| ssize.fdr-package {ssize.fdr} | R Documentation |
Sample Size Calculations for Microarray Experiments
Description
This package calculates appropriate sample sizes for one-sample, two-sample, and multi-sample microarray experiments for a desired power of the test. Sample sizes are calculated under controlled false discovery rates and fixed proportions of non-differentially expressed genes. Outputs a graph of power versus sample size.
Details
| Package: | ssize.fdr |
| Type: | Package |
| Version: | 1.3 |
| Date: | 2022-06-05 |
| License: | GPL-3 |
For all functions, the user inputs the desired power, the false
discovery rate to be controlled, the proportion(s) of non-
differentially expressed genes, and the maximum possible sample size
to be used in calculations. If the user inputs a vector of proportions
of non-differentially expressed genes, samples size calculations are
performed for each proportion. For the function ssize.twoSamp,
the user must additionally input the common difference in mean treatment
expressions as well as the common standard deviation for all genes.
This becomes the common effect size and common standard deviation for
all genes when using the function ssize.oneSamp. For the
function ssize.twoSampVary (ssize.oneSampVary)
the differences in mean treatment expressions (effect sizes) are assumed
to follow a normal distribution and the variances among genes are assumed
to follow an inverse gamma distribution, so parameters for these
distributions must be entered. For the function ssize.F,
the design matrix of the experiment, the parameter vector, and an optional
coefficient matrix or vector of linear contrasts of interest must also be
entered. The function ssize.Fvary allows the variances of
the genes to follow an inverse gamma distribution, so the shape and scale
parameters must be specified by the user.
Author(s)
Megan Orr <megan.orr@ndsu.edu>, Peng Liu <pliu@iastate.edu>
References
Liu, Peng and J. T. Gene Hwang. 2007. Quick calculation for sample size while controlling false discovery rate with application to microarray analysis. Bioinformatics 23(6): 739-746.
Examples
a<-0.05 ##false discovery rate to be controlled
pwr<-0.8 ##desired power
p0<-c(0.5,0.9,0.95) ##proportions of non-differentially expressed genes
N<-20; N1<-35 ##maximum sample size for calculations
##Example of function ssize.oneSamp
d<-1 ##effect size
s<-0.5 ##standard deviation
os<-ssize.oneSamp(delta=d,sigma=s,fdr=a,power=pwr,pi0=p0,maxN=N,side="two-sided")
os$ssize ##first sample sizes to reach desired power
os$power ##calculated power for each sample size
os$crit.vals ##calculated critical value for each sample size
##Example of function ssize.oneSampVary
dm<-2; ds<-1 ##the effect sizes of the genes follow a Normal(2,1) distribution
alph<-3; beta<-1 ##the variances of the genes follow an Inverse Gamma(3,1) distribution.
osv<-ssize.oneSampVary(deltaMean=dm,deltaSE=ds,a=alph,b=beta,fdr=a,power=pwr,
pi0=p0,maxN=N1,side="two-sided")
osv$ssize ##first sample sizes to reach desired power
osv$power ##calculated power for each sample size
osv$crit.vals ##calculated critical value for each sample size
##Example of function ssize.twoSamp
##Calculates sample sizes for two-sample microarray experiments
##See Figure 1.(a) of Liu & Hwang (2007)
d1<-1 ##difference in differentially expressed genes to be detected
s1<-0.5 ##standard deviation
ts<-ssize.twoSamp(delta=d1,sigma=s1,fdr=a,power=pwr,pi0=pi,maxN=N,side="two-sided")
ts$ssize ##first sample sizes to reach desired power
ts$power ##calculated power for each sample size
ts$crit.vals ##calculated critical value for each sample size
##Example of function ssize.twoSampVary
##Calculates sample sizes for multi-sample microarray experiments in which both the differences in
##expressions between treatments and the standard deviations vary among genes.
##See Figure 3.(a) of Liu & Hwang (2007)
dm<-2 ##mean parameter of normal distribution of differences
##between treatments among genes
ds<-1 ##standard deviation parameter of normal distribution
##of differences between treatments among genes
alph<-3 ##shape parameter of inverse gamma distribution followed
##by standard deviations of genes
beta<-1 ##scale parameter of inverse gamma distribution followed
##by standard deviations of genes
tsv<-ssize.twoSampVary(deltaMean=dm,deltaSE=ds,a=alph,b=beta,
fdr=a,power=pwr,pi0=p0,maxN=N1,side="two-sided")
tsv$ssize ##first sample sizes to reach desired power
tsv$power ##calculated power for each sample size
tsv$crit.vals ##calculated critical value for each sample sizesv
##Example of function ssize.F
##Sample size calculation for three-treatment loop design microarray experiment
##See Figure S2. of Liu & Hwang (2007)
des<-matrix(c(1,-1,0,0,1,-1),ncol=2,byrow=FALSE) ##design matrix of loop design experiment
b<-c(1,-0.5) ##difference between first two treatments is 1 and
##second and third treatments is -0.5
df<-function(n){3*n-2} ##degrees of freedom for this design is 3n-2
s<-1 ##standard deviation
p0.F<-c(0.5,0.9,0.95,0.995) ##proportions of non-differentially expressed genes
ft<-ssize.F(X=des,beta=b,dn=df,sigma=s,fdr=a,power=pwr,pi0=p0.F,maxN=N)
ft$ssize ##first sample sizes to reach desired power
ft$power ##calculated power for each sample size
ft$crit.vals ##calculated critical value for each sample sizeft$ssize
##Example of function ssize.Fvary
##Sample size calculation for three-treatment loop design microarray experiment
des<-matrix(c(1,-1,0,0,1,-1),ncol=2,byrow=FALSE) ##design matrix of loop design experiment
b<-c(1,-0.5) ##difference between first two treatments is 1 and
##second and third treatments is -0.5
df<-function(n){3*n-2} ##degrees of freedom for this design is 3n-2
alph<-3;beta<-1 ##variances among genes follow an Inverse Gamma(3,1)
a1<-0.05 ##fdr to be fixed
p0.F<-c(0.9,0.95,0.995) ##proportions of non-differentially expressed genes
ftv<-ssize.Fvary(X=des,beta=b,dn=df,a=alph,b=beta,fdr=a1,power=pwr,pi0=p0,maxN=N1)
ftv$ssize ##first sample sizes to reach desired power
ftv$power ##calculated power for each sample size
ftv$crit.vals ##calculated critical value for each sample sizeft$ssize