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 ( VE _S ) and infectiousness ( VE _I ) using outbreak size household data. Our method allows for heterogeneity in transmission probabilities due to factors that are related to individual' 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 individual' 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 VE _S and VE _I . We found that estimates of VE _I have larger bias and variance compared to those of VE _S . 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 V E _S . There is no obvious difference between the two designs in the performance of the estimates of V E _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.

Key Words:

• Bayesian methods
• Household data
• Infectious diseases
• Random effects models
• Transmission models
• Vaccine efficacy for infectiousness
• Vaccine efficacy for susceptibility

ACKNOWLEDGMENT

The authors wish to thank John Hanfelt and two reviewers for helpful comments and suggestions.

Notes

^†Model 1 – no age effect without intercepts; Model 2 – no age effect with intercepts; Model 3 − β age effect; Model 4 − γ age effect; Model 5 − β and γ age related.

⋆ any values.

^⋆Model 1 – no age effect without intercepts; Model 2 – no age effect with intercepts; Model 3 − β age effect; Model 4 − γ age effect; Model 5 − β and γ age related.

^⋆Model 1 – no age effect without intercepts; model 2 – no age effect with intercepts; model 3 − β age effect; model 4 − γ age effect; model 5 − β and γ age related.