AssocAFC (version 1.0.2)

Wqls: W Quasi-Likelihood Score

Description

The W Quasi-Likelihood Score, Wqls(), is a score for multiple rare variant association tests using the difference of the sum of minor allele frequencies between cases and controls. This test handles related individuals, unrelated individuals, or both. This test is expected to be similar to a linear mixed model.

Usage

Wqls(Genotypes, MAF, Pheno, Kin, Correlation, Weights)

Arguments

Genotypes

matrix(#Subjects * #Snps). The genotypes are coded as 0, 1, or 2 copies of the minor allele.

MAF

matrix (#Snps * 2): First column contains Minor Allele Frequency (MAF) in cases; Second column contains MAF in controls.

Pheno

matrix (#subjects * 1): this one-column matrix contains 0's amd 1's: 1 for cases and 0 for controls. No missing values are allowed.

Kin

The kinship matrix (#subjects * #subjects): the subjects must be ordered as the Pheno variable.

Correlation

Correlation matrix between SNPs (#Snps * #Snps). The user should calculate this matrix beforehand. Either based on own genotype data (in cases, controls, or both) or based on public databases (e.g., 1000 Genomes Projects, ESP, etc.). NA values are not allowed. They have to be replaced by zeros.

Weights

The weights values that can be used to up-weight or down-weight SNPs. This size of this vector is the number of Snps by 1. By default, the weights are 1 for all Snps.

Value

A vector with the following values: the sum of MAF for cases, the sum of MAF for controls, the sum of MAF for all weighted by the phenotype, the numerator of the test, the denominator of the test, the Wqls value (the main value calculated by the test), and the P-value.

References

Saad M and Wijsman EM, Association score testing for rare variants and binary traits in family data with shared controls, Briefings in Bioinformatics, 2017. Bourgain C , Hoffjan S , Nicolae R , et al. Novel case-control test in a founder population identifies P-selectin as an atopy-susceptibility locus . Am J Hum Genet 2003 ;73 :612 <U+2013>26. Thornton T , McPeek MS. Case-control association testing with related individuals: a more powerful quasi-likelihood score test. Am J Hum Genet 2007 ;81 :321 <U+2013>37.

See Also

AssocAFC Wcorrected afcSKAT

Examples

# NOT RUN {
P_WQLS <- vector("numeric")
#This data corresponds to what is used in the 1st iteration with the raw data
data("geno.afc")
data("maf.afc")
data("phenotype.afc")
data("kin.afc")
data("cor.afc")
data("weights.afc")
QLS <- Wqls(Genotypes = geno.afc, MAF = maf.afc, Pheno = phenotype.afc, Kin = kin.afc,
                                        Correlation = cor.afc, Weights = weights.afc)
P_WQLS <- c(P_WQLS, QLS[7])
print(P_WQLS)

# }
# NOT RUN {
#This example shows processing the raw data and uses kinship2,
#which AFC does not depend on

library(kinship2)
library(CompQuadForm)

P_WQLS <- vector("numeric")

