Widening eligibility to phase II trials: constant arcsine difference phase II trials

Abstract

This paper presents a method for undertaking Phase II trials in which not all patients are considered equally likely to respond to treatment. In ovarian cancer, for example, it has been shown that response is less likely in patients who have failed the previous treatment after only a short interval compared to those who have a protracted failure-free interval [Gynecol. Oncol. 36 (1990) 207]. The method is analogous to those used in phase III trials which estimate relative rather than absolute effects; a constant odds ratio, for example, encompasses multiple relationships between response rates. Phase II trials commonly test the null hypothesis H₀: P≤p₀ against the alternate hypothesis H₁: P≥p₁, where the response rate p₁ is the minimum required level of efficacy and p₀ the highest level which would indicate that the treatment is of no further interest. This approach can be extended by using the arcsine transformation to allow p₀ and p₁ to vary between patients, thus for the ith patient p_0i=(sin c_i)² and the efficacy level is set to p_1i=(sin (c_i+b))². The value of the arcsine parameter b therefore determines efficacy and the test for efficacy in the trial then becomes a test of the null hypothesis H₀: B≤0 against the alternate hypothesis H₁: B≥b. The value of b is determined by considering representative values of p₀ and p₁ and setting b=(sin⁻¹√p₁−sin⁻¹√p₀); b is thus the constant arcsine difference (CAD) between p_0i and p_1i. The variance of B is 1/4n, which is independent of P, trial designs are therefore independent of P, implying that all patients for whom this difference is identical can be entered into the same trial. This paper considers single-stage and two-stage CAD Phase II trials.