STATISTICS IN MEDICINE Statist. Med. 2000; 19:3497–3518 Baseline risk as predictor of treatment benet: three clinical meta-re-analyses ‡ Lidia R. Arends 1;*;† , Arno W. Hoes 2; 3 , Jacobus Lubsen 4 , Diederik E. Grobbee 2 and Theo Stijnen 1 1 Department of Epidemiology & Biostatistics, Erasmus University Medical School, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands 2 Julius Centre for Patient-Oriented Research, University Medical Center, P.O. Box 80035, 3508 TA Utrecht, The Netherlands 3 Department of General Practice, University Medical Center, P.O. Box 80035, 3508 TA Utrecht, The Netherlands 4 SOCAR Research SA, P.O. Box 2564, CH 1260 NYON2, Switzerland SUMMARY A relationship between baseline risk and treatment eect is increasingly investigated as a possible explanation of between-study heterogeneity in clinical trial meta-analysis. An approach that is still often applied in the medical literature is to plot the estimated treatment eects against the estimated measures of risk in the control groups (as a measure of baseline risk), and to compute the ordinary weighted least squares regression line. However, it has been pointed out by several authors that this approach can be seriously awed. The main problem is that the observed treatment eect and baseline risk measures should be viewed as estimates rather than the true values. In recent years several methods have been proposed in the statistical literature to potentially deal with the measurement errors in the estimates. In this article we propose a vague priors Bayesian solution to the problem which can be carried out using the ‘Bayesian inference using Gibbs sampling’ (BUGS) implementation of Markov chain Monte Carlo numerical integration techniques. Dierent from other proposed methods, it uses the exact rather than an approximate likelihood, while it can handle many dierent treatment eect measures and baseline risk measures. The method diers from a recently proposed Bayesian method in that it explicitly models the distribution of the underlying baseline risks. We apply the method to three meta-analyses published in the medical literature and compare the results with the outcomes of the other recently proposed methods. In particular we compare our approach to McIntosh’s method, for which we show how it can be carried out using standard statistical software. We conclude that our proposed method oers a very general and exible solution to the problem, which can be carried out relatively easily with existing Bayesian analysis software. A condence band for the underlying relationship between true eect measure and baseline risk and a condence interval for the value of the baseline risk measure for which there is no treatment eect are easily obtained by-products of our approach. Copyright ? 2000 John Wiley & Sons, Ltd. * Correspondence to: Lidia R. Arends, Institute of Epidemiology & Biostatistics, Erasmus University Medical School, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands † E-mail: arends@epib.fgg.eur.nl ‡ Presented at the International Society for Clinical Biostatistics, Nineteenth International Meeting, Dundee, U.K., August 1998. Copyright ? 2000 John Wiley & Sons, Ltd.