Equivalence of two treatments and sample size determination under exponential survival model with censoring

We present the likelihood score and F statistics for ascertaining equivalence of two treatments in survival under an exponential model with independent censoring. We provide explicit formulae for power and sample size requirement for trials using the score and F tests, and compare the score and F tests with the log rank test by Com-Nougue et al. (Statist. Med. 12 (1993) 1353). Simulation results show that empirical powers of the score, F and log rank tests are satisfactorily close to the corresponding asymptotic powers for small-to-moderate sample size. We find these three methods are essentially identical in terms of level and power. However, the score and F methods are very sensitive to departure from the exponential assumption while the log rank test is more robust. The methods are illustrated by application to data from a randomized trial of two treatments for B non-Hodgkin lymphoma.