Flexible Modelling of Correlated Multivariate Data with Applications in Animal Studies.

Abstract

Correlated data are common in many health sciences studies, where clustered, multivariate, longitudinal, hierarchical and spatially organized data are frequently observed. In clustered data, subjects within the same group are likely to be more similar than subjects among different groups. When several outcomes of interest are measured on the same individual, these multivariate outcomes are likely to be correlated. Associations in spatial data are due to spatial proximity. In all these cases, the observations under study share some common characteristics and statistical analysis requires taking such associations into account. There exist many ways to deal with these correlation structures, ranging from the most naive one of ignoring the associations to approaches that correct for correlations or model the clustering. Failure to account for the effect of clustering can result in erroneous estimation of the variability of the parameter estimates, and hence in misleading inference. Therefore, appropriate statistical techniques for the analysis of correlated measurements are of interest. An important consideration in the statistical modelling of correlated data concerns the type of outcome. Methods for clustered or multivariate continuous data are widely available, where the normal distribution with its elegant properties plays a prominent role. However, when the outcome variable is discrete or categorical, techniques for correlated data are less standard, because of the lack of a discrete analogue to the multivariate normal distribution. In general, one might record more than one outcome for each individual, with outcomes of a different type and individuals clustered within groups or spatially correlated. In this thesis, several scientific disciplines where clustering of categorical data are encountered are topic of interest. Main focus is on risk analysis modelling in developmental toxicity studies. Each of the research areas discussed involves a different study design, leading to unique and interesting statistical problems. In the next sections, we briefly describe the research areas considered in this thesis, where correlated data arise naturally in different ways.