#### Description:

Hello! In this video tutorial, we’ll show you how to calculate sample size for an inequality Test of One Proportion in PASS. The One-Sample Proportion Test is used to determine whether a population proportion, P1, is significantly different from a null hypothesized value, P0. The hypotheses may be stated in terms of proportions, differences, ratios, or odds ratios, but all four hypotheses result in the same test statistic.

As an example, suppose that 50% of patients with a certain type of cancer survive more than five years. A new treatment is being tested for efficacy in increasing this percentage. How many patients would they need to detect a 60% survival rate under the new treatment, with 90% power for a two-sided Z-test at a significance level of 0.05?

This is an example of a historically controlled trial, meaning that no control group is formed for the current study. Instead, the rate used for comparison is reported in previous studies or known to exist in the general population. Because of the many advantages that occur when an actual control group is used, historically controlled trials should only be used when a control group is either impossible to obtain or unethical.

To perform this calculation in PASS, first load the Tests for One Proportion procedure using the category tree or the search bar on the PASS Home Window.

For Solve For, select Sample Size. This procedure also allows you to solve for power and effect size.

You have 2 choices for the power calculation method: Binomial Enumeration, which results in an exact power calculation, and the normal approximation. When the sample sizes are reasonably large and the proportions are between 0.2 and 0.8, the two methods will give similar results. For smaller sample sizes and more extreme proportions, the normal approximation is not as accurate so the binomial calculations may be more appropriate. We’ll use the normal approximation method for this example.

We want the sample size for a two-sided Z-test with the standard deviation based on P0, 90% power, and an alpha level of 0.05.
To specify the effect size, we can enter proportions, differences, ratios, or odds ratios. For this example we’ll enter proportions. Set the null proportion to 0.50. The goal is to calculate the sample size needed to detect a 60% survival rate, but let’s also consider the sample sizes needed to detect 55% and 65% survival rates as well. These values are all entered as proportions, not percents.

Now, click the Calculate button to perform the calculations and get the results. The sample size needed to detect a 60% 5-year survival rate is 259 patients. A much larger sample size of 1047 is required to detect a 55% survival rate since the effect size is much smaller. Only 113 patients are required to detect a 65% survival rate.

If we go back and calculate the sample sizes using binomial enumeration instead of the normal approximation, you’ll see that the computed sample sizes are very close.