Testing for centre effects in multi-centre survival studies: a Monte Carlo comparison of fixed and random effects tests.

The problem of testing for a centre effect in multi-centre studies following a proportional hazards regression analysis is considered. Two approaches to the problem can be used. One fits a proportional hazards model with a fixed covariate included for each centre (except one). The need for a centre specific adjustment is evaluated using either a score, Wald or likelihood ratio test of the hypothesis that all the centre specific effects are equal to zero. An alternative approach is to introduce a random effect or frailty for each centre into the model. Recently, Commenges and Andersen have proposed a score test for this random effects model. By a Monte Carlo study we compare the performance of these two approaches when either the fixed or random effects model holds true. The study shows that for moderate samples the fixed effects tests have nominal levels much higher than specified, but the random effect test performs as expected under the null hypothesis. Under the alternative hypothesis the random effect test has good power to detect relatively small fixed or random centre effects. Also, if the centre effect is ignored the estimator of the main treatment effect may be quite biased and is inconsistent. The tests are illustrated on a retrospective multi-centre study of recovery from bone marrow transplantation. Copyright 1999 John Wiley & Sons, Ltd.