Power_Continuous | R Documentation |

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 |

`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 |

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)

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