Estimating marginal and incremental effects on health outcomes using flexible link and variance function models

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Generalized linear models (GLMs) are widely used for analyzing various data types.
• Traditional GLMs often assume a fixed link function and variance structure.
• Accurate model specification is crucial for reliable inference on covariate effects.

Purpose of the Study:

• To extend estimating equations in GLMs for simultaneous estimation of regression coefficients, link function, and variance structure.
• To facilitate inference on the mean of the outcome as a function of covariates.
• To define and estimate covariate effects, including an analogous parameter for discrete covariates.

Main Methods:

• Developed an extension to estimating equations within the framework of generalized linear models.
• Proposed a method for simultaneous estimation of parameters in the link function, variance structure, and regression coefficients.
• Utilized Monte Carlo simulations to assess the consistency of the parameter estimators.

Main Results:

• The proposed estimation method demonstrated consistency of parameter estimators in simulations.
• The method aids in identifying appropriate link functions and suggesting underlying distributions.
• It provides a robust estimation approach when the outcome distribution is uncertain.

Conclusions:

• The novel estimation method offers a flexible and robust approach to GLM analysis.
• It improves the ability to perform accurate inference on covariate effects.
• The method is applicable to diverse datasets, as illustrated with inpatient expenditure data.