Statistical methods for estimating the duration of protection of malaria vaccines: secondary analysis of data from the RTSS/AS02A trial in Mozambique.

Malaria vaccines are unlikely to give long-lasting protection, booster doses will be required to maintain the high levels of antibodies and cellular responses that are required for protection. Unfortunately there is no immunological marker that can reliably be used to determine if a child is protected, the duration of protection and hence recommendations about the interval between booster doses must therefore be based on analysis of the incidence of malaria in vaccinated and unvaccinated children, from clinical trial cohorts, or in phase 4 studies in areas where the vaccine has been introduced, using case control studies. However there is no established methodology for these analyses and the methods used in published literature on malaria vaccines have known biases. The purpose of this project is therefore to develop statistical methods that can be used to estimate the duration of protection. Estimating the duration of protection for malaria vaccines is complicated by several factors. Firstly, children protected by vaccination may acquire natural immunity more slowly than unvaccinated children, so an apparent waning of vaccine protection may be partly due to more rapid acquisition of natural immunity in the unvaccinated children, a form of event dependence. Secondly, exposure to malaria varies greatly from one child to another, a small number of highly exposed children may contribute many episodes of malaria to the estimates of vaccine efficacy. This heterogeneity must be take into account when reporting the degree of uncertainty in estimates of vaccine efficacy. Heterogeneity in the presence of event dependence leads to bias in the assessment of vaccine efficacy unless specific account is taken of these effects in the analysis. Heterogeneity must also be considered when estimating vaccine protection in children who have already had one or more malaria episodes. This is because the distribution of exposure in vaccinated and unvaccinated children will be different (children with relatively low exposure to malaria may never get malaria if they have been vaccinated, and so this low-risk group is under-represented among vaccinated children who have had malaria, compared to unvaccinated children who have had malaria, leading to biased estimates of vaccine efficacy). These two effects, event dependence and heterogeneity, must be taken into account to obtain valid estimates of vaccine effects. Study aims and methodsThe aim of the proposed work is to develop improved methods for estimation of the time trajectory of vaccine efficacy, and we would like to use data from the phase 2b trial of the RTSS/AS02A vaccine in Mozambique (refs 1-5) as the motivating example, using these data to develop and evaluate the methods, and to demonstrate the use of the methods. The aim of the work is to develop two methods, firstly using smoothing methods to enable flexible functions to be fitted to the data to estimate how efficacy changes over time, secondly to investigate to what extent it is possible to allow for effects of faster acquisition of immunity in the controls, in as much as children acquire immunity mainly by having malaria and the malaria episodes are recorded, it may be possible to control for this to obtain better estimates of the waning of immunological protection. The methods that have been used in the published literature on malaria vaccine trials are not optimal, analysis of waning effects that has been published have used two approaches, both problematic: methods based on incidence of first episodes discarding data on subsequent episodes, which is known to introduce distortion, and methods involving fitting parametric functions, these impose a shape on the waning function chosen by the investigator. It is preferable to base the analysis on incidence of all episodes, using all the data, and using flexible functions for efficacy that do not impose a particular functional form. Furthermore, the question of the extent to which the apparent waning is explained by faster acquisition of immunity in the controls has not been addressed using the trial data. Modelling approaches have been used, these use mechanistic models of acquired immunity, while useful this is an indirect method that relies on assumptions about the mechanisms involved. This work is a joint research project between Prof Yin Bun Cheung and Dr Ying Xu, National University of Singapore; Dr EK Lam, University of Hong Kong, and Dr Paul Milligan at the London School of Hygiene and Tropical Medicine. We propose to develop the necessary statistical methods and tools to conduct secondary analysis of the existing anonymized phase2b trial data. We will estimate vaccine efficacy using all clinical malaria episodes, using the same case definitions as in the original trial protocol. For estimation of the total effect - i.e. incorporating the secondary effect via influence on accumulation of partial immunity - we will use the Andersen-Gill model (ref 9). To study how vaccine efficacy changes over time, within the Andersen-Gill model framework, we will estimate efficacy as a non-linear function of time using fractional polynomials and other curve fitting techniques such as cubic splines. To estimate the primary effect of the vaccine - i.e. controlling for the effect of accumulation of partial immunity - we will stratify for number of previous clinical malaria episodes, in addition to fitting vaccine efficacy as a non-linear function of time. Since the stratification induces a selection bias, we will include a frailty factor to control for the selection bias (ref 6). The results of this work will be published in peer-reviewed journals and if the methods are successful they will be made available to malaria researchers via software modules in Stata. Our previous publications in this area are listed below (refs 6-9). Data managementData will be anonymized, identified by unique numeric ID but without other personal information that would identify the subject. In reports of the work, only aggregate data will be presented. Datasets provided by GSK will be held on secure servers in London, at LSHTM, in Singapore, at the Centre for Quantitative Medicine, Duke-NUS Graduate Medical School, and at the University of Hong Kong, and parts of the analyses will be done in each of these centres. Only the investigators and their immediate collaborators will have access to these data and analyses will be confined to the aims and objectives of this protocol.