power.casectrl {GeneticsDesign}R Documentation

Power for case-control genetics study

Description

Calculate power for case-control genetics study

Usage

power.casectrl(N, gamma = 4.5, p = 0.15, kp = 0.1, alpha = 0.05, fc = 0.5,
                minh = c("multiplicative", "dominant", "recessive", "partialrecessive") )

Arguments

N total number of subjects
gamma Relative risk in multiplicative model. Not used in Dominant or Recessive model.
p frequency of A (protective) allele
kp prevalence of disease
alpha significance level
fc fraction of cases
minh mode of inheritance, one of "multiplicative", "dominant", "recessive", or "partialrecessive"

Details

under HWE                       AA       Aa       aa
  fHW = p(genotype)        = c( p^2,     2pq,     q^2 )

model specification
  f.mod = relative risk    = c(gamma^2,  gamma,    1 )    #   multiplicative model
  f.mod =                  = c(  0,        0,      1 )    #         dominant model
  f.mod =                  = c(  0,        1,      1 )    #        recessive model
  f.mod =                  = c(gamma,      1,      1 )    # partialrecessive model
conditional prob.
  p(D|genotype) = f.mod*pi = c(gamma^2,  gamma,    1 )*pi

population joint prob. (f.mod = 1 under Ho)
  Case     p(D,     genotype) = p(genotype)*     p(D|genotype)  = fHW*   f.mod*pi
  Control  p(D_not, genotype) = p(genotype)*(1 - p(D|genotype)) = fHW*(1-f.mod*pi)

population conditional prob. (f.mod = 1 under Ho)
  Case     p(genotype|D)     = p(D    , genotype)/P(D    ) = P(D    , genotype)/sum(P(D    , genotype)) = fHW*   f.mod*pi  /    sum(fHW*f.mod*pi)
  Control  p(genotype|D_not) = p(D_not, genotype)/P(D_not) = P(D_not, genotype)/sum(P(D_not, genotype)) = fHW*(1-f.mod*pi) / (1-sum(fHW*f.mod*pi))

sample or allocation probability
  1:1 case-control design  p(D|Sample) = fc = 1/2
  1:2 case-control design                fc = 1/3
  a prospective design                   fc = sum(fHW*f.mod*pi)

sample joint prob. (f.mod = 1 under Ho)
for prospective design, this is the same as population joint prob. since 'fc' cancels out with 'sum(fHW*f.mod*pi)'
  Case     p(genotype,D    |sample) = p(genotype|D    )*     p(D|Sample)  =    fc *fHW*   f.mod*pi  /    sum(fHW*f.mod*pi)
  Control  p(genotype,D_not|sample) = p(genotype|D_not)*(1 - p(D|Sample)) = (1-fc)*fHW*(1-f.mod*pi) / (1-sum(fHW*f.mod*pi))

Value

power for the specified parameter values.

Author(s)

Michael Man /email{Michael.Man@pfizer.com}

References

Long, A. D. and C. H. Langley (1997). Genetic analysis of complex traits. Science 275: 1328.

Examples


# single calc
power.casectrl(p=0.1, N=50, gamma=1.1, kp=.1, alpha=5e-2, minh='r')

# for a range of sample sizes
power.casectrl(p=0.1, N=c(25,50,100,200,500), gamma=1.1, kp=.1,
              alpha=5e-2, minh='r')

# create a power table
fun <- function(p)
  power.casectrl(p=p, N=seq(100,1000,by=100), gamma=1.1, kp=.1,
                alpha=5e-2, minh='recessive')

m <- sapply( X=seq(0.1,0.9, by=0.1), fun )
colnames(m) <- seq(0.1,0.9, by=0.1)
rownames(m) <- seq(100,1000,by=100)

print(round(m,2))

[Package GeneticsDesign version 1.4.0 Index]