Statistical handling of reproduction data for exposure-response modelling

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 datasets 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 non-classical negative-binomial model was shown to correctly describe the inter-replicate variability observed in the studied datasets.