Generalized Linear Multilevel Models for Ordinal Categorical Responses: Methods and Application to Medical Data

Abstract

Statistical modeling of multilevel data has been in discussion for several years and many developments have been made in this aspect. However the field of multilevel modeling for discrete categorical responses is relatively new, with markedly few applications in the areas of ordinal categorical response modeling. Most of these applications are focused in the area of educational data. The basis of this paper is to explore the use of Generalized Linear Multilevel Models for modeling a multilevel ordinal categorical response, in the field of medicine, which is somewhat of a novel application, as these methods have seldom been utilized in modeling medical data. The application focuses on analysing the factors that affect the severity of respiratory infections diagnosed in family practice and is based on data collected at 13 family practices in Sri Lanka. The data consisted of individual patient records, clustered within the practices and thus required a multilevel modeling approach. The explanatory variables pertaining to this study were: Age, Gender, Duration and most prevailing Symptom of the patients, while the ordinal categorical response indicating the severity of the diagnosis made was termed Diagnosis. Two main approaches of the Generalized Linear Multilevel Model; namely the Proportional Odds Model and the Non-Proportional Odds Model have been applied to the data and the models compared using suitable diagnostic tests. The variables Symptom and Duration provided significant main effects while the Symptom-Gender interaction also proved to be significant. Based on the DIC diagnostic, the Non-Proportional Odds model proves to be the better of the two models.