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

Description

For given desired power, controlled false discovery rate, and user-specified proportions of non-differentially expressed genes, ssize.twoSampVaryDelta calculates appropriate sample sizes for two-sample microarray experiments in which the differences between mean treatment expression levels (delta.g for gene g) vary among genes. A plot of power versus sample size is generated.

Usage

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ssize.twoSampVaryDelta(deltaMean, deltaSE, sigma, 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.

sigma

the common standard deviation of expressions for all 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 deltaMean and standard deviation deltaSE. The standard deviations of expressions are assumed identical for all genes.

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.

Author(s)

Ran Bi biran@iastate.edu, Peng Liu pliu@iastate.edu

References

Liu, P. and Hwang, J. T. G. (2007) Quick calculation for sample size while controlling false discovery rate with application to microarray analysis. Bioinformatics 23(6): 739-746.

Orr, M. and Liu, P. (2009) Sample size estimation while controlling false discovery rate for microarray experiments using ssize.fdr package. The R Journal, 1, 1, May 2009, 47-53.

See Also

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

Examples

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dm <- 1.2; ds <- 0.1  ## the delta.g's follow a Normal(1.2, 0.1) distribution
s <- 1                ## common standard deviation
fdr <- 0.05           ## false discovery rate to be controlled
pwr <- 0.8            ## desired power
pi0 <- c(0.5, 0.8, 0.99) ## proportions of non-differentially expressed genes
N <- 35               ## maximum sample size for calculations

size <- ssize.twoSampVaryDelta(deltaMean = dm, deltaSE = ds, sigma = s, 
                               fdr = fdr, power = pwr, pi0 = pi0, 
                               maxN = N, side = "two-sided")
size$ssize                ## first sample size(s) to reach desired power
size$power                ## calculated power for each sample size
size$crit.vals            ## calculated critical value for each sample size