Analysis of variance for replicated spatial point patterns in clinical neuroanatomy

Our application concerns the analysis of the spatial distributions of pyramidal neurons in the cingulate cortex of human subjects in three diagnostic groupings. Our purpose is to develop and apply several methods for the analysis of replicated spatial point patterns to identify anatomical differences between normal, schizoaffective, and schizophrenic persons at the time of death. We begin with a scaled Poisson analysis that uncovers significant differences between the groups in the mean numbers of neurons in the sampled region, as well as a high degree of extra-Poisson variation in the distribution of cell counts within these groups. We then proceed to calculate two different functional descriptors of pattern for each subject to investigate departures from competely random patterns, both between subjects and between groups, while adjusting for cell count differences. The distributions of our main functional pattern descriptor and of our derived test statistic are unknown. For nonparametric inference, we propose a bootstrap procedure in which we resample our data to estimate the null distribution of our test statistic, even though the null hypothesis is not supported by these data. A simulation study provides evidence of the validity and power of our procedure for bootstrap hypothesis testing in our context. We conclude with a summary of what has been learned through this study about the cellular structure of cingulate cortex in persons with psychotic disorders and with some suggested directions for future research.