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

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## Abstract

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.

Supplementary materials accompanying this paper appear online.

## Keywords

Survival analysis Hazard rate Count data Multi-resolution hazard Changing at-risk population Time-varying covariates## Notes

### Acknowledgements

This work was supported by Grants NSF-GEO 1211668, NSF-DEB 1316334, and NIH-R01GM096655. The project utilized the Janus supercomputer, which is supported by the National Science Foundation (Award Number CNS-0821794) University of Colorado Boulder. The Janus supercomputer is a joint effort of University of Colorado Boulder, the University of Colorado Denver, and the National Center for Atmospheric Research. Janus is operated by the University of Colorado Boulder. The authors thank the researchers at NCAR and the REACCTING project, A. A. Forgor and A. Hodgson at Ghana Health Services, and P. Akweongo at the School of Public Health at the University of Ghana for collecting these data and for their helpful advice and input.

## Supplementary material

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