for (j in 1:10)
{
  geno.afc <- read.table(system.file("extdata", "Additive_Genotyped_Truncated.txt",
                         package = "AFC"), header = TRUE)
  geno.afc[ , "IID"] <- paste(geno.afc[ , "FID"]  , geno.afc[ , "IID"]  ,sep=".")
  geno.afc[geno.afc[,"FA"]!=0 , "FA"] <- paste(geno.afc[geno.afc[,"FA"]!=0 , "FID"],
                                      geno.afc[geno.afc[,"FA"]!=0 , "FA"]  ,sep=".")
  geno.afc[geno.afc[,"FA"]!=0 , "MO"] <- paste(geno.afc[geno.afc[,"FA"]!=0 , "FID"],
                                      geno.afc[geno.afc[,"FA"]!=0 , "MO"]  ,sep=".")
  Kinship <- makekinship(geno.afc$FID , geno.afc$IID , geno.afc$FA, geno.afc$MO)
  kin.afc <- as.matrix(Kinship)
  pheno.afc <- read.table(system.file("extdata", "Phenotype", package = "AFC"))
  phenotype.afc <- matrix(pheno.afc[,j],nc=1,nr=nrow(pheno.afc))
  geno.afc <- geno.afc[,7:ncol(geno.afc)]
  Na <- nrow(pheno.afc[pheno.afc[,j]==1,])
  Nu <- nrow(pheno.afc[pheno.afc[,j]==0,])
  N <- Nu + Na
  maf.afc <- matrix(NA , nr=ncol(geno.afc) , nc=2)
  maf.afc[,1] <- colMeans(geno.afc[phenotype.afc==1,])/2;
  maf.afc[,2] <- colMeans(geno.afc[phenotype.afc==0,])/2;
  P  <- (maf.afc[,1]*Na + maf.afc[,2]*Nu)/N
  Set <- which(P<0.05)
  maf.afc <- maf.afc[c(Set),]
  cor.afc <- cor(geno.afc[,c(Set)])
  cor.afc[is.na(cor.afc)] <- 0
  geno.afc <- as.matrix(geno.afc[,Set])
  weights.afc <- matrix(1/(maf.afc[,2]+1),nc=1,nr=length(Set))
  QLS <- Wqls(Genotypes = geno.afc, MAF = maf.afc, Pheno = phenotype.afc, Kin = kin.afc,
                                        Correlation = cor.afc, Weights = weights.afc)
  P_WQLS <- c(P_WQLS, QLS[7])
}
print(P_WQLS)
# }
# NOT RUN {
## The function is currently defined as
function(Genotypes, MAF, Pheno, Kin, Correlation, Weights)
{
  Na     <- length(Pheno[Pheno[,1]==1,])
  Nu     <- length(Pheno[Pheno[,1]==0,])
  N      <- Na + Nu

  # The three following lines: prepare the Phenotype variables
  OneN  <- matrix(1, ncol=1, nrow = N)
  Y  <- Pheno
  OneHat <- matrix( Na/N, ncol=1 , nrow=N)
  temp <- Y - OneHat

  # Estimate MAF in all subjects
  P  <- (MAF[,1]*Na + MAF[,2]*Nu)/N
  # Number of Snps
  Nsnps   <- nrow(MAF)
  if (is.null(Weights))
  {
    # Variance of SNPs (2p(1-p))
    VarSnps <- sqrt(P*(1-P))
  } else
  {
    # Variance of SNPs (2p(1-p)) accounting for the prespecified Snp weights
    VarSnps <- Weights*sqrt(P*(1-P))
  }
  VarSnps <- matrix(VarSnps,ncol=1)
  # This value will account for the correlation between Snps.
  cs      <- 2*t(VarSnps) %*% Correlation %*% VarSnps

  if (Nsnps==1)
  {
    S<-Genotypes
  }else
  {
    if (is.null(Weights))
    {
      # Rare variant score: sum of minor alleles accross all Snps.
      S <- apply(Genotypes , 1 , sum)
    }else
    {
      # Rare variant score: sum of minor alleles accross all Snps.
      S <- Genotypes %*% Weights
    }
  }
  S <- matrix(S,ncol=1,nrow=length(S))
  Kin <- 2*Kin
  KinInv <- solve(Kin)
  A <- as.numeric(t(Y) %*% KinInv %*% OneN %*% solve(t(OneN) %*% KinInv %*% OneN))
  V <- KinInv %*% Y - A * KinInv %*% OneN
  if (is.null(Weights))
  {
    num <- (sum((S[Y==1]) * rowSums(KinInv[Y==1,Y==1]))*(1-A) -2*sum(MAF[,2])*(A)*Nu)^2;
  }else
  {
    num <- (sum((S[Y==1]) * rowSums(KinInv[Y==1,Y==1]))*(1-A) -2*sum(Weights*MAF[,2])*(A)*Nu)^2;
  }
  denom <- as.numeric(cs) * (t(V)%*% Kin %*% V) ;
  W <- num/denom ;
  Pvalue <- 1-pchisq(W,1) ;
  out <- t(data.frame(c(sum(MAF[,1]), sum(MAF[,2]), sum(P), num, denom, W, Pvalue)))
  colnames(out) <- c("Sum MAF Cases", "Sum MAF Controls", "Sum MAF All Weighted", "Numerator",
                     "Denominator", "Wqls", "Pvalue")
  rownames(out) <- "Statistics"
  return(out)
}
# }