Estimating Vaccine Efficacy from Outbreak Size Household Data in the Presence of Heterogeneous Transmission Probabilities

Abstract

We develop a Bayesian approach for estimating vaccine efficacy for susceptibility (VEs) and infectiousness (VEI) using outbreak size household data. Our method allows for heterogeneity in transmission probabilities due to factors that are related to individuals' characteristics, such as age, in addition to vaccination status. It also allows for between-household heterogeneity in transmission probabilities due to random effects associated with households, such as genetic or environmental effects. Using age as a potential covariate causing heterogeneity in individuals' transmission probabilities in households consisting of adults and children, we present the results of a simulation study designed to evaluate the performance of the proposed estimators of VEs and VE(I). We found that estimates of VE(I) have larger bias and variance compared to those of VEs. We also use the approach to compare two vaccination designs: one vaccinating both adults and children, the other only children. Simulations reveal that the design that vaccinates both adults and children provides better estimates of VEs. There is no obvious difference between the two designs in the performance of the estimates of VE(I). In regard to random effects between households and the scenarios considered, models that do not account for between-households heterogeneity produce fairly robust estimates even when household-level random effects are present.

Predictive assessment of a non‐linear random effects model for multivariate time series of infectious disease counts

“…For infectious disease data, Li et al 8 allowed for household‐dependent heterogeneity in infection rates by assuming that the probability of avoiding infection varies randomly in a chain binomial model. Similarly, Davis et al 9 considered heterogeneity in transmission probabilities due to household‐specific random effects when estimating vaccine efficacy based on outbreak size household data.Zeger and Karim 10 and Lin and Zhang 11 used a generalized linear (additive) mixed model (GLMM) for the analysis of longitudinal data on respiratory infection in Indonesian children.…”

Estimating Vaccine Efficacy Under the Heterogeneity of Vaccine Action in a Nonrandomly Mixing Population

“…A few studies have estimated vaccine efficacy in a nonrandomly mixing population (Haber et al, 1991a, 1995; Halloran et al, 1996; Longini and Halloran, 1996; Davis et al, 2006); however, these studies have ignored the heterogeneity of vaccine action across the vaccinated strata. Moreover, some other studies (Becker and Starczak, 1997; Ball and Lyne, 2002; Ball et al, 2004a,b; Ball and Lyne, 2006; Pellis et al, 2009) have modeled the epidemic in such a stratified population and discussed the estimation of optimal vaccination coverage under models that do not allow for the heterogeneity of vaccine action.…”