Stratified or Multicentre Analysis with Extended Mantel–Haenszel Statistics

Abstract

AbstractSince 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 × 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 × 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 proćedure is also recommended as a simple method to overcome the potential bias due to unequally distributed prognostic factors among treatment groups.