Partitioning of Functional Data for Understanding Heterogeneity in Psychiatric Conditions

An important goal in medical research is to identify groups of subjects characterized with a particular trait or quality and to distinguish them from other subjects in a clinically relevant way. Measures of biological phenomena, in general, and of psychiatric conditions, in particular, often exhibit symmetric shapes resembling a normal distribution; yet, the statistical approaches predominantly applied have been based on an assumption of underlying categories, whether observed or latent. It is well known that members of homogeneous populations with symmetric (multivariate) unimodal distributions can exhibit very distinct characteristics. Tarpey (2007a) and Tarpey et al. (2008) notice that partitioning of such homogeneous distributions is of importance even if distinct underlying categories are not assumed to underlie the measured phenomenon. For example, guidelines for treatment for depression would require the identification of a cut off on a given depression measure, whether or not the measure exhibits evidence for distinct clusters or mixtures. The first goal of this paper is to introduce a principled statistical method for studying variation within homogeneous distributions of psychiatric data without the assumption of existing mixtures. The second goal is to obtain clinically relevant partition of the distribution of the trajectories of depressive symptoms during treatment with antidepressants. The method of (Tarpey et al., 2009) based on principal points characterization is applied to partition curves of symptoms of depression over time for the purpose of identifying responders to specific and non-specific treatment effects. Data from one study is used for determining a useful partitioning and an external validation of this partitioning is performed using a second study