ssize.oneSampVary {ssize.fdr}

Sample Size Calculations for One-Sample Microarray Experiments with Differing Mean Expressions and Standard Deviations Among Genes

Description

Calculates appropriate sample sizes for two-sample microarray experiments in which effect sizes as well as variances 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. Outputs a graph of power versus sample size. A graph of power versus sample size is created.

Usage

ssize.oneSampVary(deltaMean, deltaSE, a, b, fdr = 0.05, power = 0.8, pi0 = 0.95,
maxN = 35, side = "two-sided", cex.title=1.15, cex.legend=1)

Arguments

deltaMean

mean of normal distribution followed by effect sizes among genes

deltaSE

standard deviation of normal distribution followed by effect sizes among genes

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

side

options are "two-sided", "upper", or "lower"

cex.title

controls size of chart titles

cex.legend

controls size of chart legend

Details

The effect sizes among genes are assumed to follow a Normal distribution with mean specified by deltaMean and standard deviation specified by deltaSE. 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 >20.

Running this function may result in many warnings. Probabilities under different t-distributions with non-zero non-centrality parameters are calculated many times while the function runs. If these probabilities are virtually zero, the function pt outputs a value <1e-8 and outputs a warning of “full precision not achieved”. These values have no impact on the accuracy of the resulting calculations.

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.twoSampVary, ssize.oneSamp, ssize.oneSampVary, ssize.F, ssize.Fvary

Examples

 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.
 a2<-0.05	##false discovery rate to be controlled
 pwr2<-0.8	##desired power
 p0<-c(0.90,0.95,0.995)	##proportions of non-differentially expressed genes
 N1<-35		##maximum sample size to be used in calculations

 osv<-ssize.oneSampVary(deltaMean=dm,deltaSE=ds,a=alph,b=beta,fdr=a2,power=pwr2,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