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Analysis of phase II clinical trials in haematology and oncology: Comparison of the triangular test to the usual methods
Author(s) -
Benichou Jacques,
Bellissant Eric,
Chastang Claude
Publication year - 1991
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780100620
Subject(s) - type i and type ii errors , mathematics , statistics , wald test , sample size determination , sequential probability ratio test , odds ratio , p value , outcome (game theory) , statistical hypothesis testing , combinatorics , mathematical economics
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 p 0 , that is, to test H 0 , given by p ⩽ p 0 against H 1 given by p > p 0 . By choosing type I error α and the power 1 ‐ β and by specifying H 1 , (that is, by choosing a clinically relevant improvement p 1 ), 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 H 0 and H 1 in terms of the log odds‐ratio statistics, namely log { p (1 ‐ p 0 )/ p 0 (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 H 0 and V is the variance of Z under H 0 . 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 α and the power 1 ‐ β 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.