Sample Size Estimation Of Wilcoxon-mann-whitney Test Using Monte Carlo Simulation And Its SAS Implementation

ObjectiveTo investigate the application of Monte Carlo simulation in sample sizeestimation of Wilcoxon–Mann–Whitney(WMW) test, and develope macro programsfor Monte Carlo simulation using SAS version9.2, which were used to estimate thesample size of the WMW test for either measurement data or ordinal data, and inorder to provide an effective and reliable method for sample size estimation of theWMW test.MethodsFirstly, we developed a SAS macro program estimating the sample size ofindependent group t-test to validate Monte Carlo simulation used for sample sizeestimation. Then the sample sizes estimated by Monte Carlo simulation werecompared with the results calculated by the formula. Secondly, we developed SASmacro programs to estimate the sample size of the WMW test for either measurementdata or ordinal data, and compared the results of Monte Carlo simulation using SASwith those of sample size software PASS2008.Results(1) Validation of sample size estimation using Monte Carlo simulationSample sizes estimated by Monte Carlo simulation using SAS for independentgroup t-test were well consistent with the formula‘s results, and the results were of great stability and reliability with the maximum deviation rate of less than fivepercent.(2) Sample size estimation of the WMW testIn general, the sample size results estimated by SAS were well approximate tothose of PASS2008. In the case of balanced sample size, the difference between themean of thirty sample sizes estimated by SAS simulation and that of PASS2008were very small. However,as for the sample ratio was1to4and small sample sizewas required, there would be a relative big difference. The sample size resultsestimated for either measurement data or ordinal data by SAS were better in stablityand actual power controlling when compared with those of PASS2008.ConclusionNo matter for measurement data or ordinal data, the sample size results estimatedby SAS were well approximate to those of PASS2008and performed to be morestable and reliable. Consequently, Monte Carlo simulation using SAS would beregarded as an alternative effective method for sample size estimation of the WMWtest.