Semiparametric Regression Analysis of Multiple Right- and Interval-Censored Events

Performance of Cox regression models for composite time-to-event endpoints with component-wise censoring in randomized trials

BACKGROUND

Composite time-to-event endpoints are beneficial for assessing related outcomes jointly in clinical trials, but components of the endpoint may have different censoring mechanisms. For example, in the PRagmatic EValuation of evENTs And Benefits of Lipid-lowering in oldEr adults (PREVENTABLE) trial, the composite outcome contains one endpoint that is right censored (all-cause mortality) and two endpoints that are interval censored (dementia and persistent disability). Although Cox regression is an established method for time-to-event outcomes, it is unclear how models perform under differing component-wise censoring schemes for large clinical trial data. The goal of this article is to conduct a simulation study to investigate the performance of Cox models under different scenarios for composite endpoints with component-wise censoring.

METHODS

We simulated data by varying the strength and direction of the association between treatment and outcome for the two component types, the proportion of events arising from the components of the outcome (right censored and interval censored), and the method for including the interval-censored component in the Cox model (upper value and midpoint of the interval). Under these scenarios, we compared the treatment effect estimate bias, confidence interval coverage, and power.

RESULTS

Based on the simulation study, Cox models generally have adequate power to achieve statistical significance for comparing treatments for composite outcomes with component-wise censoring. In our simulation study, we did not observe substantive bias for scenarios under the null hypothesis or when the treatment has a similar relative effect on each component outcome. Performance was similar regardless of if the upper value or midpoint of the interval-censored part of the composite outcome was used.

CONCLUSION

Cox regression is a suitable method for analysis of clinical trial data with composite time-to-event endpoints subject to different component-wise censoring mechanisms.

Marginal proportional hazards models for clustered interval-censored data with time-dependent covariates

The Botswana Combination Prevention Project was a cluster-randomized HIV prevention trial whose follow-up period coincided with Botswana's national adoption of a universal test and treat strategy for HIV management. Of interest is whether, and to what extent, this change in policy modified the preventative effects of the study intervention. To address such questions, we adopt a stratified proportional hazards model for clustered interval-censored data with time-dependent covariates and develop a composite expectation maximization algorithm that facilitates estimation of model parameters without placing parametric assumptions on either the baseline hazard functions or the within-cluster dependence structure. We show that the resulting estimators for the regression parameters are consistent and asymptotically normal. We also propose and provide theoretical justification for the use of the profile composite likelihood function to construct a robust sandwich estimator for the variance. We characterize the finite-sample performance and robustness of these estimators through extensive simulation studies. Finally, we conclude by applying this stratified proportional hazards model to a re-analysis of the Botswana Combination Prevention Project, with the national adoption of a universal test and treat strategy now modeled as a time-dependent covariate.

Instrumental variable estimation of complier causal treatment effect with interval-censored data

Assessing causal treatment effect on a time-to-event outcome is of key interest in many scientific investigations. Instrumental variable (IV) is a useful tool to mitigate the impact of endogenous treatment selection to attain unbiased estimation of causal treatment effect. Existing development of IV methodology, however, has not attended to outcomes subject to interval censoring, which are ubiquitously present in studies with intermittent follow-up but are challenging to handle in terms of both theory and computation. In this work, we fill in this important gap by studying a general class of causal semiparametric transformation models with interval-censored data. We propose a nonparametric maximum likelihood estimator of the complier causal treatment effect. Moreover, we design a reliable and computationally stable expectation-maximization (EM) algorithm, which has a tractable objective function in the maximization step via the use of Poisson latent variables. The asymptotic properties of the proposed estimators, including the consistency, asymptotic normality, and semiparametric efficiency, are established with empirical process techniques. We conduct extensive simulation studies and an application to a colorectal cancer screening data set, showing satisfactory finite-sample performance of the proposed method as well as its prominent advantages over naive methods.

Semiparametric regression analysis of bivariate censored events in a family study of Alzheimer's disease

Assessing disease comorbidity patterns in families represents the first step in gene mapping for diseases and is central to the practice of precision medicine. One way to evaluate the relative contributions of genetic risk factor and environmental determinants of a complex trait (e.g., Alzheimer's disease [AD]) and its comorbidities (e.g., cardiovascular diseases [CVD]) is through familial studies, where an initial cohort of subjects are recruited, genotyped for specific loci, and interviewed to provide extensive disease history in family members. Because of the retrospective nature of obtaining disease phenotypes in family members, the exact time of disease onset may not be available such that current status data or interval-censored data are observed. All existing methods for analyzing these family study data assume single event subject to right-censoring so are not applicable. In this article, we propose a semiparametric regression model for the family history data that assumes a family-specific random effect and individual random effects to account for the dependence due to shared environmental exposures and unobserved genetic relatedness, respectively. To incorporate multiple events, we jointly model the onset of the primary disease of interest and a secondary disease outcome that is subject to interval-censoring. We propose nonparametric maximum likelihood estimation and develop a stable Expectation-Maximization (EM) algorithm for computation. We establish the asymptotic properties of the resulting estimators and examine the performance of the proposed methods through simulation studies. Our application to a real world study reveals that the main contribution of comorbidity between AD and CVD is due to genetic factors instead of environmental factors.

Randomization-based confidence intervals for cluster randomized trials

In a cluster randomized trial (CRT), groups of people are randomly assigned to different interventions. Existing parametric and semiparametric methods for CRTs rely on distributional assumptions or a large number of clusters to maintain nominal confidence interval (CI) coverage. Randomization-based inference is an alternative approach that is distribution-free and does not require a large number of clusters to be valid. Although it is well-known that a CI can be obtained by inverting a randomization test, this requires testing a non-zero null hypothesis, which is challenging with non-continuous and survival outcomes. In this article, we propose a general method for randomization-based CIs using individual-level data from a CRT. This approach accommodates various outcome types, can account for design features such as matching or stratification, and employs a computationally efficient algorithm. We evaluate this method's performance through simulations and apply it to the Botswana Combination Prevention Project, a large HIV prevention trial with an interval-censored time-to-event outcome.

Semiparametric regression analysis of partly interval-censored failure time data with application to an AIDS clinical trial

Failure time data subject to various types of censoring commonly arise in epidemiological and biomedical studies. Motivated by an AIDS clinical trial, we consider regression analysis of failure time data that include exact and left-, interval-, and/or right-censored observations, which are often referred to as partly interval-censored failure time data. We study the effects of potentially time-dependent covariates on partly interval-censored failure time via a class of semiparametric transformation models that includes the widely used proportional hazards model and the proportional odds model as special cases. We propose an EM algorithm for the nonparametric maximum likelihood estimation and show that it unifies some existing approaches developed for traditional right-censored data or purely interval-censored data. In particular, the proposed method reduces to the partial likelihood approach in the case of right-censored data under the proportional hazards model. We establish that the resulting estimator is consistent and asymptotically normal. In addition, we investigate the proposed method via simulation studies and apply it to the motivating AIDS clinical trial.