-Inflated Beta Regression Model for Estimating -Restricted Means and Event-Free Probabilities for Censored Time-to-Event Data.

Abstract

In this research, we propose analysis of -restricted censored time-to-event data via a -inflated beta regression ( -IBR) model. The outcome of interest is , where and are the time-to-event and follow-up duration, respectively. Our analysis goals include estimation and inference related to -restricted mean survival time ( -RMST) values and event-free probabilities at that address the censored nature of the data. In this setting, it is common to observe many individuals with , a point mass that is typically overlooked in -restricted event-time analyses. Our proposed -IBR model is based on a decomposition of into . We model the mean of this latter expression using joint logistic and beta regression models that are fit using an expectation-maximization algorithm. An alternative multiple imputation (MI) algorithm for fitting the -IBR model has the additional advantage of producing uncensored datasets for analysis. Simulations indicate excellent performance of the -IBR model(s), and corresponding -RMST estimates, in independent and dependent censoring settings. We apply our method to the Azithromycin for Prevention of Chronic Obstructive Pulmonary Disease (COPD) Exacerbations Trial. In addition to -IBR model results providing a nuanced understanding of the treatment effect, visually appealing heatmaps of the -restricted event times based on our MI datasets are given, a visualization not typically available for censored time-to-eventdata.