately determine risk for patients in intermediate risk
ranges [41]. In the risk prediction task, we chose the class with the highest
probability. Hence, the sensitivity of predicting low and moderate risk was
low as expected, since the low prevalence of events has affected the
sensitivity and specificity.

It is important to note that validating the proposed model with tuned hyper-
parameters on an additional dataset is of vital importance for the
generalization and clinical applications of the model. However, medical
imaging tabular data from different datasets/cohorts are usually distinct from
each other. This may induce bias and inconsistent results for the tabular
data-based model. It would be valuable to conduct further research to assess
our design strategy when a large dataset becomes available in the future.

In our single task learning experiment, the deep models performed poorly on
small tabular datasets and were no better than GBDT. We proposed the use of
multi-task TabPerceiver using feature embeddings and an attention-based
module. This architecture performed better than the single-task deep learning
model we experimented with. We also examined the trade offs between various
architecture, computational inference cost, and hyper-parameter optimization
time, which are important in real-world applications. Our analysis
demonstrates that the deep learning models are more sensitive to input
features. As showed in Table. 3, the prediction accuracy of GBDT is not
significantly impacted by feature selection, however, removing uninformative
features has improved the performance of deep learning models. This has also
reported in the recent study [42]. Additionally, it is much more challenging
to optimize deep models than GBDT on a new dataset, due to their large number
of hyper-parameters and high computational cost. However, we discovered that
TabPerceiver performed effectively on tabular data while incurring a lower
computational burden.

Table 3: Impact of feature selection on model performance

Models |  Number of input features |  Target |  AUC (95% CI)
---|---|---|---
GBDT |  146 |  low |  0.733 (0.721, 0.747)
medium |  0.602 (0.589, 0.616)
high |  0.719 (0.706, 0.732)
invasive test |  0.730 (0.715, 0.745)
51 |  low |  0.726 (0.712, 0.740)
medium |  0.610 (0.595, 0.626)
high |  0.715 (0.701, 0.729)
invasive test |  0.741 (0.731, 0.752)
MLP |  146 |  low |  0.660 (0.649, 0.672)
medium |  0.580 (0.571, 0.590)
high |  0.672 (0.661, 0.684)
invasive test |  0.669 (0.656, 0.682)
51 |  low |  0.685 (0.665, 0.705)
medium |  0.593 (0.577, 0.609)
high |  0.696 (0.676, 0.716)
invasive test |  0.694 (0.681, 0.706)
TabPerceiver |  146 |  low |  0.689 (0.671, 0.702)
medium |  0.573 (0.556, 0.592)
high |  0.631 (0.605, 0.658)
invasive test |  0.680 (0.669, 0.692)
51 |  low |  0.700 (0.687, 0.712)
medium |  0.593 (0.585, 0.607)
high |  0.673 (0.663, 0.682)
invasive test |  0.685 (0.676, 0.704)
ML-TabPerceiver |  146 |  low |  0.734 (0.724, 0.745)
medium |  0.595 (0.579, 0.610)
high |  0.723 (0.711, 0.735)
invasive test |  0.683 (0.664, 0.702)
51 |  low |  0.752 (0.742, 0.763)
medium |  0.629 (0.616, 0.643)
high |  0.756 (0.746, 0.767)
invasive test |  0.730 (0.715, 0.745)

GBDT, gradient boosting decision tree; MLP, multi-layer perceptron; ML, multi-
task learning; AUC, area under the receiver operating characteristic curve;
CI, confidence interval

Follow-up admission and mortality outcome information for the entire cohort is
not available in our dataset. We have thus used test readings and
interpretation to define the risk of CAD for patients, resulting in a
significant reduction in the sample size of the study cohort. This may
introduce potential bias to our study and limit the performance of our GBDT
and deep learning models, as it has been found to be tailored towards big
data. Future validation might be required using a large cohort. The
transformer-based model has showed its effectiveness in handling images, audio
and text data. The perceiver architecture is also designed to process large
input and output. In future work, we would like to incorporate both tabular
and imaging data into the model, where further performance enhancement may be
expected.

##  5 Conclusion and future work

We propose TabPerceiver, a novel deep learning tabular data modeling
architecture, that is easy to use and computationally efficient. Our deep
learning model outperforms MLP in single task learning, and the performance of
multi-tasking TabPerceiver was comparable to or better than that of the GBDT.
It appears that deep learning tabular architectures benefit from multi-task
learning. We have also demonstrated that feature selection is an essential
step for deep learning tabular data modeling. Together with proper feature
embedding (both categorical and continuous feature embedding), these
strategies address the drawbacks of deep learning on tabular data. In a future
study, we plan to incorporate more data modalities, such as actual CCTA images
and clinical text reports, into the model to improve the prediction of risk of
CAD and support the selection of downstream diagnostic testing and treatments.

