Statistical handling of reproduction data for exposure-response modeling

Environ Sci Technol. 2014 Jul 1;48(13):7544-51. doi: 10.1021/es502009r. Epub 2014 Jun 10.

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.

MeSH terms

  • Animals
  • Bayes Theorem
  • Confidence Intervals
  • Daphnia / physiology*
  • Models, Biological
  • Regression Analysis
  • Reproduction / physiology
  • Statistics as Topic*