Statistical methods for handling non-proportional hazards in clinical trials

Abstract

In this thesis, we will investigate the issue of non-proportional hazards in the analysis of time to event outcomes in randomised controlled trials (RCT’s). Our primary focus is on Phase III RCT’s with time to event data. Various methods have been proposed in the literature to restore the efficiency of statistical testing and provide an interpretable effect measure to summarize treatment effectiveness under non PH. Understandably, each method comes with its own limitations and strengths. Thus, this work explores the statistical methods available to handle non proportional hazards in terms of its statistical performance, interpretability of its effect measure, and its limitations. In addition, having an alternative effect measure similar to the hazard ratio, which allows for a causal interpretation, is highly desirable. We contribute to the sensitivity analysis framework, which identifies and estimates the causal hazard ratio, by proposing a more flexible approach for estimation.

This thesis focused on three main components. First, we investigated the weighted hazard ratio method under two different scenarios of non-proportional hazards. We investigated its performance when the weighted long-rank test statistic was the most optimal and provided the most powerful test under a specific scenario of non proportional hazard patterns. Additionally, we investigated its robustness under a misspecification. Second, we applied the methodology proposed in the literature to two real clinical trial datasets and evaluated its performance and operating characteristics under two different non-proportional hazard patterns. Through this, we learn about the interpretability of treatment effect estimation. Third, we examine the sensitivity analysis identification approach in randomized controlled trials that utilize a working frailty model to estimate causal hazard ratios. We propose a flexible parametric approach and estimate the causal hazard ratio based on these models. We present our proposed flexible parametric approach and study its properties using simulations. We also learned about this approach using a real data example.

The problems with the statistical methodology discussed in this thesis are relevant when it comes to demonstrating the success of phase-III RCT trials with time-to event outcomes in the industry. The results of this thesis will provide support to those who are interested in applying alternative methodology to the Cox model when non-PH are anticipated, in understanding the issues with the interpretation of hazard ratios, and lastly those who may be interested in using the flexible parametric approach to estimate the causal hazard ratios.

Date of Award	22 Jan 2025
Original language	English
Awarding Institution	University of Bath
Supervisor	Jonathan Bartlett (Supervisor) & Christopher Jennison (Supervisor)