##  6 Appendix

[ caption = Candidate and selected features, label=tab:feature_detail, note =
CAD, coronary artery disease; HR, heart rate; CHF, congestive heart failure;
BP, blood pressure; ACE, angiotensin-converting enzyme; ASA, acetylsalicylic
acid; AT2, angiotensin II type 2 receptors; NOACs, novel oral Anticoagulants;
PPI, proton pump inhibitors; CABG, coronary artery bypass graft surgery; Cath,
catheterization; PVD, peripheral vascular disease; RP, renal protection; CD,
conduct disorder; CT, computed tomography; DLP, dose length product; MA,
milliampere-seconds; kV, X-Ray tube voltage, ] colspec=X, width=0.5rowhead =
1, rowsep = 0pt Feature
modality Feature Type Select
Demo-graphics Age (year) cont. yes
Male binary no
Height (cm) cont. no
Weight (kg) cont. yes
Smoking CAT yes
Probability of CAD cont. yes
Vital sign Baseline HR (bpm) cont. yes
Baseline Systolic BP (mmHg) cont. no
Baseline Diastolic BP (mmHg) cont. no
Vital sign
(imaging) Imaging HR (bpm) cont. yes
Imaging Systolic BP (mmHg) cont. yes
Imaging Diastolic BP (mmHg) cont. no
Reason for test Ventricular tachycardia reason binary no
Chest pain reason binary yes
Equivocal reason binary no
Rule out CAD reason binary yes
Dyspnea reason binary no
CHF reason binary no
Other tests Stress test binary no
Stress Echo binary no
RNA binary yes
Myocardial perfusion imaging binary yes
Myocardial viability binary yes
Medications ACE inhibitors binary no
Aspirin binary yes
AT2 binary no
Beta blockers binary yes
Calcium channel blockers binary no
Insulin binary no
Metformin binary no
NOACs binary no
Statins binary no
Diuretics binary no
Ticlopidine binary no
PPI binary no
Nitrates binary no
Other oral hypoglycemics binary no
Vasodilators binary yes
Warfarin binary no
Comorbidity
and other history Valvular heart disease binary no
Valvular repair or replacement binary no
Congenital heart disease binary no
Dyspnea binary no
Hypertension binary yes
Congestive heart failure binary no
Palpitations binary yes
Cardiac implants binary no
Renal insufficiency binary yes
Hyperlipidemia binary no
Prior CABG binary yes
Prior Catheterisation binary yes
Myocardial infarction binary yes
CAD binary no
Diabetes mellitus binary no
Family history binary yes
PVD binary no
Syncope binary no
RP binary yes
CD binary no
Segment
readings Proximal right coronary artery
calcified level (P1) CAT no
stenosis level (S1) CAT yes
Mid right coronary artery
calcified level (P2) CAT yes
stenosis level (S2) CAT no
Distal right coronary artery
calcified level (P3) CAT no
stenosis level (S3) CAT yes
Posterior interventricular artery
calcified level (P4) CAT no
stenosis level (S4) CAT no
Left main
calcified level (P5) CAT yes
stenosis level (S5) CAT no
Proximal left anterior descending
artery
calcified level (P6) CAT yes
stenosis level (S6) CAT yes
Mid left anterior descending
artery
calcified level (P7) CAT yes
stenosis level (S7) CAT yes
Distal left anterior descending
artery
calcified level (P8) CAT yes
stenosis level (S8) CAT yes
The first diagonal artery (D1)
calcified level (P9) CAT yes
stenosis level (S9) CAT yes
The second diagonal artery (D2)
calcified level (P10) CAT no
stenosis level (S10) CAT yes
Proximal left circumflex artery
calcified level (P11) CAT yes
stenosis level (S11) CAT yes
The first marginal artery (M1)
calcified level (P12) CAT no
stenosis level (S12) CAT yes
Mid left circumflex artery
calcified level (P13) CAT no
stenosis level (S13) CAT no
The second marginal artery (M2)
calcified level (P14) CAT yes
stenosis level (S14) CAT no
Distal left circumflex artery
calcified level (P15) CAT no
stenosis level (S15) CAT no
Left ventricle
calcified level (P16) CAT no
stenosis level (S16) CAT no
Ramus intermedius
calcified level (P17) CAT no
stenosis level (S17) CAT yes
Other segments
calcified level (P18-22) CAT no
stenosis level (S18-22) CAT no
unevaluable (Uneval1-22) binary no
Chest pain symptoms Chest pain trigger binary yes
Chest pain relieved binary no
Chest pain binary yes
Other imaging
information Dominance CAT no
Agatston cont. yes
Contrast Bolus cont. no
Contrast CT cont. yes
Contrast Mix cont. no
Contrast Mix Percent cont. no
Contrast Mix Rate cont. no
Contrast Type CAT no
DLP Bolus cont. yes
DLP Cardiac cont. yes
DLP non contrast cont. no
Left ventricular
end-diastolic volume cont. yes
Left ventricular ejection
fraction cont. no
Left ventricular
end-systolic volume cont. no
MA cont. yes
kV cont. yes
Primary First binary yes

[ caption = Model hyper-parameter, label=tab:hyperparam, ] colspec=X, rowhead
= 1, rowsep = 0pt Model Hyper-parameters
ML-TabPerceiver
(selected 51 features) batch_size=16
num_layers=2
input_embed_dim=128
num_cross_attention_heads=4
num_self_attention_layers_per_block= 4
num_latents=8
num_latent_channels=32
bins_count=150
weight_decay=0.01
dropout=0
label_smoothing=0.3
ML-TabPerceiver
(all features) batch_size=32
num_layers=2
input_embed_dim=128
num_cross_attention_heads=8
num_self_attention_layers_per_block= 2
num_latents=16
num_latent_channels=64
bins_count=50
weight_decay=0.01
dropout=0
label_smoothing=0.3

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