Abstract
In this research, we propose analysis of τ -restricted censored time-to-event data via a τ -inflated beta regression ( τ -IBR) model. The outcome of interest is min(τ, T) , where T and τ are the time-to-event and follow-up duration, respectively. Our analysis goals include estimation and inference related to τ -restricted mean survival time ( τ -RMST) values and event-free probabilities at τ that address the censored nature of the data. In this setting, it is common to observe many individuals with min(τ, T) = τ , a point mass that is typically overlooked in τ -restricted event-time analyses. Our proposed τ -IBR model is based on a decomposition of min(τ, T) into τ[I(T ≥ τ) + (T/τ)I(T < τ)] . 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 τ -IBR model has the additional advantage of producing uncensored datasets for analysis. Simulations indicate excellent performance of the τ -IBR model(s), and corresponding τ -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 τ -IBR model results providing a nuanced understanding of the treatment effect, visually appealing heatmaps of the τ -restricted event times based on our MI datasets are given, a visualization not typically available for censored time-to-event data.