Simultaneous estimation of haplotype frequencies and quantitative trait parameters: applications to the test of association between phenotype and diplotype configuration

Abstract

The analysis of the haplotype-phenotype relationship has become more and more important. We have developed an algorithm, using individual genotypes at linked loci as well as their quantitative phenotypes, to estimate the parameters of the distribution of the phenotypes for subjects with and without a particular haplotype by an expectation-maximization (EM) algorithm. We assumed that the phenotype for a diplotype configuration follows a normal distribution. The algorithm simultaneously calculates the maximum likelihood (L0max) under the null hypothesis (i.e., nonassociation between the haplotype and phenotype), and the maximum likelihood (Lmax) under the alternative hypothesis (i.e., association between the haplotype and phenotype). Then we tested the association between the haplotype and the phenotype using a test statistic, -2 log(L0max/Lmax). The above algorithm along with some extensions for different modes of inheritance was implemented as a computer program, QTLHAPLO. Simulation studies using single-nucleotide polymorphism (SNP) genotypes have clarified that the estimation was very accurate when the linkage disequilibrium between linked loci was rather high. Empirical power using the simulated data was high enough. We applied QTLHAPLO for the analysis of the real data of the genotypes at the calpain 10 gene obtained from diabetic and control subjects in various laboratories.

Figure 1.—

Histograms of the statistic −2 log(L_0max/L_max) produced under the null hypothesis. Simulation was performed under the null hypothesis, μ₁ = μ₂ = 160, σ = 5.0. Sample size N was either (A) 100 or (B) 1000, and number of repeats for a simulation was 10,000. The histograms of the statistic are shown with bars. The probability density function of χ² distribution with 1 d.f. is shown with curves.

Figure 2.—

Power of the test with regard to sample size and |μ₁ − μ₂|/σ. The solid line is for N = 100, and the dashed line is for N = 1000.