ssize.Fvary {ssize.fdr}

Sample Size Calculations for Multi-Sample Microarray Experiments with Differing Variances among Genes

Description

Calculates appropriate sample sizes for multi-sample microarray experiments in which standard deviations vary among genes. Sample sizes are determined based on a desired power, a controlled false discovery rate, and user-specified proportions of non-differentially expressed genes and design matrix. A graph of power versus sample size is created.

Usage

ssize.Fvary(X, beta, L = NULL, dn, a, b, fdr = 0.05, power = 0.8, pi0 = 0.95, maxN = 20,
  cex.title=1.15, cex.legend=1)

Arguments

X

design matrix of experiment

beta

parameter vector

L

coefficient matrix or vector for linear contrasts of interest

dn

a function of the degrees of freedom based on the design of the experiment

a

shape parameter of inverse gamma distribution followed by variances of genes

b

scale parameter of inverse gamma distribution followed by variances of genes

fdr

the false discovery rate to be controlled

power

the desired power to be achieved

pi0

a vector (or scalar) of proportions of non-differentially expressed genes

maxN

the maximum sample size used for power calculations

cex.title

controls size of chart titles

cex.legend

controls size of chart legend

Details

The variances among genes are assumed to follow an Inverse Gamma distribution with shape parameter a and scale parameter b.

If a vector is input for pi0, sample size calculations are performed for each proportion.

Value

ssize

sample sizes (for each treatment) at which desired power is first reached

power

power calculations with corresponding sample sizes

crit.vals

critical value calculations with corresponding sample sizes

Note

Numerical integration used in calculations performed by the function integrate, which uses adaptive quadrature of functions.

Powers calculated to be 0 may be negligibly conservative.

Critical values calculated as ‘NA’ are values >100.

Author(s)

Megan Orr [e-mail], Peng Liu [e-mail]

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.

See Also

ssize.twoSamp, ssize.twoSampVary, ssize.oneSamp, ssize.oneSampVary, ssize.F

Examples

 ##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
 pwr<-0.8	##desired power
 p0<-c(0.9,0.95,0.995)		##proportions of non-differentially expressed genes
 N1<-35		##maximum sample size to be used in calculations

 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