R/LD.R

In genetics: Population Genetics

# $Id: LD.R 453 2005-11-09 17:04:02Z warnes $

# R translation of Cathy Stack's SAS macro
# Assumes 2-alleles

LD <- function(g1,...)
  UseMethod("LD",g1)

LD.data.frame <- function(g1,...)
  {
    gvars <- sapply( g1, function(x) (is.genotype(x) && nallele(x)==2) )
    if(any(gvars==FALSE))
      {
        warning("Non-genotype variables or genotype variables ",
                "with more or less than two alleles detected. ",
                "These variables will be omitted: ",                
                paste( colnames(g1)[!gvars] , collapse=", " )
                )
        g1 <- g1[,gvars]
      }
    

    P <- matrix(nrow=ncol(g1),ncol=ncol(g1))
    rownames(P) <- colnames(g1)
    colnames(P) <- colnames(g1)

    P <- D <- Dprime <- nobs <- chisq <- p.value <- corr <- R.2 <- P

    for(i in 1:(ncol(g1)-1) )
      for(j in (i+1):ncol(g1) )
        {
          ld <- LD( g1[,i], g1[,j] )
          
          D      [i,j] <- ld$D
          Dprime [i,j] <- ld$"D'"
          corr   [i,j] <- ld$"r"
          R.2    [i,j] <- ld$"R^2"          
          nobs   [i,j] <- ld$"n"
          chisq  [i,j] <- ld$"X^2"
          p.value[i,j] <- ld$"P-value"
        }
    
    retval <- list(
                   call=match.call(),
                   "D"=D,
                   "D'"=Dprime,
                   "r" = corr,
                   "R^2" = R.2,
                   "n"=nobs,
                   "X^2"=chisq,
                   "P-value"=p.value
           )

    class(retval) <- "LD.data.frame"
    
    retval
  }

LD.genotype <- function(g1,g2,...)
  {
    if(is.haplotype(g1) || is.haplotype(g2))
      stop("Haplotype options are not yet supported.")
    
    if(nallele(g1)!=2 || nallele(g2)!=2)
      stop("This function currently only supports 2-allele genotypes.")

    prop.A <- summary(g1)$allele.freq[,2]
    prop.B <- summary(g2)$allele.freq[,2]
    
    major.A <- names(prop.A)[which.max(prop.A)]
    major.B <- names(prop.B)[which.max(prop.B)]
    pA <- max(prop.A, na.rm=TRUE)
    pB <- max(prop.B, na.rm=TRUE)
    pa <- 1-pA
    pb <- 1-pB

    Dmin <- max(-pA*pB, -pa*pb)
    pmin <- pA*pB + Dmin;

    Dmax <- min(pA*pb, pB*pa);
    pmax <- pA*pB + Dmax;

    counts <- table(
                    allele.count(g1, major.A),
                    allele.count(g2, major.B)
                    )

    n3x3 <- matrix(0, nrow=3, ncol=3)
    colnames(n3x3) <- rownames(n3x3) <- 0:2

    # ensure the matrix is 3x3, with highest frequency values in upper left
    for(i in rownames(counts))
      for(j in colnames(counts))
        n3x3[3-as.numeric(i),3-as.numeric(j)] <- counts[i,j]

    
    loglik <- function(pAB,...)
      {
        (2*n3x3[1,1]+n3x3[1,2]+n3x3[2,1])*log(pAB) +
        (2*n3x3[1,3]+n3x3[1,2]+n3x3[2,3])*log(pA-pAB) +
        (2*n3x3[3,1]+n3x3[2,1]+n3x3[3,2])*log(pB-pAB) +
        (2*n3x3[3,3]+n3x3[3,2]+n3x3[2,3])*log(1-pA-pB+pAB) + 
        n3x3[2,2]*log(pAB*(1-pA-pB+pAB) + (pA-pAB)*(pB-pAB))
      }

    # SAS code uses:
    #
    #s <- seq(pmin+0.0001,pmax-0.0001,by=0.0001)
    #lldmx <- loglik(s)
    #maxi <- which.max(lldmx)
    #pAB <- s[maxi]

    # but this should be faster:
    solution <- optimize(
                         loglik,
                         lower=pmin+.Machine$double.eps,
                         upper=pmax-.Machine$double.eps,
                         maximum=TRUE
                         )
    pAB <- solution$maximum

    estD <- pAB - pA*pB
    if (estD>0)  
      estDp <- estD / Dmax
    else
      estDp <- estD / Dmin

    n <-  sum(n3x3)

    corr <- estD / sqrt( pA * pB * pa * pb )
    
    dchi <- (2*n*estD^2)/(pA * pa * pB* pb)
    dpval <- 1 - pchisq(dchi,1)

    retval <- list(
                   call=match.call(),
                   "D"=estD,
                   "D'"=estDp,
                   "r" = corr,
                   "R^2" = corr^2,
                   "n"=n,
                   "X^2"=dchi,
                   "P-value"=dpval
                   )

    class(retval) <- "LD"
    
    retval
    
  }