Generalized Cochran Mantel Haenszel test for multilevel correlated categorical data: an algorithm and R function

Abstract

Multilevel data are a commonly encountered phenomenon in many data structures. Modelling such data requires careful consideration of the association between underlying variables at each level of the data structure. This requires the use of effective univariate techniques prior to modelling. However, currently no univariate tests are used to handle this situation. This paper presents the modification and novel application of a test developed by Zhang and Boos for testing the association between categorical variables measured on clusters of observations, for examining initial association in a multilevel framework. Zhang and Boos have used a SAS/IML programme (unpublished) for performing their test. This paper presents an R function for the application of the test, which will be freely available to users, since R is an open source software. The function is tested on a dataset from the medical field pertaining to respiratory disease severity of patients, attending several different clinics. The explanatory variables pertaining to this study are Age, Gender, Duration and Symptom, while the response variable indicating the severity of the diagnosis made is termed Diagnosis. The results indicate that when the experimental units show low levels of correlation within clusters with respect to a particular explanatory variable, the test performs similarly to the Standard Cochran Mantel Haenszel (CMH) test. When the corresponding correlation is high, the Generalized CMH (GCMH) test results in a smaller p-value than the Standard CMH test. Of the four variables, only Symptom and Duration are significant with respect to association with Diagnosis.