haplo.stats (version 1.7.6)

haplo.power.qt: 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.

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

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).

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)