pbsize: Power for population-based association design

In gap: Genetic Analysis Package

Power for population-based association design

Description

Power for population-based association design

Usage

pbsize(kp, gamma = 4.5, p = 0.15, alpha = 5e-08, beta = 0.2)

Arguments

kp	population disease prevalence.
gamma	genotype relative risk assuming multiplicative model.
p	frequency of disease allele.
alpha	type I error rate.
beta	type II error rate.

Details

This function implements \insertCitesph97;textualgap statistics for population-based association design. This is based on a contingency table test and accurate level of significance can be obtained by Fisher's exact test.

Value

The returned value is scaler containing the required sample size.

Author(s)

Jing Hua Zhao extracted from rm.c.

References

\insertAllCited

Long AD, Grote MN, Langley CH (1997). Genetic analysis of complex traits. Science 275: 1328.

\insertRef

rosner00gap

\insertRef

armitage05gap

See Also

fbsize

Examples

kp <- c(0.01,0.05,0.10,0.2)
models <- matrix(c(
    4.0, 0.01,
    4.0, 0.10,
    4.0, 0.50, 
    4.0, 0.80,
    2.0, 0.01,
    2.0, 0.10,
    2.0, 0.50,
    2.0, 0.80,
    1.5, 0.01,    
    1.5, 0.10,
    1.5, 0.50,
    1.5, 0.80), ncol=2, byrow=TRUE)
outfile <- "pbsize.txt"
cat("gamma","p","p1","p5","p10","p20\n",sep="\t",file=outfile)
for(i in 1:dim(models)[1])
{
  g <- models[i,1]
  p <- models[i,2]
  n <- vector()
  for(k in kp) n <- c(n,ceiling(pbsize(k,g,p)))
  cat(models[i,1:2],n,sep="\t",file=outfile,append=TRUE)
  cat("\n",file=outfile,append=TRUE)
} 
table5 <- read.table(outfile,header=TRUE,sep="\t")
unlink(outfile)

# Alzheimer's disease
g <- 4.5
p <- 0.15
alpha <- 5e-8
beta <- 0.2
z1alpha <- qnorm(1-alpha/2)   # 5.45
z1beta <- qnorm(1-beta)
q <- 1-p
pi <- 0.065                   # 0.07 and zbeta generate 163
k <- pi*(g*p+q)^2
s <- (1-pi*g^2)*p^2+(1-pi*g)*2*p*q+(1-pi)*q^2
# LGL formula
lambda <- pi*(g^2*p+q-(g*p+q)^2)/(1-pi*(g*p+q)^2)
# mine
lambda <- pi*p*q*(g-1)^2/(1-k)
n <- (z1alpha+z1beta)^2/lambda
cat("\nPopulation-based result: Kp =",k, "Kq =",s, "n =",ceiling(n),"\n")

gap documentation built on Aug. 26, 2023, 5:07 p.m.