Censoring-robust treatment effect estimation in clinical trials with time-to-event outcomes

A common goal in many clinical studies is to test a well-defined hypothesis regarding the association between a predictor of interest Z and the time to some specified event T. When hypothesis testing is the scientific goal it is important to maintain certain operating characteristics (e.g. Frequentist type I and II errors or Bayesian posterior probabilities). As such, a priori definition of the statistical model that will be used to estimate the association between Z and T is critical. In the absence of model checking it is desirable to choose a statistical model that is robust to model misspecification. The most commonly employed regression models for time-to-event outcomes are the Cox model, which postulates that the predictors are multiplicative on the hazard scale, and the accelerated failure time model, which postulates that the predictors are multiplicative on the survival time scale. Semi-parametric estimation of the predictor effects are available for both models and are usually considered to be robust owing to their freedom from requiring specification of the error density function. However when the population regression function is misspecified, which will nearly always be true, the commonly used estimators are consistent for a parameter that depends on the censoring distribution. The impact of censoring on parameter estimates is of great scientific relevance as the interpretation given to association parameters is typically not made with respect to the observed censoring distribution. In this dissertation we present a series of papers that investigate this issue further and we propose estimators for both the multiplicative hazards model and the accelerated failure time model that remove this dependence. Design and implementation of group sequential clinical trials using the proposed censoring robust multiplicative hazards model estimator are considered. In addition, a method based on multiple imputation is proposed as an alternative tool for removing the censoring explicitly at the observation level. Future directions for applications of the multiple imputation procedure are discussed. It is suggested that the proposed censoring- robust estimators become the preferred approach for estimating treatment effects in prospectively designed clinical trials.