Rank-Based Methods for Survival Data With Multiple Outcomes

Abstract

In clinical studies of survival, additional endpoints on patients may be collected over the course of the study that give additional insight into a treatment's effect. We propose three methods to analyze right censored survival data in the presence of multiple outcomes. In order to make limited parametric assumptions on the data-generating mechanisms, the methods are based on Wilcoxon-type rank statistics. Each method is applied to a recent clinical trial of Ceftriaxone in patients with amyotrophic lateral sclerosis.

In chapter 1, we modify the Gehan-Wilcoxon test for survival to account for auxiliary information on intermediate disease states (e.g. progression) that subjects may pass through before failure. We use multi-state modeling to compute expected ranks for each subject conditional on their last observed disease states and censoring time, and these ranks form the basis of our test statistic. Simulations demonstrate that the proposed test can improve power over the log-rank and generalized Wilcoxon tests in some settings while maintaining the nominal type 1 error rate.

In chapter 2, we propose an estimator for an accelerated failure time model based on the test statistic proposed in chapter 1. We use the statistic as an estimating equation for a parameter that accelerates the time to each subsequent disease state. The estimator incorporates the intermediate states in a manner relevant to the survival outcome, yielding interpretable treatment and covariate effects that consider the entire trajectory of the patient. Simulations demonstrate that the estimator is unbiased, and that the proposed standard error estimator is near the empirical value.

In chapter 3, we aim to assess the treatment effect globally across any types of multiple endpoints. The test we propose is based on a simple scoring mechanism applied to each pair of subjects for each endpoint. The scores for each pair of subjects are then reduced to a summary score, and a rank-sum test is applied to the summary scores. This can be seen as a generalization of several other global rank tests in the literature. Additionally, for certain statistics we describe optimal weighting schemes with respect to statistical power, and provide a method of selecting outcome weights adaptively.