gLRTH_L: The function for the likelihood ratio test for genetic...
In gLRTH: Genome-Wide Association and Linkage Analysis under Heterogeneity

Description Usage Arguments Value Author(s) References Examples

View source: R/gLRTH_L.R

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 ≥ 2),

P_{η}(X_D=g)=∑_{j=1}^J α_j B_2(g, θ_j), \; g=0, 1, 2, \; J ≥q 2, \; ∑_{j=1}^J α_j=1, \; θ_j, α_j \in (0, 1),

where η=(η_j)_{j ≤q J}, η_j=(θ_j, α_j)^T, j=1, …, J, B_2(g, θ_j) is the probability mass function for a binomial distribution X \sim Bin(2, θ_j), and θ_i=θ_j if and only if i=j. θ_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 ≥ 2.

1	gLRTH_L(n0, n1, n2)

`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

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

Xiaoxia Han and Yongzhao Shao

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.