haplo.power.qt: Compute either power or sample size for haplotype...

In haplo.stats: Statistical Analysis of Haplotypes with Traits and Covariates when Linkage Phase is Ambiguous

Compute either power or sample size for haplotype associations with a quantitative trait.

Description

For a given set of haplotypes, their population frequencies, and assumed linear regression coefficients (additive model of haplotype effects on a quantitative trait), determine either the sample size to achieve a stated power or the power for a stated sample size.

Usage

haplo.power.qt(haplo, haplo.freq, base.index, haplo.beta, y.mu, y.var,
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 amount of expected change per haplotype from the base-line average, and the beta for the base-line (indexed by base.index) is the beta for the intercept.
y.mu	population mean of quantitative trait, y.
y.var	popultaion variance of quantitative trait, y.
alpha	type-I error rate
sample.size	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 F 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.qt) 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

find.haplo.beta.qt, haplo.em, haplo.power.cc

Examples

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

# Because it can be easier to speficy genetic effect size in terms of
# a regression model R-squared value (r2), we use an
# auxiliary function to set up haplo.beta based on a specifed r2 value:

tmp <- find.haplo.beta.qt(haplo,haplo.freq,base.index,haplo.risk,
r2=0.01, y.mu=0, y.var=1)

haplo.beta <- tmp$beta  

# Compute sample size for given power

haplo.power.qt(haplo, haplo.freq, base.index, haplo.beta, y.mu=0,
y.var=1, alpha=.05, power=.80) 

# Compute power for given sample size

haplo.power.qt(haplo, haplo.freq, base.index, haplo.beta, y.mu=0,
y.var=1, alpha=.05, sample.size = 2091)  

haplo.stats documentation built on May 29, 2024, 9:53 a.m.