Statistical models to capture the association between progression-free and overall survival in oncology trials

Weber, Enya and Titman, Andrew (2020) Statistical models to capture the association between progression-free and overall survival in oncology trials. PhD thesis, Lancaster University.

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Abstract

In oncology trials, different clinical endpoints can be measured. For the survival analysis of patients, the most traditional primary endpoint is overall survival (OS), which is defined as the time from study entry to death from any cause. Besides, progression-free related measurements such as progression-free survival (PFS) might be also considered. For assessing the performance of therapies, OS is the most reliable endpoint. However, utilizing earlier endpoints such as information from disease progression might lead to a gain in efficiency. However, the gain in efficiency might depend on the relationship between those two endpoints. This thesis explores various statistical models for capturing the association between PFS and OS. The research is partitioned into three topics. At first, it considers methods for quantifying the association between PFS and OS in oncology trials, in terms of Kendall’s τ rank correlation rather than Pearson correlation. Copula-based, non-parametric, and illness-death model–based methods are reviewed. In addition, the approach based on an underlying illness-death model is generalized to allow general parametric models. The simulations suggest that the illness-death model–based method provides good estimates of Kendall’s τ across several scenarios. In some situations, copula-based methods Perform well but their performance is sensitive to the choice of copula. The Clayton copula is most appropriate in scenarios which might realistically reflect an oncology trial, but the use of copula models in practice is questionable. In the second and third topic, the estimation of the group difference faces the issue of non-proportionality for treatments effects. Instead of the standard hazard ratio we use the average hazard ratio for estimating the group difference as it is able to cope with non-proportional hazards well as it considers group difference depending on time. Subsequently, it compares methods for jointly modelling time-to-progression and time-to-death within a Bayesian framework. By incorporating treatment effects, we investigate an illness-death model-based approach and also copula-based approaches. According to the simulations results the Gaussian copula-based model performed the best overall, but the illness-death model-based approach showed a good performance as well. However, in contrast to the good performance of the Clayton copula-based approach in the first topic, the Clayton copula model did not perform well regarding the estimation of AHR. The third topic explores various semi-parametric multi-state model-based methods for gaining efficiency in testing for, and estimating the treatment effects in terms on, overall survival in oncology trials compared to standard methods based on directly applying Cox regression or the log-rank test. The semi-parametric multi-state model-based method fits a Cox model to (a subset of) transition intensities in an illness-death model assuming either a Markov or semi-Markov model and uses AHR to measure treatment effect. In most of the situations, the semi-parametric multi-state model-based methods perform better than the Cox-based approach. The performance of the methods in each topic is investigated by simulations and also illustrated using data from a clinical trial of treatments for advanced ovarian cancer in topic 2 and for colon cancer in topics 1 and 3.