markerSearchPower {markerSearchPower}R Documentation

Function of power calculation

Description

Analytically calculate statistical power for three model selection methods in genome-wide association studies: marginal selection, exhaustive search, and forward selection. Power definitions are (A) the probability of identifying exactly the true model (in marginal selection, it is the probability of detecting both true markers); and (b) the probability of detecting at least one of the true markers.

Usage

markerSearchPower(mainEff1, mainEff2, epistasisEff, noiseSD, alleleFreq1, alleleFreq2, 
                 alleleFreq3 = 0.5, DetectionN, obsN, markerN, 
                 strategy = c("marginal", "exhaustive", "forward"), 
                 powerDef = c("both", "either"), samplePointN = 20000,
                 decompMethod = c("svd", "chol", "eigen"))

Arguments

mainEff1 The main effect of associated marker 1. It is represented by b1 in the true genetic model. See Details below.
mainEff2 The main effect of associated marker 2. It is represented by b2 in the true genetic model. See Details below.
epistasisEff The epistatic effect (interaction) between markers 1 and 2. It is represented by b3 in the true genetic model.
noiseSD The standard deviation of noise term.
alleleFreq1 The frequency of the effective allele at marker 1.
alleleFreq2 The frequency of the effective allele at marker 2.
alleleFreq3 Allele frequency of other non-associated markers. This value has little effect on power calculation.
DetectionN The number of top models selected. For power of detecting both associated markers in marginal selection, DetectionN >= 2.
obsN Sample size.
markerN Number of markers genptyped.
strategy The stratgy of marker searching: "marginal", "exhaustive", or "forward". Default is "marginal".
powerDef Definition of power. Either "all" indicates the probability of identifying exactly the true model (in marginal selection, it is the probability of detecting both true markers); or "either" indicates the probability of detecting at least one of the true markers.
samplePointN Number of random points for Monte Carlo integration. Default is 20,000.
decompMethod Matrix decomposition used to determine the matrix root of sigma, possible methods are singular value decomposition ("svd", default), eigenvalue decomposition ("eigen"), and Cholesky decomposition ("chol"). This argument is only useful for forward selection identifying either true SNP.

Details

The power calculation is based on a hypothetical true underlying genetic model of a two biallelic marker system for a quantitative trait: y = b0 + b1*X1 + b2*X2 + b3*X1*X2 + noise. Noise has normal distribution with mean zero and standard deviation noiseSD. X1 and X2 are the genotypes of markers 1 and 2, respectively. Genotype values are based on the assumption of additive allelic effect: it is equal to the number of copies of the effective allele. For the main covariates, the signs of coefficients b1 and b2 illustrate the direction of effective alleles of markers 1 and 2. The coefficient b3 for the interaction term represents the direction and magnitude of epistasis. The power calculation for binary trait is under development.

Value

The power of a given marker search strategy under a given definition either (A) or (B).

Author(s)

Zheyang Wu and Hongyu Zhao (Maintainer: Zheyang Wu <zheyang.wu@yale.edu>)

References

Zheyang Wu and Hongyu Zhao (2009) Statistical Power of Model Selection Strategies for Genome-Wide Association Studies. Submitted.

Examples


markerSearchPower (mainEff1=0.1, mainEff2=0.1, epistasisEff=2.4, noiseSD=sqrt(3), 
     alleleFreq1=0.7, alleleFreq2=0.7, DetectionN=2, obsN=100, markerN=300);
markerSearchPower (mainEff1=0.1, mainEff2=0.1, epistasisEff=2.4, noiseSD=sqrt(3), 
     alleleFreq1=0.7, alleleFreq2=0.7, DetectionN=1, obsN=100, markerN=300, 
     powerDef = "either");
markerSearchPower (mainEff1=0.1, mainEff2=0.1, epistasisEff=1.4, noiseSD=sqrt(3), 
     alleleFreq1=0.7, alleleFreq2=0.7, DetectionN=1, obsN=100, markerN=300, 
     strategy = "exhaustive", powerDef = "either");
markerSearchPower (mainEff1=0.1, mainEff2=0.1, epistasisEff=1.4, noiseSD=sqrt(3), 
     alleleFreq1=0.7, alleleFreq2=0.7, DetectionN=1, obsN=100, markerN=300, 
     strategy = "exhaustive", powerDef = "both");
markerSearchPower (mainEff1=0.1, mainEff2=0.1, epistasisEff=1.4, noiseSD=sqrt(3), 
     alleleFreq1=0.7, alleleFreq2=0.7, DetectionN=5, obsN=100, markerN=300, 
     strategy = "forward", powerDef = "both");
markerSearchPower (mainEff1=0.1, mainEff2=0.1, epistasisEff=1.4, noiseSD=sqrt(3), 
     alleleFreq1=0.7, alleleFreq2=0.7, DetectionN=5, obsN=100, markerN=300, 
     strategy = "forward", powerDef = "either");


[Package markerSearchPower version 1.0 Index]