Composite endpoints defined as the time to the earliest of two or more events are often used as primary endpoints in clinical trials. Component-wise censoring arises when different components of the composite endpoint are censored differently. We focus on a composite of death and a non-fatal event where death time is right censored and the non-fatal event time is interval censored because the event can only be detected during study visits. Such data are most often analysed using methods for right censored data, treating the time the non-fatal event was first detected as the time it occurred. This can lead to bias, particularly when the time between assessments is long. We describe several approaches for estimating the event-free survival curve and the effect of treatment on event-free survival via the hazard ratio that are specifically designed to handle component-wise censoring. We apply the methods to a randomized study of breastfeeding versus formula feeding for infants of mothers infected with human immunodeficiency virus.

UNASSIGNED: Previous investigations into multiple sclerosis (MS) risk factors predominantly relied on retrospective studies, which do not consider different follow-up times and assume a constant risk effect throughout lifetime.
UNASSIGNED: We aimed to evaluate the impact of genetic and early life factors on MS diagnosis by employing a time-to-event analysis in a prospective cohort.
UNASSIGNED: We used the UK Biobank data, considering the observation period from birth up to 31 December 2022. We considered genetic risk, using a multiple sclerosis polygenic risk score (MS-PRS), and various early life factors. Tobacco smoking and infectious mononucleosis diagnosis were also considered as time-varying variables along the follow-up. Using a Cox proportional hazards model, we examined the associations between these factors and MS diagnosis instantaneous risk.
UNASSIGNED: We analyzed 345,027 participants, of which 1669 had an MS diagnosis. Our analysis revealed age-dependent effects for sex (females vs males) and higher MS-PRS, with greater hazard ratios observed in young adults.
UNASSIGNED: The age-dependent effects suggest that retrospective studies could have underestimated sex and genetic variants\' risk roles during younger ages. Therefore, we emphasize the importance of a time-to-event approach using longitudinal data to better characterize age-dependent risk effects.

In oncology trials, health-related quality of life (HRQoL), specifically patient-reported symptom burden and functional status, can support the interpretation of survival endpoints, such as progression-free survival. However, applying time-to-event endpoints to patient-reported outcomes (PRO) data is challenging. For example, in time-to-deterioration analyses clinical events such as disease progression are common in many settings and are often handled through censoring the patient at the time of occurrence; however, disease progression and HRQoL are often related leading to informative censoring. Special consideration to the definition of events and intercurrent events (ICEs) is necessary. In this work, we demonstrate time-to-deterioration of PRO estimands and sensitivity analyses to answer research questions using composite, hypothetical, and treatment policy strategies applied to a single endpoint of disease-related symptoms. Multiple imputation methods under both the missing-at-random and missing-not-at-random assumptions are used as sensitivity analyses of primary estimands. Hazard ratios ranged from 0.52 to 0.66 over all the estimands and sensitivity analyses modeling a robust treatment effect favoring the treatment in time to disease symptom deterioration or death. Differences in the estimands include how people who experience disease progression or discontinue the randomized treatment due to AEs are accounted for in the analysis. We use the estimand framework to define interpretable and principled approaches for different time-to-deterioration research questions and provide practical recommendations. Reporting the proportions of patient events and patient censoring by reason helps understand the mechanisms that drive the results, allowing for optimal interpretation.

In a randomized controlled trial with time-to-event endpoint, some commonly used statistical tests to test for various aspects of survival differences, such as survival probability at a fixed time point, survival function up to a specific time point, and restricted mean survival time, may not be directly applicable when external data are leveraged to augment an arm (or both arms) of an RCT. In this paper, we propose a propensity score-integrated approach to extend such tests when external data are leveraged. Simulation studies are conducted to evaluate the operating characteristics of three propensity score-integrated statistical tests, and an illustrative example is given to demonstrate how these proposed procedures can be implemented.

OBJECTIVE: Joint modeling of longitudinal and time-to-event data has gained attention over recent years with extensive developments including nonlinear models for longitudinal outcomes and flexible time-to-event models for survival outcomes, possibly involving competing risks. However, in popular software such as R, the function used to describe the biomarker dynamic is mainly linear in the parameters, and the survival submodel relies on pre-implemented functions (exponential, Weibull, ...). The objective of this work is to extend the code from the saemix package (version 3.1 on CRAN) to fit parametric joint models where longitudinal submodels are not necessary linear in their parameters, with full user control over the model function.
METHODS: We used the saemix package, designed to fit nonlinear mixed-effects models (NLMEM) through the Stochastic Approximation Expectation Maximization (SAEM) algorithm, and extended the main functions to joint model estimation. To compute standard errors (SE) of parameter estimates, we implemented a recently developed stochastic algorithm. A simulation study was proposed to assess (i) the performances of parameter estimation, (ii) the SE computation and (iii) the type I error when testing independence between the two submodels. Four joint models were considered in the simulation study, combining a linear or nonlinear mixed-effects model for the longitudinal submodel, with a single terminal event or a competing risk model.
RESULTS: For all simulation scenarios, parameters were precisely and accurately estimated with low bias and uncertainty. For complex joint models (with NLMEM), increasing the number of chains of the algorithm was necessary to reduce bias, but earlier censoring in the competing risk scenario still challenged the estimation. The empirical SE of parameters obtained over all simulations were very close to those computed with the stochastic algorithm. For more complex joint models (involving NLMEM), some estimates of random effects variances had higher uncertainty and their SE were moderately under-estimated. Finally, type I error was controlled for each joint model.
CONCLUSIONS: saemix is a flexible open-source package and we adapted it to fit complex parametric joint models that may not be estimated using standard tools. Code and examples to help users get started are freely available on Github.

