pbsize {gap}

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 Scott et al. (1997) 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

Scott WK, Pericak-Vance MA, Haines JL (1997). “Genetic analysis of complex diseases.” Science, 275(5304), 1327; author reply 1329-30. ISSN 0036-8075 (Print) 0036-8075.

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

Rosner B (2000). Fundamentals of biostatistics, 5 edition. Duxbury, Pacific Grove, CA. ISBN 9780534370688.

Armitage P, Colton T (eds.) (2005). Encyclopedia of biostatistics, 2 edition. John Wiley, Chichester, West Sussex, England ; Hoboken, NJ. ISBN 9780470849071.

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")