A Bayesian methodological framework for setting fish tumor occurrence delisting criteria: A case study in St. Marys River area of concern

Fish tumors and other deformities are a class of Beneficial Use Impairment (BUIs) established by the International Joint Commission to identify Areas of Concern (AOC) in the Great Lakes basin. The St. Marys River has been impaired by fish tumors and other deformities since its designation as an AOC in 1987. In this study, we present a Bayesian modeling framework that is founded upon the explicit consideration of the sampling bias in tumor observations as well as the causal association between important covariates and tumor occurrence. Data from 2009 indicate that fish tumor incidence rates were generally elevated at the Bellevue Marina and Partridge Point exposed locations relative to the Batchawana Bay reference site. Fish age was the single most important covariate of the tumor incidence rates, followed by the fork length, and the liver or gonad weights. Using the Bayesian counterpart of the two one-side tests for equivalence, the exposed site was practically equivalent to the reference location in regards to the neoplasm and pre-neoplasm incidence rates. However, the mean probability of neoplasm incidence was predicted to be lower than 10% in 70% and 95% of the cases in the exposed and reference sites, respectively. The predicted mean pre-neoplasm frequency never fell below 10% in all the samples collected at the exposed site, whereas ≈40% of the cases are predicted to fall below the proposed cut-off level in the reference site suggesting that the exposed site may still be impaired.