Introduction
death
DISEASE PROGRESSION, EVENT, SDH, REGRESSION, EVENTS
Randomized controlled trials (RCTs) are used to evaluate the effect of a new therapy and the efficacy and safety of experimental treatment versus control treatment. In survival analysis, there are three approaches, namely parametric, semi-parametric and nonparametric to analyze time-to-event outcomes. A semi-parametric model is a statistical model that contains both parametric and nonparametric components. A well-known example of a semi-parametric model is the Cox proportional hazards modelIn RCTs, if all patients remain in their randomized allocated group until the end of the follow-up period and fully adhere to their assigned treatment, naive methods for estimating treatment effect, such as the log-rank test, may not be subject to bias. In reality, however, some patients may switch from their assigned treatment to the other treatment and/or discontinue treatment due to disease progression or other reasons. In most cases, switching from the standard treatment to the experimental treatment is decided by the investigator or the Ethics CommitteeThe main advantage of this method is that the randomization is preserved, but it does not directly address the impact of switchers on the estimate of efficacy when comparing the experimental treatment and the standard treatment. This may lead to underestimate the appropriate efficacy of a new treatmentThe first approach of PP analysis includes those patients who follow their assigned treatment and excludes completely patients who do not follow the treatment from the analysis (PP-ex approach). This approach may induce selection bias if switching is concerned with prognostic factors. In the second of approach of PP, patients who switched treatment groups are censored (PP-cen approach). Therefore, prognosis is likely different for patients who switch treatment, which is prone to biasIn classical time-to-event or survival analyses, subjects are at risk of a terminal event. In this case, the usual classical techniques such as Kaplan–Meier, log-rank test, and Cox proportional hazards model are used to analyze survival data. However, in many oncology trials some patients are at risk for more than one mutually exclusive event or endpoint. For example, time to a cancer-specific death is considered as primary endpoint. A competing event is an event whose occurrence either precludes the occurrence of another event under examination or fundamentally alters the probability of this other event. However, other events—so-called competing risks (CR)—may preclude the occurrence of the event of interestCurrent techniques ignore the event type, and combine multiple primary endpoints into a single composite endpoint. Composite endpoints are defined as experiencing any events among a given set of competing events in a follow-up period. In the presence of CR, the use of classical analysis based on composite endpoints leads to bias. If the competing events are heterogeneous, that means, endpoints have different importance for patients or they show different treatment effects, there will be a risk of misinterpretation of resultsCR analyses allow extracting the contribution of a treatment on each competing event type separately. In the context of CR, the two common methods of the cause-specific hazard (CSH) regression model and the sub-distribution hazard (SDH) regression model are often usedAmong the various proposed methods in noncompliance simulation studies, the RPSFT method and the GE algorithm appear to have gained popularity and produced the best results in situations where the treatment effect was time-independentThe standard approach to assess the impact of prognostic variables on CR is to assume that each CSH follows a proportional hazards model. Assuming proportional CSH models, the proportional SDH models are misspecified. In this article, to study competing risks, data were generated based on CSH with the noncompliance assumption and with respect to disease progression in RCTsThis article is organized as follows: in 