Optimal Designs for Discrete-time Survival Analysis with Heterogeneity

Abstract

An event history is a longitudinal record of timing of the occurrence of an event. The underlying event process usually operates in continuous time. In practice, event times are most often measured in time intervals leading to discrete-time or interval-censored event history data. Since only the time interval in which an event occurred is known, it is more natural to use a model for discrete event times. Randomized controlled trials (RCTs) are considered the most rigorous method to compare the effectiveness of different treatments. A design for a RCT with discrete-time survival data may vary on many characteristics like the number of subjects, the group sizes, and the number of time intervals, among others. An important design issue is to compute the best combination of these characteristics that maximizes the efficiency of the treatment effect estimator given a maximal budget. A design with the maximal efficient treatment effect estimators is a so-called optimal design. For discrete-time survival models, it is yet unclear whether and how other relevant information influences optimal designs. Examples are types of a design, the anticipated treatment effect pattern and the adjustment of baseline covariates. This thesis extends previous research on optimal designs to provide insight in evaluating optimal designs given heterogeneity and shows how the selection of an optimal design depends on design settings at the planning stage of a study.