τ$$ \tau $$‐Inflated beta regression model for censored recurrent events

Abstract

This research introduces a multivariate ‐inflated beta regression (‐IBR) modeling approach for the analysis of censored recurrent event data that is particularly useful when there is a mixture of (a) individuals who are generally less susceptible to recurrent events and (b) heterogeneity in duration of event‐free periods amongst those who experience events. The modeling approach is applied to a restructured version of the recurrent event data that consists of censored longitudinal times‐to‐first‐event in length follow‐up windows that potentially overlap. Multiple imputation (MI) and expectation‐solution (ES) approaches appropriate for censored data are developed as part of the model fitting process. A suite of useful analysis outputs are provided from the ‐IBR model that include parameter estimates to help interpret the (a) and (b) mixture of event times in the data, estimates of mean ‐restricted event‐free duration in a ‐length follow‐up window based on a patient's covariate profile, and heat maps of raw ‐restricted event‐free durations observed in the data with censored observations augmented via averages across MI datasets. Simulations indicate good statistical performance of the proposed ‐IBR approach to modeling censored recurrent event data. An example is given based on the Azithromycin for Prevention of COPD Exacerbations Trial.