Abstract
BackgroundMalaria transmission is highly heterogeneous and analysis of incidence data must account for this for correct statistical inference. Less widely appreciated is the occurrence of a large number of zero counts (children without a malaria episode) in malaria cohort studies. Zero-inflated regression methods provide one means of addressing this issue, and also allow risk factors providing complete and partial protection to be disentangled.MethodsPoisson, negative binomial (NB), zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) regression models were fitted to data from two cohort studies of malaria in children in Ghana. Multivariate models were used to understand risk factors for elevated incidence of malaria and for remaining malaria-free, and to estimate the fraction of the population not at risk of malaria.ResultsZINB models, which account for both heterogeneity in individual risk and an unexposed sub-group within the population, provided the best fit to data in both cohorts. These approaches gave additional insight into the mechanism of factors influencing the incidence of malaria compared to simpler approaches, such as NB regression. For example, compared to urban areas, rural residence was found to both increase the incidence rate of malaria among exposed children, and increase the probability of being exposed. In Navrongo, 34% of urban residents were estimated to be at no risk, compared to 3% of rural residents. In Kintampo, 47% of urban residents and 13% of rural residents were estimated to be at no risk.ConclusionThese results illustrate the utility of zero-inflated regression methods for analysis of malaria cohort data that include a large number of zero counts. Specifically, these results suggest that interventions that reach mainly urban residents will have limited overall impact, since some urban residents are essentially at no risk, even in areas of high endemicity, such as in Ghana.
Highlights
Malaria transmission is highly heterogeneous and analysis of incidence data must account for this for correct statistical inference
9.56% of the total burden of malaria episodes was borne by urban residents (16% of the population)
Comparison of different regression models In both cohorts, the Poisson and negative binomial models tended to underestimate the number of children with zero malaria attacks, and overestimate the number with one malaria attack (Figures 3 and 4)
Summary
Malaria transmission is highly heterogeneous and analysis of incidence data must account for this for correct statistical inference. In the case of malaria, a child who is exposed to bites from infectious mosquitoes may not experience malaria during a particular study, because, by chance, s/he happens not to become infected or does not become unwell during the time observed. These ‘sampling’ zeroes are estimated by the count section of the model. A child may not experience malaria because they are never exposed to infection so cannot become unwell These ‘certain’ zeros, estimated by the binary component of the model, are responsible for the excessive number of zero counts observed. Zero-inflated models allow these two distinct processes to be disentangled, and the fraction of the population not at risk to be estimated
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