gLRTH_L {gLRTH}

The function for the likelihood ratio test for genetic linkage under transmission heterogeneity

Description

We consider a binary trait and focus on detecting a transmission heterogeneity at a single locus with two alleles A and a. We consider independent families each with one marker homozygous (AA) parent, one marker heterozygous parent (Aa) and two diseased children. This likelihood ratio test is to test transmission heterogeneity of preferential transmission of marker allele "a" to an affected child based on a binomial mixture model with J components (J \ge 2),

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 transmission of the allele of interest in a subgroup of families j. In particular, J is likely to be quite large for many of the complex disease under transmission heterogeneity. Note that this LRT can be applied to genome-wide linkage analysis without the need to know the exact value of J while allowing J \ge 2.

Usage

gLRTH_L(n0, n1, n2)

Arguments

n0

Number of affected sibling pairs both of which inherited A from their heterozygous parent Aa

n1

Number of affected sibling pairs which one inherited A and the other inherited a from their heterozygous parent Aa

n2

Number of affected sibling pairs both of which inherited a from their heterozygous parent Aa

Value

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

Author(s)

Xiaoxia Han and Yongzhao Shao

References

Shao Y. (2014) Linkage analysis, originally published in Encyclopedia of Quantitative Risk Analysis and Assessment, John Wiley & Sons, Ltd, USA, 2008, and republished in Wiley StatsRef: Statistics Reference Online 2014.

Examples

gLRTH_L(n0=100, n1=70, n2=30)