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

• Published in: Statistics in medicine Vol. 31; no. 29; pp. 4023 - 4039
• Main Authors: Xu, Ying, Cheung, Yin Bun, Lam, K. F., Milligan, Paul
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 20.12.2012; Wiley Subscription Services, Inc
• Subjects: Algorithms; Antimalarials - therapeutic use; Clinical trials; Computer Simulation; Disease prevention; Drug Combinations; event dependence; expectation-maximization (EM) algorithm; frailty mixture model; Ghana; Humans; Infant; Louis's formula; Malaria; Malaria - mortality; Malaria - prevention & control; Medical statistics; Models, Statistical; Monte Carlo Method; Poisson Distribution; Pyrimethamine - therapeutic use; Randomized Controlled Trials as Topic - statistics & numerical data; Simulation; Sulfadoxine - therapeutic use; summary protective efficacy; Survival Analysis; Vaccines; Ghana
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.5458

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. Copyright © 2012 John Wiley & Sons, Ltd.