R/gLRTH_L.R

In gLRTH: Genome-Wide Association and Linkage Analysis under Heterogeneity

#' 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 \eqn{A} and \eqn{a}. We consider independent families each with one marker homozygous (\eqn{AA}) parent, one marker
#' heterozygous parent (\eqn{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 \eqn{J} components (\eqn{J \ge 2}),
#'\deqn{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 \eqn{\eta=(\eta_j)_{j \leq J}, \eta_j=(\theta_j, \alpha_j)^T, j=1, \ldots, J},
#' \eqn{B_2(g, \theta_j)} is the probability mass function for a binomial distribution \eqn{X \sim Bin(2, \theta_j)},
#' and \eqn{\theta_i=\theta_j} if and only if \eqn{i=j}. \eqn{\theta_j} is the probability
#' of transmission of the allele of interest in a subgroup of families \eqn{j}.
#' In particular, \eqn{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 \eqn{J} while allowing \eqn{J \ge 2}.
#'
#' @return The test statistic and asymptotic p-value for the likelihood ratio test for linkage analysis under genetic heterogeneity
#' @param n0 Number of affected sibling pairs both of which inherited A from their heterozygous parent Aa
#' @param n1 Number of affected sibling pairs which one inherited A and the other inherited a from their heterozygous parent Aa
#' @param n2 Number of affected sibling pairs both of which inherited a from their heterozygous parent Aa
#' @author 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)
#' @export
#' @importFrom stats pchisq

gLRTH_L<-function(n0, n1, n2){
  n<-n0+n1+n2
  pD<-(n2+n1/2)/n

  LRT.stat<-ifelse(4*n0*n2>n1^2,
                   2*log( (n0/(n*(1-pD)^2))^n0*(n1/(n*2*pD*(1-pD)))^n1*(n2/(n*pD^2))^n2 ),
                   0 )

  A1<-2*log( ((1-pD)/(1/2))^(2*n0) * (pD*(1-pD)/((1/2)*(1-1/2)))^(n1) * (pD/(1/2))^(2*n2))

  LRT.linkage<-A1 + LRT.stat
  pval<-1/2*pchisq(LRT.linkage, 2, lower.tail = F) + 1/2*pchisq(LRT.linkage, 1, lower.tail = F)

  return(list(chisq.stat=LRT.linkage, pval=pval))
}