Analysis of phase II clinical trials in haematology and oncology: comparison of the triangular test to the usual methods

Phase II cancer clinical trials are non-comparative trials which are designed to determine whether the response rate p to the treatment under study is greater than a certain value p0, that is, to test H0, given by p less than or equal to p0 against H1 given by p greater than po. By choosing type I error alpha and the power 1-beta and by specifying H1, that is, by choosing a clinically relevant improvement p1), one can compute the number of patients N to be included for a fixed-sample approach. Various other approaches have been proposed such as multistage methods and Wald's continuous sequential probability ratio test (SPRT). As an alternative approach, we extended the triangular test (TT), proposed by Whitehead for comparative trials, to the situation of non-comparative trials with a binary outcome. We expressed H0 and H1 in terms of the log odds-ratio statistics, namely log p(1-p0)/p0-(1-p)]. With this choice, the two statistics of interest, Z and V, have simple expressions: Z is the difference between the observed number of positive outcomes and the expected number under H0 and V is the variance of Z under H0. After every group of n patients, Z is plotted against V, and the trial proceeds until a boundary is crossed. In our simulations, type I error alpha and the power 1-beta were close to nominal values with the TT and the average sample size was close to Wald's continuous SPRT and compared favourably with the multistage methods proposed by Herson and Fleming. Given its statistical properties and its easy use, the TT should be considered for planning and analysing cancer phase II trials.