STRATIFIED OR MULTICENTER ANALYSIS WITH EXTENDED MANTEL-HAENSZEL STATISTICS

Since its introduction in 1959 the ability of the classical Mantel-Haenszel (M-H) procedure for combining the odds ratios of a set of I 2 x 2 tables has led to its use also in stratified or multicentre type clinical trials. A familiar application is the M-H logrank test in survival analysis. An extension of the M-H procedure covering the case of 2 x K contingency tables (MANTEL, 1963) with ordered levels retains the essential property of pooling the results of I homogeneous tables (i.e. in absence of qualitative interactions). The assignment of some score for the K columns of a table is essential for the use of the method (in comparing 2 treatments). Some possibilities of score assignment are discussed: for clinical outcome variables such as the degree of severity of a disease, pain and so on, the score is at hand in a natural way. A less well-known type of scoring consists in ranking the observations of a continuous variable, leading to cell sizes of 1 or 0. In this case, however, if equidistant ranking was used, the E-M-H procedure appears as an extension of Wilcoxon's rank sum test and represents a powerful non-parametric approach in stratified or multicentre type designs with non normally distributed outcome variables. The results of some Monte-Carlo simulations for 2 possible equidistant ranking procedures are presented, which indicate only a moderate gain in power as compared to Wilcoxon's rank sum test under the common situation of centre effects not exceeding treatment effects. Use of the E-M-H procedure is also recommended as a simple method to overcome the potential bias due to unequally distributed prognostic factors among treatment groups.