τ $\tau$ -Inflated Beta Regression Model for Estimating τ $\tau$ -Restricted Means and Event-Free Probabilities for...

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