products: Multi-Stage Trial Design with ExpDesign Studio

Multi-Stage Trial Studio is one of the components in ExpDesign Studio. It can also be used as stand-alone software.

Input Features Output Features
  • Single, two-stage or three-stage design
  • Proportion or odds ratio
  • Power and significance level
  • Utility specification
  • Input examples
  • Exact stop boundaries
  • Stopping probabilities
  • Expected and maximum sample size
  • Sample size at each stage
  • Utility index
  • Confidence interval
  • Design report
  • And more...


A biotech company is planning a single arm Phase-II trial to investigate the efficacy and safety of the experiment drug called AntiGen in cancer patients. The primary endpoint is cancer response (complete response + partial response). It is specified that if the response rate is less that 5%, there is no desire to conduct a next trial and if the response rate is greater than 20%, a further investigation will be pursued. The company recognizes the importance to stop the trial early if the testing drug is not promising, but is willing to spend more if the drug is promising. More specifically the importance of minimizing the expected sample size under the null hypothesis is rated 8 out of 10 and the importance of minimizing the maximum sample size is rated 2 out of 10. We use ExpDesign to generate two-stage designs and three-stage designs, and select the final design that meets our needs through comparisons.

Two-Stage Designs
Based on the information provided in the example, we specify the input as follows: Two-stage design, Proportion for Ho = 0.05, Proportion for Ha = 0.20, alpha = 0.05, power = 0.8 and 2 and 8 for the utility weights (See the figure below). Click the Compute button to generate the two-stage designs and click the Report icon on the toolbar to review the design report.

Figure 1: Two-Stage Designs

Three-Stage Designs
Similarly, we can generate results for following three stage designs.

Figure 2: Three-Stage Designs

Selection of Final Design
Since the utility is specified, we should use the Maximum Utility design. Comparing the three-stage design and two-stage design, the three-stage design provides a large utility value (1.6) than that for the two-stage design (1.5). However, the three-stage design requires a maximum of 30 patients (expected 15.8 patients) and the two-stage design requires maximum of 29 patients (expected 17.6). The main concern is that the three-stage design is more complicated and difficult to implement, partially because when the interim analysis is done, all patients would have been enrolled in the trial. Therefore, the two-stage Maximum Utility design is chosen for the trial. The stopping rules are specified as follows: At stage 1, stop trial and accept the null hypothesis if the response rate is less than or equal to 0/13. Otherwise, continue to stage 2. At stage 2, stop and accept the null hypothesis if the response rate is less than or equal to 3/29. Otherwise, stop and reject the null hypothesis. Compared to the fixed sample size design with utility 1, the two-stage design gains 50% more in utility.