powerEQTL.ANOVA: Power Calculation for EQTL Analysis Based on Un-Balanced...
In sterding/powerEQTL: Power and Sample Size Calculation for eQTL Analysis

Description Usage Arguments Details Value Author(s) References See Also Examples

Power calculation for eQTL analysis that tests if a SNP is associated to a gene probe by using un-balanced one-way ANOVA.

powerEQTL.ANOVA(MAF,
                typeI = 0.05,
                nTests = 2e+05,
                myntotal = 200,
                mystddev = 0.13,
                deltaVec = c(0.13, 0.13),
                verbose = TRUE)

`MAF`	Minor allele frequency.
`typeI`	Type I error rate for testing if a SNP is associated to a gene probe.
`nTests`	integer. Number of tests in eQTL analysis.
`myntotal`	integer. Number of subjects.
`mystddev`	Standard deviation of gene expression levels in one group of subjects. Assume all 3 groups of subjects (mutation homozygote, heterozygote, wild-type homozygote) have the same standard deviation of gene expression levels.
`deltaVec`	A vector having 2 elements. The first element is equal to mu_2 - mu_1 and the second elementis equalt to mu_3 - mu_2, where mu_1 is the mean gene expression level for the mutation homozygotes, mu_2 is the mean gene expression level for the heterozygotes, and mu_3 is the mean gene expression level for the wild-type gene expression level.
`verbose`	logic. indicating if intermediate results should be output.

The assumption of the ANOVA approach is that the association of a SNP to a gene probe is tested by using un-balanced one-way ANOVA (e.g. Lonsdale et al. 2013). According to SAS online document https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_power_a0000000982.htm, the power calculation formula is

power = Pr(F >= F(1 - alpha, k - 1, N - k)| F ~ F(k - 1, N - k, lambda)),

where k = 3 is the number of groups of subjects, N is the total number of subjects, F_{1 - alpha}(k - 1, N - k) is the 100 * (1 - alpha)-th percentile of central F distribution with degrees of freedoms k - 1 and N - k, and F_{k - 1, N - k, lambda} is the non-central F distribution with degrees of freedoms k - 1 and N - k and non-central parameter (ncp) lambda. The ncp lambda is equal to

lambda = N * sum(wi * (mu_i - mu)^2, i = 1,.., k)/sigma^2,

where mu_i is the mean gene expression level for the i-th group of subjects, w_i is the weight for the i-th group of subjects, sigma^2 is the variance of the random errors in ANOVA (assuming each group has equal variance), and mu is the weighted mean gene expression level

mu = sum(w_i * mu_i, i = 1, ..., k).

The weights w_i are the sample proportions for the 3 groups of subjects. Hence, sum(w_i, i = 1, 2, 3) = 1.

power of the test after Bonferroni correction for multiple testing.

Xianjun Dong <XDONG@rics.bwh.harvard.edu>, Tzuu-Wang Chang <Chang.Tzuu-Wang@mgh.harvard.edu>, Scott T. Weiss <restw@channing.harvard.edu>, Weiliang Qiu <stwxq@channing.harvard.edu>

Lonsdale J and Thomas J, et al. The Genotype-Tissue Expression (GTEx) project. Nature Genetics, 45:580-585, 2013.

minEffectEQTL.ANOVA, powerEQTL.ANOVA2, ssEQTL.ANOVA, ssEQTL.ANOVA2

powerEQTL.ANOVA(
          MAF = 0.1,
          typeI = 0.05,
          nTests = 200000,
          myntotal = 234,
          mystddev = 0.13,
          deltaVec = c(0.13, 0.13))