Estimation and interpretation of heterogeneous vaccine efficacy against recurrent infections

Vaccine-induced protection may not be homogeneous across individuals. It is possible that a vaccine gives complete protection for a portion of individuals, while the rest acquire only incomplete (leaky) protection of varying magnitude. If vaccine efficacy is estimated under wrong assumptions about such individual level heterogeneity, the resulting estimates may be difficult to interpret. For instance, population-level predictions based on such estimates may be biased. We consider the problem of estimating heterogeneous vaccine efficacy against an infection that can be acquired multiple times (susceptible-infected-susceptible model). The estimation is based on a limited number of repeated measurements of the current status of each individual, a situation commonly encountered in practice. We investigate how the placement of consecutive samples affects the estimability and efficiency of vaccine efficacy parameters. The same sampling frequency may not be optimal for efficient estimation of all components of heterogeneous vaccine protection. However, we suggest practical guidelines allowing estimation of all components. For situations in which the estimability of individual components fails, we suggest to use summary measures of vaccine efficacy.