A LOGISTIC MODEL FOR TREND IN 2X2XK TABLES WITH APPLICATIONS TO METAANALYSES

There recently has been an increased interest in examining the relatio nship between the baseline (control) risk of an adverse outcome and th e magnitude of the treatment effect (Brand and Kragt, 1992, Statistics in Medicine 11, 2077-2082; Davey Smith, Song, and Sheldon, 1993, The British Medical Journal 306, 1367-1373; Senn, 1994, Statistics in Medi cine 13, 293-294). To facilitate such an examination, we propose a log istic model in which the relationship between the treatment effect, as measured by the log odds ratio, and the baseline risk is specified pa rametrically. This procedure is founded on a product-binomial likeliho od and generates maximum likelihood estimates of the baseline event ra tes and two parameters characterizing the trend in the treatment effec t. We fit this model to data from a meta-analysis involving the treatm ent of women at risk of preterm labor and contrast our findings with t hose of an earlier analysis.