Estimability and Interpretation of Vaccine Efficacy Using Frailty Mixing Models

Abstract

The authors consider estimability and interpretation of vaccine efficacy based on time to event data, allowing that some of the population might have a very low probability of acquiring disease, and the rest have partial, possibly continuously distributed, susceptibility. The efficacy parameters of interest in the frailty mixing model include the fraction highly unlikely to acquire the infection or disease due to the vaccine, the degree of partial protection in those still susceptible, and the average protection or summary measure of efficacy under heterogeneity. The efficacy estimates can still be usefully interpreted when the heterogeneity results from heterogeneity in contact patterns, contact rates, or infectiousness of the contacts, as long as these are equal in the vaccinated and unvaccinated groups. A likelihood-based method allows estimation of the efficacy parameters of interest from grouped time to event data. Simulated vaccine studies assuming different levels and distributions of efficacy demonstrate that ignoring heterogeneity in susceptibility or exposure to infection generally results in underestimation of vaccine efficacy as well as incorrect interpretation of the estimates. The approach is also applicable to other covariates affecting susceptibility or exposure to infection in infectious diseases. Exploitation of the dependent happening structure of infectious diseases to obtain a shape for the baseline hazard may help identifiability. The authors recommend fitting several models to time to event data in vaccine studies.

Transmission dynamics of Ebola virus disease and intervention effectiveness in Sierra Leone

“…We suggest that future vaccination trials or campaigns be accompanied by carefully designed household, contact-tracing cluster, hospital, or community transmission studies, so that various aspects of VE can be measured: e.g., the VEs in reducing susceptibility, infectiousness, and pathogenicity (34). Plans could be made now, using the methods presented here, to help with the conduct and analysis of such vaccine trials, as well as with assessing the effectiveness of vaccination control strategies.…”

Modeling a Field Trial of the Rts,s/As02a Malaria Vaccine

“…In the model this difference is an effect of naturally acquired blood-stage immunity. This introduces to both arms of the trial heterogeneity in the probability that an infection will be patent at the time of a cross-sectional survey, and consequently 4 leads to a small downward bias in VÊ p . This bias is greater in adults than in children and can thus explain the higher efficacy observed in Mozambique than in the Gambian trial.…”

“…Such heterogeneities consistently lead to reduction in estimates of efficacy in preventing infection. 4 The different efficacy values all have wide confidence intervals (Table 1), and can therefore be reconciled with a statistical null hypothesis that the variation between them represents only a result of chance. However there are good reasons for expecting malaria vaccines to have different efficacies against different outcomes.…”

Mathematical Modeling of the Impact of Malaria Vaccines on the Clinical Epidemiology and Natural History of Plasmodium Falciparum Malaria: Overview

“…Pre-existing immunity and heterogeneity in the efficacy of a vaccine both lead to reduction in the effectiveness in preventing infection. 18 The efficacy of vaccination against postinfection outcomes such as morbidity and mortality may be very different from that against infection. 19 A model to predict population impact of a vaccine needs to include these processes that modulate the impact of infection.…”