T-Inflated Beta Regression Model for Censored Time-to-Event and Recurrent Event Data

Abstract

τ-Restricted Mean Survival Time (τ-RMST) models are popular for modeling censored time-to-event data. One data feature that has not received adequate attention in τ-RMST literature is the point mass of events at τ for the τ-restricted event time, min(τ,T). Individuals who remain event-free during the restricted follow-up time are certainly of interest when evaluating impacts of factors. This dissertation introduces a novel model framework that takes advantage of the point mass to improve the precision of the estimation of RMST and understanding of the association of the predictors and τ-restricted times-to-event. We explore three different settings within this dissertation and demonstrate that our proposed model provides statistical advantages in each of these settings after effectively handling censoring as part of model fitting process. In Chapter 2, we leverage mixture distribution ideas from cure rate model literature, viewing the study cohort as a mixture of patients who experience the event versus do not experience the event during the restricted follow-up time. We propose a τ-inflated beta regression (τ-IBR) model using joint logistic and beta regression to explore associations between predictors and a potentially censored time-to-event in these two sub-populations and improve the precision of RMST estimation. To deal with censored nature of the data and fit our proposed models we develop both expectation-maximization (EM) and multiple imputation (MI) approaches. Simulations indicate excellent performance of the τ-IBR model(s), and higher precision of corresponding τ-RMST estimates compared to the traditional τ-RMST model, in independent and dependent censoring setting. In Chapter 3, we generalize the τ-IBR model framework proposed in Chapter 2 to the set- ting with potentially censored recurrent event times. We first restructure recurrent-event data into a censored longitudinal data structure of τ-restricted-times-to-first-event observed in τ-duration follow-up windows initiated at regularly-spaced intervals. Models used to analyze single restricted event times in Chapter 2 are then applied to the censored longitudinal dataset of times-to-first- event; a generalized estimating equation (GEE) approach is used to address the correlated nature of the τ-restricted times-to-first-event across the follow-up windows. Multiple imputation (MI) and expectation-solution (ES) approaches appropriate for censored data are developed as part of the model fitting process. Simulations indicate good statistical performance of the proposed τ-IBR approach to modeling censored recurrent event data. In Chapter 4 we extend the τ-inflated beta model to the setting with dependently censored data. This chapter is motivated by lung allocation waitlist survival data, where waitlist deaths are dependently censored as more urgent patients are selected for transplantation. An inverse probability of censoring algorithm is incorporated into the multiple imputation of the censored waitlist death times. Ideas from Chapters 2 and 3 are used to develop an appropriate τ-restricted inflated beta regression model that allow for improved 1-year RMST estimation, which is an essential component of the current lung allocation score that measures waitlist urgency.