Robust evaluation of vaccine effects based on estimation of vaccine efficacy curve

Abstract

The Cox model and its extensions assuming proportional hazards is widely used to estimate vaccine efficacy (VE). However, when VE wanes over time, estimates can become sensitive to study duration and timing of vaccine delivery relative to disease seasonality, and may be biased due to sample attrition. Additionally, estimates of vaccine impact such as number of cases averted (NCA) are sensitive to background disease incidence and timing of vaccine delivery. Comparison of the estimates between trials with different implementation features can be misleading. We propose estimation of VE as a function of time in the Cox model framework, using the area under the VE curve as a summary measure of VE, and extension of the method to estimate vaccine impact. We use simulations and re-analysis of a RTS,S/AS01 malaria vaccine trial dataset to demonstrate their properties and applications. Simulation under scenarios with different trial duration, magnitude of sample attrition and timing of vaccine delivery, all assuming vaccine protection wanes over time, demonstrated problems of conventional methods assuming proportional hazard, robustness of the proposed methods, and comparability of the proposed estimates of vaccine efficacy and impact across trials with different implementation features. Furthermore, the proposed NCA estimators are informative in determining the optimal vaccine delivery strategy in regions with highly seasonal disease transmission. The proposed method based on estimation of vaccine efficacy trajectory provides a robust, unbiased, and flexible approach to evaluate vaccine effects.