Erratum: sample size determination for the false discovery rate

We have made corrections to the routines that were provided to implement Pounds and Cheng (2005) method to determine the sample size for a microarray experiment that uses the false discovery rate as the ultimate measure of statistical significance. Some routines in the original R and S-plus libraries did not properly account for differences between the definition of the noncentrality parameter in Equations (18) and (19) of Pounds and Cheng (2005) and the definition of the non-centrality parameter used by the internal R or S-plus function to evaluate the cumulative distribution function of the non-central F-distribution. A corrected version of the R routine library is now available for download from www.stjuderesearch.org/depts/biostats/fdrsampsize/index.html. To avoid confusion, all routines in the revised library use the definition of Equations (18) and (19) of Pounds and Cheng (2005). For a variety of settings involving a single two-sided test, the accuracy of the revised routine library has been checked by comparing the results of the avepow.oneway routine to the results of proc power in SAS and the built-in R function power.anova.test (Appendix). Corrected results of the simulation studies of Pounds and Cheng (2005) are reported in Tables 1 and 2 and Figure 1. Table 1 gives the simulation estimate of the expected value (EV) of the average power, i.e. the EV of the ratio D of the number of true discoveries to the number of false null hypotheses when sample size is determined using the true values of the proportion π of null hypotheses that are true and the effect size η of the false null hypotheses. The SD of D observed over 1000 simulation replications is also reported. In all but two settings, the determined sample size gives an estimate of the average power that is greater than or equal to the desired average power δ. In two settings, the simulation estimate of average power is slightly less than the desired average power. Table 2 reports the corrected results of a series of simulations that generated F-statistics for a background study with per-group sample size 4 from the assumed setting. The background F-statistics, instead of the actual effect size parameters, were used to determine sample with the method of Pounds and Cheng (2005). In all settings, the simulation estimate of the average power exceeded the desired average power δ. Figure 1 gives corrected results for the ‘real data simulation’ performed by resampling from a real data set that is described in section 4.2 of Pounds and Cheng (2005). The mean of the SPLOSH