Statistica Sinica 18(2008), 1569-1591

STATISTICAL MODELLING OF BRAIN MORPHOLOGICAL

MEASURES WITHIN FAMILY PEDIGREES

Hongtu Zhu$^{1}$, Yimei Li$^{1}$, Niansheng Tang$^{2}$,

Ravi Bansal$^3$, Xuejun Hao$^3$, Myrna M. Weissman$^3$

and Bradley S. Peterson$^3$

$^1$University of North Carolin at Chapel Hill, $^2$Yunnan University

and $^3$Columbia University

Abstract: Large, family-based imaging studies can provide a better understanding of the interactions of environmental and genetic influences on brain structure and function. The interpretation of imaging data from large family studies, however, has been hindered by the paucity of well-developed statistical tools for that permit the analysis of complex imaging data together with behavioral and clinical data. In this paper, we propose two methods for these analyses. First, a variance components model, along with score statistics, is used to test linear hypotheses of unknown parameters, such as the associations of brain measures (e.g., cortical and subcortical surfaces) with their potential genetic determinants. Second, we develop a test procedure, based on a resampling method, to simultaneously assess the statistical significance of linear hypotheses across the entire brain. The value of these methods lies in their computational simplicity and in their applicability to a wide range of imaging data. Simulation studies show that our test procedure can accurately control the family-wise error rate. We apply our methods to the detection of statistical significance of gender-by-age interactions, and of the effects of genetic variation on the thickness of the cerebral cortex in a family study of major depressive disorder.

Key words and phrases: Cortical thickness, linear hypothesis, morphology, resampling method, variance components model.