A Bayesian approach to the analysis of dose-response data: estimating natural survivorship without Abbott's correction and inclusion of overdispersion estimates.

We assessed the utility of a Bayesian analysis of dose-mortality curves using probit analysis. A Bayesian equivalent of a conventional single population probit analysis using Abbott's correction demonstrated the ability of the Bayesian model to recover parameters from generative data. We then developed a model that removed Abbott's correction and estimated natural survivorship as part of the overall model fitting process. Based on WAIC (information content) scores, this model was selected over the model using Abbott's corrected data in 196 out of 200 randomly generated datasets. This suggests that considerable information on control survivorship exists in response to treated doses in a bioassay, information that is partially removed when using Abbott's correction. Overdispersion in count data is common in ecological data, and a final model was developed that estimated overdispersion (kappa) as part of the model fitting process. When this model was compared to a model without overdispersion, it was selected as the best model in all 200 randomly generated datasets when kappa was low (5-20, high levels of overdispersion), while the 2 models performed equally well when kappa was large (500-2,000, low levels of overdispersion). The model with overdispersion was used to estimate parameters from bioassays of 10 populations of Helicoverpa zea (Lepidoptera: Noctuidae) exposed to Vip3a toxin, identifying 26 out of 45 pairwise comparisons that showed strong evidence of differences in LC50 estimates, adjusted for multiple comparisons.