gLRTH_A {gLRTH}

The function for the likelihood ratio test for genome-wide association under genetic heterogeneity with genotype frequencies as input values

Description

We consider a binary trait and focus on detecting association with disease at a single locus with two alleles A and a. The likelihood ratio test is based on a binomial mixture model of J components (J \ge 2) for diseased cases:

P_{\eta}(X_D=g)=\sum_{j=1}^J \alpha_j B_2(g, \theta_j), \; g=0, 1, 2, \; J \geq 2, \; \sum_{j=1}^J \alpha_j=1, \; \theta_j, \alpha_j \in (0, 1),

where \eta=(\eta_j)_{j \leq J}, \eta_j=(\theta_j, \alpha_j)^T, j=1, \ldots, J, B_2(g, \theta_j) is the probability mass function for a binomial distribution X \sim Bin(2, \theta_j), and \theta_i=\theta_j if and only if i=j. \theta_j is the probability of having the allele of interest on one chromosome for a subgroup of case j. In particular, J is likely to be quite large for many of the complex disease with genetic heterogeneity. Note that the LRT-H can be applied to association studies without the need to know the exact value of J while allowing J \ge 2.

Usage

gLRTH_A(n0, n1, n2, m0, m1, m2)

Arguments

n0

AA genotype frequency in case

n1

Aa genotype frequency in case

n2

aa genotype frequency in case

m0

AA genotype frequency in control

m1

Aa genotype frequency in control

m2

aa genotype frequency in control

Value

The test statistic and asymptotic p-value for the likelihood ratio test for GWAS under genetic heterogeneity

Author(s)

Xiaoxia Han and Yongzhao Shao

References

Qian M., Shao Y. (2013) A Likelihood Ratio Test for Genome-Wide Association under Genetic Heterogeneity. Annals of Human Genetics, 77(2): 174-182.

Examples

gLRTH_A(n0=2940, n1=738, n2=53, m0=3601, m1=1173, m2=117)