# Sample Size Calculations for Two-Sample RNA-seq Experiments with Differing Mean and Dispersion Among Genes This function calculates appropriate sample sizes for two-sample RNA-seq experiments for a desired power in which mean and dispersion vary among genes. Sample size calculations are performed at controlled false discovery rates, user-specified proportions of non-differentially expressed genes, mean counts in control group, dispersion, and fold change. A plot of power versus sample size is generated. ```r ssizeRNA_vary(nGenes = 10000, pi0 = 0.8, m = 200, mu, disp, fc, up = 0.5, replace = TRUE, fdr = 0.05, power = 0.8, maxN = 35, side = "two-sided", cex.title = 1.15, cex.legend = 1) ``` ## Arguments - `nGenes`: total number of genes, the default value is `10000`. - `pi0`: proportion of non-differentially expressed genes, the default value is `0.8`. - `m`: pseudo sample size for generated data. - `mu`: a vector (or scalar) of mean counts in control group from which to simulate. - `disp`: a vector (or scalar) of dispersion parameter from which to simulate. - `fc`: a vector (or scalar, or a function that takes an integer n and generates a vector of length n) of fold change for differentially expressed (DE) genes. - `up`: proportion of up-regulated genes among all DE genes, the default value is `0.5`. - `replace`: sample with or without replacement from given parameters. See Details for more information. - `fdr`: the false discovery rate to be controlled. - `power`: the desired power to be achieved. - `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. ## Returns - **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. ## Details If a vector is input for `pi0`, sample size calculations are performed for each proportion. If the total number of genes is larger than length of `mu` or `disp`, `replace` always equals `TRUE`. ## Examples ```r library(edgeR) library(Biobase) data(hammer.eset) ## load hammer dataset (Hammer, P. et al., 2010) counts <- exprs(hammer.eset)[, phenoData(hammer.eset)$Time == "2 weeks"] counts <- counts[rowSums(counts) > 0,] trt <- hammer.eset$protocol[which(hammer.eset$Time == "2 weeks")] mu <- apply(counts[, trt == "control"], 1, mean) ## average read count in control group for each gene d <- DGEList(counts) d <- calcNormFactors(d) d <- estimateCommonDisp(d) d <- estimateTagwiseDisp(d) disp <- d$tagwise.dispersion ## dispersion for each gene ## fixed fold change fc <- 2 size <- ssizeRNA_vary(mu = mu, disp = disp, fc = fc, m = 30, maxN = 15, replace = FALSE) size$ssize ## first sample size to reach desired power size$power ## calculated power for each sample size size$crit.vals ## calculated critical value for each sample size ## varying fold change ## fc1 <- function(x){exp(rnorm(x, log(2), 0.5*log(2)))} ## size1 <- ssizeRNA_vary(pi0 = 0.8, mu = mu, disp = disp, fc = fc1, ## m = 30, maxN = 20, replace = FALSE) ``` ## 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. Law, C. W., Chen, Y., Shi, W., Smyth, G. K. (2014). Voom: precision weights unlock linear model analysis tools for RNA-seq read counts. **Genome Biology** 15, R29. ## See Also `ssizeRNA_single` ## Author(s) Ran Bi biranpier@gmail.com , Peng Liu pliu@iastate.edu

ssizeRNA_vary function