A Hierarchical Model for the Skew-normal Distribution with Application in Developmental Neurotoxicology

The distribution of the mean of a random sample drawn from a skew-normal population was derived by Chen et al. (2004). Here, we consider a hierarchical structure and derive the distribution of the sample mean when the location parameter itself is a random variable with a normal distribution. In neurotoxicological bioassay experiments with laboratory animals, often the response of interest is continuous in nature and the mean of responses is used for inferential purposes (Chen, 2006). However, in developmental neurotoxicity experiments where the neurological effect of a compound on the developing fetus is of interest, because of the intra-litter correlation, the mean of the response distribution may vary from one litter to another. The unconditional distribution of the litter sample mean is derived and its application in the analysis of data from developmental neurotoxicology is described. An example with real experimental data is used to provide further illustration.