ssize (version 1.46.0)

pow: Compute and plot power, reqired sample-size, or detectible effect size for gene expression experiment

Description

Compute and plot power, reqired sample-size, or detectible effect size for gene expression experiment

Usage

pow(sd, n, delta, sig.level, alpha.correct = "Bonferonni")
power.plot(x, xlab = "Power", ylab = "Proportion of Genes with Power >= x",  marks = c(0.7, 0.8, 0.9), ...)
ssize(sd, delta, sig.level, power, alpha.correct = "Bonferonni")
ssize.plot(x, xlab = "Sample Size (per group)", ylab = "Proportion of Genes Needing Sample Size <= n",="" marks =" c(2," 3,="" 4,="" 5,="" 6,="" 8,="" 10,="" 20),="" ...)<="" div="">
delta(sd, n, power, sig.level, alpha.correct = "Bonferonni")
delta.plot (x, xlab = "Fold Change", ylab = "Proportion of Genes with Power >= 80% at Fold Change=delta", marks = c(1.5, 2, 2.5, 3, 4, 6, 10), ...)

Arguments

sd

Vector of standard deviations for control samples, *on the log2 scale*

n

Number of observations (per group)

delta

Hypothetical True difference in expression, on the log2 scale.

sig.level

Significance level (Type I error probability)

power

Power

alpha.correct

Type of correction for multiple comparison. One of "Bonferonni" or "None".

x

Vector of powers generated by pow

xlab, ylab

x and y axis labels

marks

Powers at which percent of genes achieving the specified cutoff is annotated on the plot.

...

Additional graphical parameters

Value

pow returns a vector containing the power for each standard deviation.

Details

The pow function computes power for each element of a gene expression experiment using an vector of estimated standard deviations. The power is computed separately for each gene, with an optional correction to the significance level for multiple comparison. The power.plot function generates a cumulative power plot illustrating the fraction and number of genes achieve a given power for the specified sample size, significance level, and delta.

Periods are printed for every 10 calculations so that the user can see that the computation is proceeding.

References

Warnes GR and Fasheng Li Warnes GR and Liu P, ``Sample Size Selection for Microarray Experiments'' submitted to Biometrics. Warnes GR and Fasheng Li, ``Sample Size Selection for Microarray based Gene Expression Studies,'' Talk, "2003 FDA/Industry Statistics Workshop: From Theory to Regulatory Acceptance", American Statistical Association, Bethesda, MD, Sept 18-19, 2003. http://www.warnes.net/Research/PresentationFolder/SampleSize.pdf

See Also

ssize, ssize.plot, delta, delta.plot

Examples

library(gdata) # for nobs()

data(exp.sd)


# Histogram of the standard deviations

hist(exp.sd,n=20, col="cyan", border="blue", main="",
     xlab="Standard Deviation (for data on the log scale)")
dens <- density(exp.sd)
lines(dens$x, dens$y*par("usr")[4]/max(dens$y),col="red",lwd=2)

title("Histogram of Standard Deviations")

# 1) What is the power if using 6 patients 3 measurements assuming
#    Delta=1.0, Alpha=0.05 and Observed SDs?
#
n=6; fold.change=2.0; power=0.8; sig.level=0.05;
#
all.power <- pow(sd=exp.sd, n=n, delta=log2(fold.change),
                 sig.level=sig.level)

power.plot(all.power, lwd=2, col="blue")
xmax <- par("usr")[2]-0.05; ymax <- par("usr")[4]-0.05
legend(x=xmax, y=ymax,
       legend= strsplit( paste("n=",n,",",
                              "fold change=",fold.change,",",
                              "alpha=", sig.level, ",",
                              "# genes=", nobs(exp.sd), sep=''), "," )[[1]],
       xjust=1, yjust=1, cex=1.0)
title("Power to Detect 2-Fold Change")

# 2) What is necessary sample size for 80% power using 3 measurements/patient
#    assuming Delta=1.0, Alpha=0.05 and Observed SDs?
#
all.size  <- ssize(sd=exp.sd, delta=log2(fold.change),
                   sig.level=sig.level, power=power)
ssize.plot(all.size, lwd=2, col="magenta", xlim=c(1,20))
xmax <- par("usr")[2]-1; ymin <- par("usr")[3] + 0.05
legend(x=xmax, y=ymin,
       legend= strsplit( paste("fold change=",fold.change,",",
                              "alpha=", sig.level, ",",
                              "power=",power,",",
                              "# genes=", nobs(exp.sd), sep=''), "," )[[1]],
       xjust=1, yjust=0, cex=1.0)
title("Sample Size to Detect 2-Fold Change")


# 3) What is necessary fold change to achieve 80% power using 3
# measurements/patient assuming n=6, Delta=1.0, Alpha=0.05 and Observed
# SDs?
#
all.delta  <- delta(sd=exp.sd, power=power, n=n,
                    sig.level=sig.level)
delta.plot(all.delta, lwd=2, col="magenta", xlim=c(1,10))
xmax <- par("usr")[2]-1; ymin <- par("usr")[3] + 0.05
legend(x=xmax, y=ymin,
       legend= strsplit( paste("n=",n,",",
                              "alpha=", sig.level, ",",
                              "power=",power,",",
                              "# genes=", nobs(exp.sd), sep=''), "," )[[1]],
       xjust=1, yjust=0, cex=1.0)
title("Fold Change to Achieve 80% Power")