Analysis of variance for replicated spatial point patterns in clinical neuroanatomy

Peter J. Diggle, Nicholas Lange, Francine M. Beneš

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)618-625
Number of pages8
JournalJournal of the American Statistical Association
Volume86
Issue number415
DOIs
StatePublished - 1991
Externally publishedYes

Keywords

  • Bootstrap hypothesis testing
  • Cingulate cortex
  • Extra-Poisson variation
  • Inhibition process
  • K-function
  • Poisson process
  • Pyramidal neurons
  • Schizophrenia

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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