How to Use SAS for Logistic Regression with Correlated Data

Abstract

Many study designs in applied sciences give rise to correlated data. For example, subjects are followed over time, are repeatedly treated under different experimental conditions, or are observed in logical units (e.g. clinics, families, litters). Statistical methods for regression analysis for this kind of data with continuous responses are quite established and the SAS® system offers a variety of procedures (GLM procedure, MIXED procedure) for analysis. For discrete responses, however, we have to face a greater mathematical complexity and statistical analysis is not that straightforward any longer. We show the different options that the SAS® system offers for the analysis of binary responses with correlated data (GENMOD procedure, %GLIMMIX, %NLINMIX, NLMIXED procedure, PHREG/LOGISTIC procedure and Meta-Analytic methods), investigate their statistical properties, and illustrate them by an example of a multicenter study. We conclude that it is difficult to give general recommendations which of the methods to use because this depends on the data at hand and on the desired interpretation of parameters, but in our data set we feel most comfortable with the results from the NLMIXED and the PHREG/LOGISTIC procedure.