Importance of Distributional Forms for the Assessment of Protozoan Pathogens Concentrations in Drinking-Water Sources

The identification of appropriately conservative statistical distributions is needed to predict microbial peak events in drinking water sources explicitly. In this study, Poisson and mixed Poisson distributions with different upper tail behaviors were used for modeling source water Cryptosporidium and Giardia data from 30 drinking water treatment plants. Small differences (<0.5-log) were found between the "best" estimates of the mean Cryptosporidium and Giardia concentrations with the Poisson-gamma and Poisson-log-normal models. However, the upper bound of the 95% credibility interval on the mean Cryptosporidium concentrations of the Poisson-log-normal model was considerably higher (>0.5-log) than that of the Poisson-gamma model at four sites. The improper choice of a model may, therefore, mislead the assessment of treatment requirements and health risks associated with the water supply. Discrimination between models using the marginal deviance information criterion (mDIC) was unachievable because differences in upper tail behaviors were not well characterized with available data sets ( $$ ). Therefore, the gamma and the log-normal distributions fit the data equally well but may predict different risk estimates when they are used as an input distribution in an exposure assessment. The collection of event-based monitoring data and the modeling of larger routine monitoring data sets are recommended to identify appropriately conservative distributions to predict microbial peak events.