title: Statistical handling of reproduction data for exposure-response modeling.
abstract: 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.
authors.affiliation: Université de Lyon , F-69000, Lyon, France.
authors.forename: Marie Laure
authors.initials: ML
authors.lastname: Delignette-Muller
authors.forename: Christelle
authors.initials: C
authors.lastname: Lopes
authors.forename: Philippe
authors.initials: P
authors.lastname: Veber
authors.forename: Sandrine
authors.initials: S
authors.lastname: Charles
mesh_terms: D000818:Animals; D001499:Bayes Theorem; D016001:Confidence Intervals; D003621:Daphnia / Q000502:physiology*; D008954:Models, Biological; D012044:Regression Analysis; D012098:Reproduction / Q000502:physiology; D013223:Statistics as Topic