High Resolution T2 Association Tests of Complex Diseases Based on Family Data

Abstract

This paper proposes family based Hotelling's T(2) tests for high resolution linkage disequilibrium (LD) mapping or association studies of complex diseases. Assume that genotype data of multiple markers or haplotype blocks are available for a sample of nuclear families, in which some offspring are affected. Paired Hotelling's T(2) test statistics are proposed for a high resolution association study using parents as controls for affected offspring, based on two coding methods: haplotype/allele coding and genotype coding. The paired Hotelling's T(2) tests take not only the correlation between the haplotype blocks or markers into account, but also take the correlation within each parent-offspring pair into account. The method extends two sample Hotelling's T(2) test statistics for population case control association studies, which are not valid for family data due to correlation of genetic data among family members. The validity of the proposed method is justified by rigorous mathematical and statistical proof under the large sample theory. The non-centrality parameter approximations of the test statistics are calculated for power and sample size calculations. From power comparison and type I error calculations, it is shown that the test statistic based on haplotype/allele coding is advantageous over the test statistic of genotype coding. Analysis using multiple markers may provide higher power than single marker analysis. If only one marker is utilized the power of the test statistic based on haplotype/allele coding is nearly identical to that of 1-TDT. Moreover, a permutation procedure is provided for data analysis. The method is applied to data from a German asthma family study. The results based on the paired Hotelling's T(2) statistic tests confirm the previous findings. However, the paired Hotelling's T(2) tests produce much smaller P-values than those of the previous study. The permutation tests produce similar results to those of the previous study; moreover, additional marker combinations are shown to be significant by permutation tests. The proposed paired Hotelling's T(2) statistic tests are potentially powerful in mapping complex diseases. A SAS Macro, Hotel_fam.sas, has been written to implement the method for data analysis.