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

Abstract

This research introduces a multivariate $\tau$ -inflated beta regression ( $\tau$ -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 $\tau$ 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 $\tau$ -IBR model that include parameter estimates to help interpret the (a) and (b) mixture of event times in the data, estimates of mean $\tau$ -restricted event-free duration in a $\tau$ -length follow-up window based on a patient's covariate profile, and heat maps of raw $\tau$ -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 $\tau$ -IBR approach to modeling censored recurrent event data. An example is given based on the Azithromycin for Prevention of COPD Exacerbations Trial.

Keywords: expectation-solution; generalized estimating equation; inflated beta regression; multiple imputation of censored times-to-event; recurrent events analysis.