A Genralzied Estimating Equations Approach To Categorical Data

Repeated measures data is ubiquitous in medical research. There are perfect models to the quantitive data with the family of Gaussian or normal probability distributions which is easy to implement. But it is difficult to analyse the categorical data, such as binary and ordinal data. In the article we arise both generalized estimating equation (GEE) and alternating logistic regressions (ALR) to accommodate the binary data. Firstly we introduce the basic theory of GEE, that is generalized linear model. However, generalized linear model have some limitations in practice that the data is independent. So it must be extended and GEE is proposed by Liang and Zeger. Then we reserves as a review of ALR and criterion measures of GEE. Finally some examples are given to show the application of models. GENMOD is user-friendly SAS(9.0) modules for the result of GEE and ALR. Criterion measures of GEE are obtained using qic module with STATA7.0 and it evaluate the goodness of fit of the model which are the prime correlation structure and the subset of covariates in particular model. Through examples, it comes a conclusion that GEE and ALR can account for the correlation among the repeated observations of a given subject, can be designed to guarantee consistency of the regression coefficient estimates, and can allow imbalance to different observation times. However ALR perform well relative efficiency.In the article, GEE is accommodated to fit repeated measures data with ordinal response, it has been proposed by S.R Lipsitz, K Kim and L.Zhao in 1994 and it is based on GEE originally proposed by Zeger and Liang in 1986. Here we introduce the theory of model and evaluate the model using examples. An SAS macro which implements model is available, and valid options of correlation structure have independence, exchangeable, banded and unstructured structure. GENMOD module in SAS can also be useed to result it, but it only account for independence structure. So the SAS macro extends GEE in practice. Simultaneitily, mixed-effects model is introduced too which is proposed by Hedeker and Gibbons in 1994 which can analyse random-effect of multilevel. The NLMIXED procedure in SAS is used to fit the mixed-effects models for the ordinal response data. Owing to the flexibility of model, it is well established. And it can cope with missing data. But it is difficult to estimate parameter and random-effect through integration when there is too many random-effects.In a word, GEE can solve the problem of correlation among repeated measures and can provide inferences that are robust with respect to some forms of model misspecification, particularly misspecification of serial effects in repeated measures, and it can solve missing data.