GMM logistic regression models for longitudinal data with time-dependent covariates and extended classifications.

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Statistical Modeling

Background:

• Analyzing longitudinal data requires accounting for correlations from repeated measures and feedback loops between responses and predictors over time.
• Generalized estimating equations with independent working correlation are a common approach, but may not fully utilize all moment conditions.

Purpose of the Study:

• To explore an alternative approach using a generalized method of moments (GMM) for estimating regression coefficients in longitudinal data.
• To develop a GMM approach that utilizes all valid moment conditions for time-dependent and time-independent covariates without assuming constant feedback.
• To implement and evaluate a continuously updating GMM logistic regression model for time-dependent covariates.

Main Methods:

• Developed a generalized method of moments approach for longitudinal data analysis.
• Utilized continuously updating GMM for parameter estimation.
• Fitted GMM logistic regression models with time-dependent covariates using SAS PROC IML and R.
• Employed adjusted p-values for multiple correlated tests to select appropriate moment conditions.

Main Results:

• The proposed GMM approach effectively incorporates time-dependent and time-independent covariates.
• The method does not require assumptions about the presence or degree of feedback over time.
• Demonstrated the application of the GMM logistic regression model using re-hospitalization data and child BMI-morbidity data.
• Conducted a simulation study to compare the performance of extended classifications.

Conclusions:

• The generalized method of moments provides a robust and flexible framework for analyzing longitudinal data with complex correlation structures.
• This approach enhances regression coefficient estimation by leveraging all relevant moment conditions.
• The GMM logistic regression model is a valuable tool for researchers working with time-dependent covariates in various fields.