Estimation of the primary, secondary and composite effects of malaria vaccines using data on multiple clinical malaria episodes

Abstract

Background: An effective malaria vaccine affects the risk of malaria directly, through the vaccine-induced immune response (the primary effect), and indirectly, as a consequence of reduced exposure to malaria infection and disease, leading to slower acquisition of natural immunity (the secondary effect). The beneficial primary effect may be offset by a negative secondary effect, resulting in a smaller or nil composite effect. Reports of malaria vaccine trials usually present only the composite effect. We aimed to demonstrate how the primary and secondary effects can also be estimated from trial data. Methods: We propose an enhancement to the conditional frailty model for the estimation of primary effect using data on disease episodes. We use the Andersen-Gill model to estimate the composite effect. We consider taking the ratio of the hazard ratios to estimate the secondary effect. We used directed acyclic graphs and data from a randomized trial of the RTS,S/AS02 malaria vaccine to illustrate the problems and solutions. Time-varying effects were estimated by partitioning the follow-up into four time periods. Results: The primary effect estimates from our proposed model were consistently stronger than the conditional frailty model in the existing literature. The primary effect of the vaccine was consistently stronger than the composite effect across all time periods. Both the primary and composite effects were stronger in the first three months, with hazard ratios (95% confidence interval) 0.62 (0.49–0.79) and 0.68 (0.54–0.84), respectively; the hazard ratios weakened over time. The secondary effect appeared mild, with hazard ratio 1.09 (1.02–1.16) in the first three months. Conclusions: The proposed analytic strategy facilitates a more comprehensive interpretation of trial data on multiple disease episodes. The RTS,S/AS02 vaccine had modest primary and secondary effects that waned over time, but the composite effect in preventing clinical malaria remained positive up to the end of the study. Clinical trials registration: ClinicalTrials.gov NCT00197041