Coping with time and space in modelling malaria incidence: a comparison of survival and count regression models

To study the effect of a mega hydropower dam in southwest Ethiopia on malaria incidence, we have set up a longitudinal study. To gain insight in temporal and spatial aspects, that is, in time (period  =  year-season combination) and location (village), we need models that account for these effects. The frailty model with periodwise constant baseline hazard (a constant value for each period) and a frailty term that models the clustering in villages provides an appropriate tool for the analysis of such incidence data. Count data can be obtained by aggregating for each period events at the village level. The mixed Poisson regression model can be used to model the count data. We show the similarities between the two models. The risk factor in both models is the distance to the dam, and we study the effect of the risk factor on malaria incidence. In the frailty model, each subject has its own risk factor, whereas in the Poisson regression model, we also need to average the risk factors of all subjects contributing to a particular count. The power loss caused by using village averaged distance instead of individual distance is studied and quantified. The loss in the malaria data example is rather small. In such a setting, it might be advantageous to use less labor-intensive sampling schemes than the weekly individual follow-up scheme used in this study; the proposed alternative sampling schemes might also avoid community fatigue, a typical problem in such research projects.