Generalized Estimating Equations (GEE) are a method for analyzing correlated response data, such as repeated measurements on the same subject or observations clustered within groups. GEE extends the framework of Generalized Linear Models (GLMs) to situations where the assumption of independence between observations is not appropriate.
GEE estimates population-averaged (marginal) effects, making it suitable for research questions focused on the average response in a population rather than subject-specific effects. Brief introduction to GEE can be found in the practical statistics blog here or more mathematical details in SAS documentation. GEE is available in BESH stat starting from version 0.23.
Example
Example taken from SAS proc GEE documentation. The response is the number of epileptic seizures, which was measured at the end of each of eight two-week treatment periods over sixteen weeks. The first eight weeks were the baseline period (during which no treatment was given), and the second eight weeks were the treatment period, during which patients received either a placebo or the drug progabide. The question of scientific interest is whether progabide is effective in reducing the rate of epileptic seizures. You can download the data here.
Outcome represents the rate of epileptic seizures (number of epileptic seizures per time interval). Treatment (progabide/placebo), treatment period (week 0 to 8 (baseline)/week 8 to 16(treatment), and interaction are used as an explanatory variables.
Poisson regression is commonly used to model count data. In this example, the log-linear Poisson model is specified by the Poisson variance function and a log link function. Because the visits represent repeated measurements, the responses from the same individual are correlated and inferences need to take this into account. The correlations between the counts are modeled using unstructured correlation structure. In the fitted model, the regression parameters are interpreted in terms of the log seizure rate.
To run the analysis in BESH stat open the seizures.csv in excel and select <Generalized Estimating Equations (GEE)> from the BESH stat <Regression Models> menu. Then populated fields as on the screenshots below.
Results
BESH stat results match those provided in SAS documentation.