Comparing methods for analyzing overdispersed count data in aquatic toxicology

Abstract

Endpoints in aquatic toxicity tests can be measured using a variety of measurement scales including dichotomous (survival), continuous (growth) and count (number of young). A distribution is assumed for an endpoint and analyses proceed accordingly. In certain situations, the assumed distribution may be incorrect and this may lead to incorrect statistical inference. The present study considers the analysis of count effects, here motivated by the Ceriodaphnia dubia reproduction study. While the Poisson probability model is a common starting point, this distribution assumes that the mean and variance are the same. This will not be the case if there is some extraneous source of variability in the system, and in this case, the variability may exceed the mean. A computer simulation study was used to examine the impact of overdispersion or outliers on the analysis of count data. Methods that assumed Poisson or negative binomially distributed outcomes were compared to methods that accommodated this potential overdispersion using quasi-likelihood (QL) or generalized linear mixed models (GLMM). If the data were truly Poisson, the adjusted methods still performed at nominal type I error rates. In the cases of overdispersed counts, the Poisson assumed methods resulted in rejection rates that exceeded nominal levels and standard errors for regression coefficients that were too narrow. The negative binomial methods worked best in the case when the data were, in fact, negative binomial but did not maintain nominal characteristics in other situations. In general, the QL and GLMM methods performed reasonably based on the present study, although all procedures suffered some impact in the presence of potential outliers. In particular, the QL is arguably preferred because it makes fewer assumptions than the GLMM and performed well over the range of conditions considered.