Compute either power or sample size for haplotype associations in a case-control study.

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Description

For a given set of haplotypes, their population frequencies, and assumed logistic regression coefficients (log-odds-ratios per haplotype, assuming a log-additive model of haplotype effects), determine either the sample size (total number of subjects) to achieve a stated power or the power for a stated sample size.

Usage

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haplo.power.cc(haplo, haplo.freq, base.index, haplo.beta, case.frac,
prevalence, alpha, sample.size=NULL, power=NULL)

Arguments

haplo

matrix of haplotypes, with rows the different haplotypes and columns the alleles of the haplotypes. For H haplotypes of L loci, haplo has dimension H x L.

haplo.freq

vector of length H for the population haplotype frequencies (corresponding to the rows of haplo)

base.index

integer index of the haplotype considered to be the base-line for logistic regression (index between 1 and H); often, the most common haplotype is chosen for the base-line.

haplo.beta

vector of length H for the haplotype effects: each beta is the log-odds-ratio for the corresponding haplotype effect. The base-line hapoltype should have a beta=0, as this base-line beta coefficient will be automatically calculated according to the haplotype frequencies, the other haplo.beta's, and the disease prevalence.

case.frac

fraction of cases in the total sample size (e.g., case.frac = .5 for typical case-control studies with equal numbers of cases and controls)

prevalence

popultaion disease prevalence (used to calculate the base-line intercept beta)

alpha

type-I error rate

sample.size

total sample size (if power is to be calcualted). Either sample.size or power must be specified, but not both.

power

desired power (if sample.size is to be calculated). Either sample.size or power must be specified, but not both.

Details

Asympotic power calcuations are based on the non-centrality parameter of a non-central chi-square distribution. This non-centrality parameter is determined by the specified regression coefficients ( values in haplo.beta), as well as the distribution of haplotypes (determined by haplo.freq). To account for haplotypes with unknown phase, all possible haplotype pairs are enumerated, and the EM algorithm is used to determine the posterior probabilities of pairs of haplotypes, conditional on unphased genotype data. Because this function uses the function haplo.em, the number of possible haplotypes can be large when there is a large number of loci (i.e., large number of columns in the haplo matrix). If too large, the function haplo.em will run out of memory, making this function (haplo.power.cc) fail. If this occurs, then consider reducing the "size" of the haplotypes, by reducing the number of columns of haplo, and adjusting the corresponding vectors (e.g., haplo.freq, haplo.beta).

Value

list with components:

ss.phased.haplo

sample size for phased haplotypes

ss.unphased.haplo

sample size for unphased haplotypes

power.phased.haplo

power for phased haplotypes

power.unphased.haplo

power for unphased haplotypes

References

Schaid, DJ. Power and sample size for testing associations of haplotypes with complex traits. Ann Hum Genet (2005) 70:116-130.

See Also

haplo.em haplo.power.qt

Examples

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haplo <- rbind(
               c(     1,    2,    2,    1,    2),
               c(     1,    2,    2,    1,    1),
               c(     1,    1,    2,    1,    1),
               c(     1,    2,    1,    1,    2),
               c(     1,    2,    2,    2,    1),
               c(     1,    2,    1,    1,    1),
               c(     1,    1,    2,    2,    1),
               c(     1,    1,    1,    1,    2),
               c(     1,    2,    1,    2,    1),
               c(     1,    1,    1,    2,    1),
               c(     2,    2,    1,    1,    2),
               c(     1,    1,    2,    1,    2),
               c(     1,    1,    2,    2,    2),
               c(     1,    2,    2,    2,    2),
               c(     2,    2,    2,    1,    2),
               c(     1,    1,    1,    1,    1),
               c(     2,    1,    1,    1,    1),
               c(     2,    1,    2,    1,    1),
               c(     2,    2,    1,    1,    1),
               c(     2,    2,    1,    2,    1),
               c(     2,    2,    2,    1,    1))
dimnames(haplo)[[2]] <- paste("loc", 1:ncol(haplo), sep=".")
haplo <- data.frame(haplo)

haplo.freq <- c(0.170020121, 0.162977867, 0.123742455, 0.117706237, 0.097585513, 0.084507042,
                0.045271630, 0.039235412, 0.032193159, 0.019114688, 0.019114688, 0.013078471,
                0.013078471, 0.013078471, 0.013078471, 0.006036217, 0.006036217, 0.006036217,
                0.006036217, 0.006036217, 0.006036217)

# define index for risk haplotypes (having alleles 1-1 at loci 2 and 3)
haplo.risk <- (1:nrow(haplo))[haplo$loc.2==1 & haplo$loc.3==1]

# define index for baseline haplotype
base.index <-  1

# specify OR for risk haplotypes
or <- 1.25

# determine beta regression coefficients for risk haplotypes

haplo.beta <- numeric(length(haplo.freq))
haplo.beta[haplo.risk] <-  log(or)

# Note that non-risk haplotypes have beta=0, as does the intercept
# (haplotype with base.index value). 

# Compute total sample size for given power

haplo.power.cc(haplo, haplo.freq, base.index, haplo.beta, case.frac=.5,
prevalence=.1, alpha=.05, power=.8)

# Compute power for given sample size

haplo.power.cc(haplo, haplo.freq, base.index, haplo.beta, case.frac=.5,
prevalence=.1, alpha=.05, sample.size=11978)

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