ssize.twoSampVary: Sample Size Calculations for Two-Sample Microarray...

In ssize.fdr: Sample Size Calculations for Microarray Experiments

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

Description

Calculates appropriate sample sizes for two-sample microarray experiments in which the differences between mean treatment expression levels (delta.g for gene g) as well as 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. A graph of power versus sample size is created.

Usage

ssize.twoSampVary(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	location (mean) parameter of normal distribution followed by each delta.g
deltaSE	scale (standard deviation) parameter of normal distribution followed by each delta.g
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

Each delta.g is 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

 ##See Figure 3.(a) of Liu & Hwang (2007)
 dm<-2; ds<-1	##the delta.g's follow a Normal(2,1) distribution
 alph<-3; beta<-1	##the variances of genes follow an Inverse Gamma(a,b) 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

 tsv<-ssize.twoSampVary(deltaMean=dm,deltaSE=ds,a=alph,b=beta,fdr=a2,power=pwr2,pi0=p0,
 maxN=N1,side="two-sided")
 tsv$ssize	##first sample size(s) to reach desired power
 tsv$power	##calculated power for each sample size
 tsv$crit.vals	##calculated critical value for each sample size

ssize.fdr documentation built on June 7, 2022, 9:06 a.m.