Estimation of summary protective efficacy using a frailty mixture model for recurrent event time data

Recurrent event time data are common in experimental and observational studies. The analytic strategy needs to consider three issues: within-subject event dependence, between-subject heterogeneity in event rates, and the possibility of a nonsusceptible fraction. Motivated by the need to estimate the summary protective efficacy from recurrent event time data as seen in many infectious disease clinical trials, we propose a two-part frailty mixture model that simultaneously accommodates all the three issues. In terms of vaccine action models, the proposed model is a combination of the 'all-or-none' and the 'leaky' models, and the summary protective efficacy is a unified measure of the vaccine's twofold effects in completely or partially protecting the vaccinated individuals against the study event. The model parameters of interest are estimated using the expectation-maximization algorithm with their respective variances estimated using Louis's formula for the expectation-maximization algorithm. The summary protective efficacy is estimated by a composite estimand with its variance estimated using the delta method. The performance of the proposed estimation approach is investigated by a simulation study. Data from a trial of malaria prophylaxis conducted in Ghana are reanalyzed.