One-Sample Proportion Testing Procedures for Hypothesis of Inequality

Abstract

The primary objective of a phase II single arm clinical trial is to determine whether a new treatment is of sufficient activity for a disease to warrant further development. This paper presents single arm one-stage and two-stage designs for testing the response rate of a test treatment against the response rate of an existing treatment. The null and alternative hypotheses are the response rate of the test treatment is equal and unequal to that of the existing treatment respectively. The testing procedures are calculated with exact binomial distribution. Two-stage designs presented minimize total sample size and satisfy type I and II error constraints, with flexibility in the fraction of the total sample size to use in the first stage.

Key Words:

• Exact binomial distribution
• Hypothesis of inequality
• Minimized two-stage design
• Phase 2 clinical trial
• Single arm

ACKNOWLEDGMENT

The authors thank two referees for their helpful comments and suggestions.

Notes

^a For each combination of p _c , p _t , α, and β, r/s/n gives the cutoffs r and s for rejecting H ₀, and the total number of patients n. Conclude if the number of responses is <r and conclude if the number of responses is >s.

^a For each value of p _c , p _t , α, β, (r ₁/n ₁, r/s/n) give the first stage sample size n ₁ and cutoff r ₁ for concluding , i.e., early terminate the trial when the number of responses is ≤r ₁. n is the total number of patients needed if the trial proceeds to the second stage, and r and s are cutoffs for rejecting H ₀. Conclude if the number of responses is <r, and conclude if the number of responses is >s.

^a For each value of p _c , p _t , α, β, (r ₁/n ₁, r/s/n) give the first stage sample size n ₁ and cutoff r ₁ for concluding , i.e., early terminate the trial when the number of responses is ≤r ₁. n is the total number of patients needed if the trial proceeds to the second stage, and r and s are cutoffs for rejecting H ₀. Conclude if the number of responses is <r, and conclude if the number of responses is >s

^a For each value of p _c , p _t , α, β, (r ₁/n ₁, r/s/n) give the first stage sample size n ₁ and cutoff r ₁ for concluding , i.e., early terminate the trial when the number of responses is ≤r ₁. n is the total number of patients needed if the trial proceeds to the second stage, and r and s are cutoffs for rejecting H ₀. Conclude if the number of responses is <r, and conclude if the number of responses is >s