Power_Continuous: Power calculation, continuous traits
In lin-lab/SKAT: SNP-Set (Sequence) Kernel Association Test

Description Usage Arguments Details Value Author(s) Examples

Compute an average power of SKAT and SKAT-O for testing association between a genomic region and continuous phenotypes with a given disease model.

Power_Continuous(Haplotypes=NULL, SNP.Location=NULL, SubRegion.Length=-1
, Causal.Percent=5, Causal.MAF.Cutoff=0.03, alpha =c(0.01,10^(-3),10^(-6))
, N.Sample.ALL = 500 * (1:10), Weight.Param=c(1,25), N.Sim=100
, BetaType = "Log", MaxBeta=1.6, Negative.Percent=0)

 
Power_Continuous_R(Haplotypes=NULL, SNP.Location, SubRegion.Length=-1
, Causal.Percent=5, Causal.MAF.Cutoff=0.03, alpha =c(0.01,10^(-3),10^(-6))
, N.Sample.ALL = 500 * (1:10), Weight.Param=c(1,25), N.Sim=100
, BetaType = "Log", MaxBeta=1.6, Negative.Percent=0, r.corr=0)

`Haplotypes`	a haplotype matrix with each row as a different individual and each column as a separate SNP (default= NULL). Each element of the matrix should be either 0 (major allel) or 1 (minor allele). If NULL, SKAT.haplotype dataset will be used to compute power.
`SNP.Location`	a numeric vector of SNP locations that should be matched with the SNPs in the Haplotype matrix (default= NULL). It is used to obtain subregions. When Haplotype=NULL, it should be NULL.
`SubRegion.Length`	a value of the length of subregions (default= -1). Each subregion will be randomly selected, and then the average power will be calculated by taking the average over the estimated powers of all subregions. If SubRegion.Length=-1 (default), the length of the subregion will be the same as the length of the whole region, so there will no random selection of subregions.
`Causal.Percent`	a value of the percentage of causal SNPs among rare SNPs (MAF < Causal.MAF.Cutoff)(default= 5).
`Causal.MAF.Cutoff`	a value of MAF cutoff for the causal SNPs. Only SNPs that have MAFs smaller than the cutoff will be considered as causal SNPs (default= 0.03).
`alpha`	a vector of the significance levels (default= c(0.01,10^(-3),10^(-6))).
`N.Sample.ALL`	a vector of the sample sizes (default= 500 * (1:10)).
`Weight.Param`	a vector of parameters of beta weights (default= c(1,25)).
`N.Sim`	a value of number of causal SNP/SubRegion sets to be generated to compute the average power (default= 100). Power will be computed for each causal SNP/SubRegion set, and then the average power will be obtained by taking average over the computed powers.
`BetaType`	a type of effect sizes (default= “Log”). “Log” indicates that effect sizes of causal variants equal to c\|log10(MAF)\|, and “Fixed” indicates that effect sizes of all causal variants are the same.
`MaxBeta`	a numeric value of the maximum effect size (default= 1.6). When BetaType="Log", the maximum effect size is MaxBeta (when MAF=0.0001). When BetaType="Fixed", all causal variants have the same effect size (= MaxBeta). See details
`Negative.Percent`	a numeric value of the percentage of coefficients of causal variants that are negative (default= 0).
`r.corr`	(Power_Continuous_R only) the ρ parameter for the compound symmetric correlation kernel (default= 0). See details.

By default it uses the haplotype information in the SKAT.haplotypes dataset. So if you want to use the SKAT.haplotypes dataset, you can left Haplotypes and SNP.Location as NULL.

When BetaType=“Log”, MaxBeta is a coeffecient value (β) of the causal SNP at MAF = 10^{-4} and used to obtain c value of the function c|log10(MAF)|. For example, if MaxBeta=1.6, c = 1.6/4 = 0.4. Then a variant with MAF=0.001 has β = 1.2 and a variant with MAF=0.01 has β = 0.8.

When SubRegion.Length is small such as 3kb or 5kb, it is possible that you can have different estimated power for each run with N.Sim = 50 \sim 100. Then, please increase the N.Sim to 500 \sim 1000 to obtain stable results.

R.sq is computed under the no linkage disequilibrium assumption.

Power_Continuous_R computes power with new class of kernels with the compound symmetric correlation structure. It uses a slightly different approach, and thus Power_Continuous and Power_Continuous_R can produce slightly different results although r.corr=0.

If you want to computer power of SKAT-O by estimating the optimal r.corr, use r.corr=2. The estimated optimal r.corr is r.corr = p_1^2 ( 2p_2-1)^2, where p_1 is a proportion of causal variants, and p_2 is a proportion of negatively associated causal variants among the causal variants.

`Power`	A matrix with each row as a different sample size and each column as a different significance level. Each element of the matrix is the estimated power.
`R.sq`	Proportion of phenotype variance explained by genetic variants.
`r.corr`	r.corr value. When r.corr=2 is used, it provides the estimated r.corr value. See details.

Seunggeun Lee

#
#	Calculate the average power of randomly selected 3kb regions 
#	with the following conditions.
#
#	Causal percent = 20%
#	Negative percent = 20%
#	Max effect size  = 2 at MAF = 10^-4
#
#	When you use this function, please increase N.Sim (more than 100)	
#

out.c<-Power_Continuous(SubRegion.Length=3000, 
Causal.Percent= 20, N.Sim=5, MaxBeta=2,Negative.Percent=20)
out.c

#
#	Calculate the required sample sizes to achieve 80% power

Get_RequiredSampleSize(out.c, Power=0.8)