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Estimation of summary protective efficacy using a frailty mixture model for recurrent event time data
Author(s) -
Xu Ying,
Cheung Yin Bun,
Lam K. F.,
Milligan Paul
Publication year - 2012
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.5458
Subject(s) - observational study , econometrics , expectation–maximization algorithm , estimation , statistics , event (particle physics) , computer science , maximization , variance (accounting) , proportional hazards model , mathematics , maximum likelihood , mathematical optimization , physics , business , management , accounting , quantum mechanics , economics
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.