Risk assessment for Cryptosporidium: a hierarchical Bayesian analysis of human dose response data

Three dose-response studies were conducted with healthy volunteers using different Cryptosporidium parvum isolates (IOWA, TAMU, and UCP). The study data were previously analyzed for median infectious dose (ID50) using a simple cumulative percent endpoint method (Reed and Muench, 1938). ID50s were derived using two definitions of infection: one as subjects having oocysts detected in stool by direct fluorescence assay, and the other by a clinical finding of diarrhea with or without detected oocysts (Chappell et al., 1998; Okhuysen et al., 1999). In the present study, the data were analyzed using the broader definition of infection (i.e., presence of oocysts in stool and/or diarrheal illness characteristic of cryptosporidiosis). Maximum likelihood dose-response parameter estimates for UCP, IOWA, and TAMU were 2980, 190, and 17.5, respectively. Based on these estimates, the ID50s of the three respective isolates were 2066, 132, and 12.1. The three oocyst isolates were considered representative of a larger population of human-infecting strains and analyzed as combined data using a hierarchical Bayesian model. Hyperparameters defined the distribution of dose-response parameters for the population of strains. Output from Markov Chain Monte Carlo analysis described posterior distributions for the hyperparameters and for the parameters of the IOWA, TAMU, and UCP strains. Point estimates of dose-response parameters produced by this analysis were similar to the maximum likelihood estimates. Finally, the utility of these results for probabilistic risk assessment was evaluated. The risk of infection from single oocyst doses was derived for a mixture of the three isolates (where IOWA, TAMU, or UCP are equally likely), and for an oocyst selected at random from the larger population of strains. These estimated risks of infection were 0.018 and 0.028, respectively.