The GEE Procedure

The GEE procedure implements the generalized estimating equations (GEE) approach (Liang and Zeger 1986), which extends the generalized linear model to handle longitudinal data (Stokes, Davis, and Koch 2012; Fitzmaurice, Laird, and Ware 2011; Diggle et al. 2002). For longitudinal studies, missing data are common, and they can be caused by dropouts or skipped visits. If missing responses depend on previous responses, the usual GEE approach can lead to biased estimates. So the GEE procedure also implements the weighted GEE method to handle missing responses that are caused by dropouts in longitudinal studies (Robins and Rotnitzky 1995; Preisser, Lohman, and Rathouz 2002). The GEE procedure in SAS/STAT 14.1 does not support the weighted GEE method for the multinomial distribution for polytomous responses.

The GEE method fits a marginal model to longitudinal data. The regression parameters in the marginal model are interpreted as population-averaged. For more information about the GEE method, see Fitzmaurice, Laird, and Ware (2011); Hardin and Hilbe (2003); Diggle et al. (2002); Lipsitz et al. (1994).

The GEE procedure compares most closely to the GENMOD procedure in SAS/STAT software. Both procedures implement the standard generalized estimating equation approach for longitudinal data; this approach is appropriate for complete data or when data are missing completely at random (MCAR). When the data are missing at random (MAR), the weighted GEE method produces valid inference. Molenberghs and Kenward (2007); Fitzmaurice, Laird, and Ware (2011); Mallinckrodt (2013); O’Kelly and Ratitch (2014) describe the weighted GEE method.

The GEE procedure includes alternating logistic regression (ALR) analysis for binary and ordinal multinomial responses. In ordinary GEEs, the association between pairs of responses are modeled with correlations. The ALR approach provides an alternative by using the log odds ratio to model the association between pairs. For more information about the log odds ratio and the ALR method, see the section Alternating Logistic Regression. For binary responses the ALR algorithm of Carey, Zeger, and Diggle (1993) is implemented in both the GEE and GENMOD procedures. The GEE procedure also implements the ALR algorithm of Heagerty and Zeger (1996), which extends the ALR approach to ordinal multinomial responses. An ordinary GEE with the independent working correlation structure is also available for both nominal and ordinal multinomial data.