Predictive Bayesian Microbial Dose‐Response Assessment Based on Suggested Self‐Organization in Primary Illness Response: Cryptosporidium parvum

The probability of illness caused by very low doses of pathogens cannot generally be tested due to the numbers of subjects that would be needed, though such assessments of illness dose response are needed to evaluate drinking water standards. A predictive Bayesian dose‐response assessment method was proposed previously to assess the unconditional probability of illness from available information and avoid the inconsistencies of confidence‐based approaches. However, the method uses knowledge of the conditional dose‐response form, and this form is not well established for the illness endpoint. A conditional parametric dose‐response function for gastroenteric illness is proposed here based on simple numerical models of self‐organized host‐pathogen systems and probabilistic arguments. In the models, illnesses terminate when the host evolves by processes of natural selection to a self‐organized critical value of wellness. A generalized beta‐Poisson illness dose‐response form emerges for the population as a whole. Use of this form is demonstrated in a predictive Bayesian dose‐response assessment for cryptosporidiosis. Results suggest that a maximum allowable dose of 5.0 × 10 −7 oocysts/exposure (e.g., 2.5 × 10 −7 oocysts/L water) would correspond with the original goals of the U.S. Environmental Protection Agency Surface Water Treatment Rule, considering only primary illnesses resulting from Poisson‐distributed pathogen counts. This estimate should be revised to account for non‐Poisson distributions of Cryptosporidium parvum in drinking water and total response, considering secondary illness propagation in the population.