power.bc {qtlDesign}R Documentation

Power calculations for Backcross

Description

Power calculation and minimum detectable effect sizes for backcross

Usage

power.bc(n, prop, thresh = 3, alpha = 1, theta = 0, effective.n = FALSE)
detectable.bc(n, power=0.8, thresh = 3, alpha = 1, theta = 0, delta = FALSE)

Arguments

n Sample size
prop Proportion of variance explained by the QTL
power Desired power level
thresh LOD threshold for declaring significance
alpha Selection fraction
theta Width of marker interval
effective.n Logical flag indicating whether effective sample size should be returned
delta Logical flag indicating whether the QTL effect should be returned instead of proportion variance explained

Details

These calculations are done assuming that the asymptotic chi-square regimes apply. The function will not work if the effective sample size is less than 30. First we calculate the effective sample size using the width of the marker interval and the selection fraction. The QTL is assumed to be in the middle of the marker interval. Then we use the fact that the non-centrality parameter of the likelihood ration test is m*delta^2, where m is the effctive sample size and delta is the QTL effect measured as the deviation of the genotype means from the overall mean. The chi-squared approximation is used to calculate the power. The minimum detectable effect size (measured in proportion variance explained or the QTL effect) is obtained by numerical equation solving using uniroot.

Value

For power.bc the power is returned, unless the flag effective.n is set to TRUE in which case a list with values

power Power of detecting QTL
effective.n Effective sample size

is returned.
For detectable.bc the minimum detectable proportion of variance explained is returned, unless the flag delta is set to TRUE in which case the QTL effect size is returned.

Author(s)

Saunak Sen, Jaya Satagopan, and Gary Churchill

References

Sen, Satagopan, and Churchill (2004), QTL study design from an information perspective, http://repositories.cdlib.org/cbmb/QTLdesign.

See Also

uniroot

Examples

power.bc(100,0.2,alpha=0.5,theta=0.1)
detectable.bc(100,0.8,alpha=0.5,theta=0.1)

[Package qtlDesign version 0.32 Index]