L4-power
Hae Kyung Im
2020-01-14
Last updated: 2020-01-15
Checks: 5 1
Knit directory: hgen471/
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library(tidyverse)Registered S3 methods overwritten by 'ggplot2':
method from
[.quosures rlang
c.quosures rlang
print.quosures rlang── Attaching packages ───────────────────────────── tidyverse 1.2.1 ──✔ ggplot2 3.1.1 ✔ purrr 0.3.2
✔ tibble 2.1.2 ✔ dplyr 0.8.1
✔ tidyr 0.8.3 ✔ stringr 1.4.0
✔ readr 1.3.1 ✔ forcats 0.4.0── Conflicts ──────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()fastlm = function(xx,yy)
{
## compute betahat (regression coef) and pvalue with Ftest
## for now it does not take covariates
df1 = 2
df0 = 1
ind = !is.na(xx) & !is.na(yy)
xx = xx[ind]
yy = yy[ind]
n = sum(ind)
xbar = mean(xx)
ybar = mean(yy)
xx = xx - xbar
yy = yy - ybar
SXX = sum( xx^2 )
SYY = sum( yy^2 )
SXY = sum( xx * yy )
betahat = SXY / SXX
RSS1 = sum( ( yy - xx * betahat )^2 )
RSS0 = SYY
fstat = ( ( RSS0 - RSS1 ) / ( df1 - df0 ) ) / ( RSS1 / ( n - df1 ) )
pval = 1 - pf(fstat, df1 = ( df1 - df0 ), df2 = ( n - df1 ))
res = list(betahat = betahat, pval = pval)
return(res)
}power calculation - simulate Y=phenotype under null and alternative
nsim = 10000
nsam = 1000
maf = 0.30
r2 = 0.01 ## effect size is calculated as r2 = beta^2 *2*maf*(1-maf)
sig2Y = 1
beta = sqrt( r2 * sig2Y / (2*maf*(1-maf)) )
sig2epsi = sig2Y * (1 - r2)
simpower = function(nsim,nsam,maf,beta)
{
Xfather = matrix( rbinom(nsam * nsim,1,maf), nsam, nsim )
Xmother = matrix( rbinom(nsam * nsim,1,maf), nsam, nsim )
Xboth = Xfather+ Xmother
Yalt = matrix( rnorm(nsam*nsim), nsam, nsim)*sig2epsi + Xboth * beta
Ynull = matrix( rnorm(nsam*nsim), nsam, nsim)*sig2Y
return(list(Yalt=Yalt, Ynull=Ynull, Xmat=Xboth))
}
simp = simpower(nsim,nsam,maf,beta)define some functions
runassoc = function(X,Y)
{
pvec = rep(NA,ncol(X))
bvec = rep(NA,ncol(X))
for(ss in 1:ncol(X))
{
fit = fastlm(X[,ss], Y[,ss])
pvec[ss] = fit$pval
bvec[ss] = fit$betahat
}
list(pvec=pvec, bvec=bvec)
}
p2z = function(b,p)
{
## calculate zscore from p-value and sign of effect size
sign(b) * abs(qnorm(p/2))
}
calcz = function(X,Y)
{
tempo = runassoc(X,Y)
p2z(tempo$bvec,tempo$pvec)
}calculate test statistics under the null and alternative
Zalt = calcz(simp$Xmat, simp$Yalt)
Znull = calcz(simp$Xmat, simp$Ynull)
tibble(Y = c(Zalt,Znull), type=c(rep("alt",length(Zalt)),rep("null",length(Znull))) ) %>% ggplot(aes(Y,fill=type)) + geom_density(color=NA,alpha=0.6) + theme_bw(base_size = 15)
calculate power
## define significance level
alpha = 0.01
## find threshold for rejection; we want P(Znull > alpha/2) two-sided
threshold = quantile(Znull, 1 - alpha/2)
## calculate proportion of Zalt above threshold
mean(Zalt > threshold)[1] 0.7341
sessionInfo()R version 3.6.0 (2019-04-26)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Mojave 10.14.6
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] forcats_0.4.0 stringr_1.4.0 dplyr_0.8.1 purrr_0.3.2
[5] readr_1.3.1 tidyr_0.8.3 tibble_2.1.2 ggplot2_3.1.1
[9] tidyverse_1.2.1
loaded via a namespace (and not attached):
[1] Rcpp_1.0.2 cellranger_1.1.0 plyr_1.8.4 pillar_1.4.1
[5] compiler_3.6.0 git2r_0.25.2 workflowr_1.3.0 tools_3.6.0
[9] digest_0.6.19 lubridate_1.7.4 jsonlite_1.6 evaluate_0.14
[13] nlme_3.1-139 gtable_0.3.0 lattice_0.20-38 pkgconfig_2.0.2
[17] rlang_0.4.1 cli_1.1.0 rstudioapi_0.10 yaml_2.2.0
[21] haven_2.1.0 xfun_0.7 withr_2.1.2 xml2_1.2.0
[25] httr_1.4.0 knitr_1.23 hms_0.4.2 generics_0.0.2
[29] fs_1.3.1 rprojroot_1.3-2 grid_3.6.0 tidyselect_0.2.5
[33] glue_1.3.1 R6_2.4.0 readxl_1.3.1 rmarkdown_1.13
[37] modelr_0.1.4 magrittr_1.5 backports_1.1.4 scales_1.0.0
[41] htmltools_0.4.0 rvest_0.3.4 assertthat_0.2.1 colorspace_1.4-1
[45] labeling_0.3 stringi_1.4.3 lazyeval_0.2.2 munsell_0.5.0
[49] broom_0.5.2 crayon_1.3.4