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by William D. Dupont and Walton D. Plummer, Jr.

PS is an interactive program for performing power and sample size calculations. The program runs on the Microsoft Windows operating systems (Windows 95 and later). It can be used for studies with dichotomous, continuous, or survival response measures. The alternative hypothesis of interest may be specified either in terms of differing response rates, means, or survival times, or in terms of relative risks or odds ratios. Studies with dichotomous or continuous outcomes may involve either a matched or independent study design. The program can determine the sample size needed to detect a specified alternative hypothesis with the required power, the power with which a specific alternative hypothesis can be detected with a given sample size, or the specific alternative hypotheses that can be detected with a given power and sample size.

The PS program can produce graphs to explore the relationships between power, sample size and detectable alternative hypotheses. It is often helpful to hold one of these variables constant and plot the other two against each other. The program can generate graphs of sample size versus power for a specific alternative hypothesis, sample size versus detectable alternative hypotheses for a specified power, or power versus detectable alternative hypotheses for a specified sample size. Linear or logarithmic axes may be used for either axes. Multiple curves can be plotted on a single graphic.

Downloading the Software

The PS program is freely available on the Internet. To obtain this software on your computer click PS (5.2 MB). Instruct your browser to download the file to a folder on your computer. A file called PSsetup.exe will be downloaded to this location. Run PSsetup.exe to extract the needed files and install the program.

To run the PS program after it has been installed, click the Start button, select Programs and then click PS. Click the Overview button for an introduction to the program and instruction on its use. PS is a self-documented program with extensive interactive help.

We are interested in feedback. If you have any questions or comments about our software please send email to dale.plummer@vanderbilt.edu. It will be appreciated.

Study Designs That Can Be Evaluated By This Program

1. Survival Studies: Evaluation of independent cohorts using the log-rank test. The approach of Schoenfeld and Richter3 is used. The ratio of number of patients in the cohorts being compared may be specified by the user.
2. Continuous Response Measures in Two Groups: Paired and independent t tests. The approach of Dupont and Plummer1 is used for paired and independent samples. The ratio of number of patients in the samples being compared may be specified by the user. This method produces results that are in close agreement with those of Pearson and Hartley.4
3. Linear Regression: Tests of slopes, comparisons of slopes and intercepts from independent regressions. The methods of Dupont and Plummer2 is used. They may be used to design studies in which we wish to detect a regression slope of a given magnitude. They may also be used when we wish to determine whether the slopes or intercepts of two independent regression lines differ by a given amount. The values of the independent (x) variable(s) of the regression line(s) may either be specified by the investigator or determined observationally when the study is performed. In the latter case, the investigator must estimate the standard deviation(s) of the independent variable(s).
4. Independent Case-Control Studies: Corrected and uncorrected chi-square contingency table tests, Fisher's exact test. The method of Schlesselman5 is used for studies with independent case and control groups that will be analyzed using an uncorrected chi-square test; the method of Casagrande et al.6 is used for independent studies that will be analyzed using continuity corrected chi-square statistics or Fisher's exact test. When the case and control sample sizes are unequal, PS uses the generalization of Casagrande's method proposed by Fleiss.7 The alternative hypotheses may be specified in terms of odds ratios or exposure prevalence rates.
5. Matched Case-Control Studies: McNemar's Test. The method of Dupont8 is used for studies with paired or matched cases and controls. The alternative hypotheses may be specified in terms of odds ratios or exposure prevalence rates.
6. Cohort Studies With Dichotomous Outcomes: Independent contingency table tests, McNemar's test. The methods of Schlesselman,5 Casagrande,6 Fleiss7 and Dupont8 are available. The alternative hypotheses may be specified in terms of relative risks or outcome probabilities.

References

1. Dupont WD, Plummer WD, Jr: Power and Sample Size Calculations: A Review and Computer Program. Controlled Clinical Trials 11:116-128, 1990
2. Dupont WD, Plummer WD, Jr: Power and Sample Size Calculations for Studies Involving Linear Regression. Controlled Clinical Trials 19:589-601, 1998
3. Schoenfeld DA, Richter JR: Nomograms for calculating the number of patients needed for a clinical trial with survival as an endpoint. Biometrics 38:163-170, 1982
4. Pearson ES, Hartley HO: Biometrika Tables for Statisticians Vol. I 3rd Ed. Cambridge: Cambridge University Press, 1970
5. Schlesselman JJ: Case-Control Studies: Design, Conduct, Analysis. New York: Oxford University Press, 1982
6. Casagrande JT, Pike MC, Smith PG: An improved approximate formula for calculating sample sizes for comparing two binomial distributions. Biometrics 34:483-486, 1978
7. Fleiss JL: Statistical Methods for Rates and Proportions. 2nd Ed. New York: John Wiley & Sons, 1981
8. Dupont WD: Power calculations for matched case-control studies. Biometrics 44:1157-1168, 1988