Statistical Handling of Reproduction Data for Exposure-Response Modeling

Reproduction data collected through standard bioassays are classically analyzed by regression in order to fit exposure-response curves and estimate ECx values (x% effective concentration). But regression is often misused on such data, ignoring statistical issues related to (i) the special nature of reproduction data (count data), (ii) a potential inter-replicate variability, and (iii) a possible concomitant mortality. This paper offers new insights in dealing with those issues. Concerning mortality, particular attention was paid not to waste any valuable databy dropping all the replicates with mortalityor to bias ECx values. For that purpose we defined a new covariate summing the observation periods during which each individual contributes to the reproduction process. This covariate was then used to quantify reproductionfor each replicate at each concentrationas a number of offspring per individual-day. We formulated three exposure-response models differing by their stochastic part. Those models were fitted to four data sets and compared using a Bayesian framework. The individual-day unit proved to be a suitable approach to use all the available data and prevent bias in the estimation of ECx values. Furthermore, a nonclassical negative-binomial model was shown to correctly describe the inter-replicate variability observed in the studied data sets.