Abstract
Vaccine efficacy (VE) is commonly estimated through proportional hazards modelling of the time to first infection or disease, even when the event of interest can recur. These methods can result in biased estimates when VE is heterogeneous across levels of exposure and susceptibility in subjects. These two factors are important sources of unmeasured heterogeneity, since they vary within and across areas, and often cannot be individually quantified. We propose an estimator of VE per exposure that accounts for heterogeneous susceptibility and exposure for a repeated measures study with binary recurrent outcomes. The estimator requires only information about the probability distribution of environmental exposures. Through simulation studies, we compare the properties of this estimator with proportional hazards estimation under the heterogeneity of exposure. The methods are applied to a reanalysis of a malaria vaccine trial in Brazil.
Highlights
Vaccine efficacy (VE) is defined as the per cent reduction in the probability or hazard of disease conferred by the vaccine to an individual
The repeated measures model presented in this paper constitutes a practical way to estimate the individual VE or the VE conditional on exposure when the intensity of exposure is heterogeneous, even when the only knowledge about exposure relies on the estimated intensity of exposure from an environmental study
Under unmeasured heterogeneity of the intensity of exposure in the population, our repeated measures model results in more accurate and more robust estimates of VE than the proportional hazards modelling of time to first event and offers an alternative to multiple events survival methods when the time interval of events rather than the exact event time is known
Summary
Vaccine efficacy (VE) is defined as the per cent reduction in the probability or hazard of disease conferred by the vaccine to an individual. Even when studies combine active case detection with passive case detection (detection of the event whenever people seek care), many of their cases are found through active detection and have event time interval censored Under those circumstances, the exact failure time could be approximated, a repeated measures analysis for a binary outcome represents a practical alternative to handle the sequential monitoring of subjects, intervalcensored observations, recurrent episodes and non-proportional hazards. Recent randomized trials have been performed in which the VE is primarily estimated based on the proportional hazards modelling of time to first event (Alonso et al 2005; Bejon et al 2006, 2007).
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