Study Design and Analysis of Censored Longitudinal Time-to-Event and Recurrent Event Data

Abstract

This dissertation pursues a paradigm shift from traditionally recorded censored time-to-event and time-to-recurrent event data and corresponding analyses. Instead these data are repurposed into censored short-term outcomes measured longitudinally over potentially overlapping follow-up periods with prespecified length. Previous work by Tayob and Murray (2014, 2016, 2017) exploited this framework, with univariable and multivariable methods for estimating behavior of restricted outcomes drawn from a single time-to-event and with a two-sample test developed for comparing censored longitudinal outcomes drawn from the recurrent events setting. This thesis considers three practical settings that can benefit statistically from repurposing traditional data into this censored longitudinal data structure.

Chapter II addresses the first research setting. This chapter develops a two-sample test and corresponding group sequential methodology for comparing overall restricted means between treatment groups, where each patient contributes many overlapping follow-up windows of information during the course of the clinical trial. Operating characteristics explored through simulation compare favorably with existing nonparametric methods for group sequentially monitored test statistics in this setting, including the traditional restricted mean test and the logrank test. The proposed method performs especially well in cases where there is a delayed treatment effect and/or a subset of cured patients. This chapter considers symmetric and asymmetric error spending approaches and makes recommendations for how to choose appropriate group sequential stopping boundaries in a variety of settings.

Chapter III addresses the second research setting. Very few methods are currently available for group sequential analysis of recurrent events data subject to a terminal event in the clinical trial setting. Chapter 3 helps fill this gap by developing methods for sequentially monitoring the nonparametric, two-sample Tayob and Murray (2014) statistic. This chapter briefly reviews the TM statistic, develops and describes how to use the proposed group sequential analysis methods, and through simulation compares its operating characteristics with those of Cook and Lawless (1996) as well as a time-to-first-event analysis based on the logrank test. Our advantages include high power to detect treatment differences when there is correlation between event times in an individual and elegantly avoiding dependent censoring bias.

One important component of using the TM statistic, as well as Chapter III methodology for group sequential monitoring, is to wisely construct the censored longitudinal data framework for the recurrent events. Chapter IV formalizes the corresponding guidance. A useful metric, the expected proportion of recurrent events captured as the first event in at least one follow-up window, is derived, and operating characteristics of the TM statistic are summarized. For design and analysis purposes, we formulate recommendations based on the special case with independent exponentially distributed gap times.

Chapter V develops multivariable restricted time models appropriate for analysis of recurrent events data, where data is repurposed into censored longitudinal outcomes in follow-up windows. This chapter develops two approaches for addressing the censored nature of the outcomes: a pseudo-observations (PO) approach and a multiple imputations (MI) approach. Each of these approaches allows for complete data methods, such as generalized estimating equations, to be used for the analysis of the newly constructed correlated outcomes. Through simulation, this chapter assesses the performance of the proposed PO and MI methods. Both PO and MI approaches show attractive results with either correlated or independent gap times.