τ $\tau$ -Inflated Beta Regression Model for Estimating τ $\tau$ -Restricted Means and Event-Free Probabilities for Censored Time-to-Event Data

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 $\tau \left[I\right(T\ge \tau )+(T/\tau \left)I\right(T<\tau \left)\right]$. 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.