Comparison of Models Analyzing a Small Number of Observed Meningitis Cases in Navrongo, Ghana.

The "meningitis belt" is a region in sub-Saharan Africa where annual outbreaks of meningitis occur, with epidemics observed cyclically. While we know that meningitis is heavily dependent on seasonal trends, the exact pathways for contracting the disease are not fully understood and warrant further investigation. Most previous approaches have used large sample inference to assess impacts of weather on meningitis rates. However, in the case of rare events, the validity of such assumptions is uncertain. This work examines the meningitis trends in the context of rare events, with the specific objective of quantifying the underlying seasonal patterns in meningitis rates. We compare three main classes of models: the Poisson generalized linear model, the Poisson generalized additive model, and a Bayesian hazard model extended to accommodate count data and a changing at-risk population. We compare the accuracy and robustness of the models through the bias, RMSE, and standard deviation of the estimators, and also provide a detailed case study of meningitis patterns for data collected in Navrongo, Ghana.