In this note, we express our viewpoint regarding power considerations, via simulation studies, in clinical study design using hierarchical composite endpoint and Finkelstein-Schoenfeld test.

Stratification in randomization and analysis are widely employed to balance treatment groups in clinical trials. However, the potential power loss due to under-stratification or over-stratification has not been thoroughly evaluated in the typical setting of confirmatory clinical trials. In cases where there are too many strata and some have small sample sizes or a small number of events, it is common practice to combine these small strata during analysis. However, there is a lack of guidance on how those small strata should be combined. This paper presents extensive simulation studies to evaluate the impact of under-stratification or over-stratification on the power of survival analysis and the estimate of hazard ratio using stratified log-rank test and Cox PH model, respectively. The difference in power between stratified and unstratified log-rank tests is also investigated under different scenarios. Our results suggest that failing to consider prognostic stratification factors with strong effects, and/or accounting for non-prognostic factors such as noise and predictive factors, may reduce the power of the stratified log-rank test. Additionally, methods of combining small strata are explored and compared.

In clinical trials, evaluating the accuracy of risk scores (markers) derived from prognostic models for prediction of survival outcomes is of major concern. The time-dependent receiver operating characteristic curve and the corresponding area under the receiver operating characteristic curve are appealing measures to evaluate the predictive accuracy. Several estimation methods have been proposed in the context of classical right-censored data which assumes the event time of individuals are independent. In many applications, however, this may not hold true if, for example, individuals belong to clusters or experience recurrent events. Estimates may be biased if this correlated nature is not taken into account. This paper is then aimed to fill this knowledge gap to introduce a time-dependent receiver operating characteristic curve and the corresponding area under the receiver operating characteristic curve estimation method for right-censored data that take the correlated nature into account. In the proposed method, the unknown status of censored subjects is imputed using conditional survival functions given the marker and frailty of the subjects. An extensive simulation study is conducted to evaluate and demonstrate the finite sample performance of the proposed method. Finally, the proposed method is illustrated using two real-world examples of lung cancer and kidney disease.

Prediction models are increasingly developed and used in diagnostic and prognostic studies, where the use of machine learning (ML) methods is becoming more and more popular over traditional regression techniques. For survival outcomes the Cox proportional hazards model is generally used and it has been proven to achieve good prediction performances with few strong covariates. The possibility to improve the model performance by including nonlinearities, covariate interactions and time-varying effects while controlling for overfitting must be carefully considered during the model building phase. On the other hand, ML techniques are able to learn complexities from data at the cost of hyper-parameter tuning and interpretability. One aspect of special interest is the sample size needed for developing a survival prediction model. While there is guidance when using traditional statistical models, the same does not apply when using ML techniques. This work develops a time-to-event simulation framework to evaluate performances of Cox regression compared, among others, to tuned random survival forest, gradient boosting, and neural networks at varying sample sizes. Simulations were based on replications of subjects from publicly available databases, where event times were simulated according to a Cox model with nonlinearities on continuous variables and time-varying effects and on the SEER registry data.

A priori estimation of sample size and subject accrual in multi-site, time-to-event clinical trials is often challenging. Such trials are powered based on the number of events needed to detect a clinically significant difference. Sample size based on number of events relates to the expected duration of observation time for each subject. Temporal patterns in site initiation and subject enrollment ultimately affect when subjects can be accrued into the study. Lag times are common as the site start-up process optimizes, resulting in delays that may curtail observational follow-up and therefore undermine power. The proposed method introduces a Program Evaluation and Review Technique (PERT) model into the sample size estimation which accounts for the lag in site start-up. Additionally, a PERT model is introduced into a Poisson-Gamma subject accrual model to predict the quantity of study sites needed. The introduction of the PERT model provides greater flexibility in both a priori power assessment and planning the number of sites, as it specifically allows for the inclusion of anticipated delays in site start-up time. This model results in minimal power loss even when PERT distribution inputs are misspecified compared to the traditional assumption of simultaneous start-up for all sites. Together these updated formulations for sample size and subject accrual models offer an improved method for designing a multi-site time-to-event clinical trial that accounts for a flexible site start-up process.