Sample Size Determination Example

Step 1:
Select the POT11 Two Stage Phase II Design (Simon’s Design) table from the Select Test window.

This can be done using the radio buttons or alternatively, you can use the search bar at the end of the Select Test window.

Step 2:
Enter the parameter values for sample size calculation taken from the study design. The required sample size will automatically calculate once values for ⍺, 𝜋 0 , 𝜋 1 and Power are entered. (Note that the “Optimum Search Value” and “Lower N Limit” parameters are only required under the “Optimum” design criterion.)

The analysis results in a total sample size of 14, with 7 patients at stage one and a further 7 added for stage two. The actual significance level is 0.027 and the power of the test is 81.01%. At the final analysis, if two or less responses are observed in total, then the drug is rejected. The overall probability of early termination is 69.8%

Step 3:
Once the calculation is completed, nQuery provides an output statement summarizing the results.

It states:
“Under the minimax design criterion, a sample size of 14 is required to test a null hypothesis of H₀: π ≤ 0.05 versus an alternative hypothesis of H₁: π ≥ 0.3 with a one-sided significance level of 0.027 and 81.01% power, where π is the true proportion of successes. This design results in an expected sample size of 9.112 and a probability of early termination of 0.698.

If the number of responses is less than or equal to 0 out of 7 subjects in the first stage then the trial will be stopped. If the trial proceeds to the second stage, 14 subjects in total will be studied. If 2 or less responses are observed, then the drug or treatment is rejected.”

Step 4:
We can compare the Minimax design with the Optimum and Single Stage designs by completing two additional columns in nQuery with the same ⍺, 𝜋 0 , 𝜋 1 and power parameters and selecting the appropriate Design Criterion.

In this case, the optimum design results in a total sample size of 18, while the single-stage and
minimax designs result in a total sample size of 14.

Step 5:
nQuery advanced also provides plotting options. To access the plotting tools, highlight the
completed columns that you wish to work with, go to the menu and select:
Plot > User-Selected Rows.

In this case, we will display how the total sample size for each design criterion is affected when the maximum ineffective proportion varies between 0.01 and 0.1.

The Edit button at the top of the output allows users to customise the appearance of the plot.