Malformed frogs: Bayesian and random-effect model analyses

Historical data (1958–1963) on frog malformations in Minnesota, USA, are compared to malformation data collected from 1996 to 1999, at many of the same collection sites, to investigate malformation risk changes between the study periods. We initially consider Mantel-Haenszel and simple logistic regression analyses. Potential variation in risk across data collection sites lead to random-effect logistic regression and hierarchical Bayesian models. We find clear evidence of increased malformation risk in the 1990s data collection period. The random-effect logistic regression and Bayesian logistic regression analyses produce similar point estimates of relative risk, and uncertainty, but Bayesian models allow analysts to view the impact of additional information on the inferences. Bayesian analyses programs in WinBUGS and SAS are provided.