[Paper Review] R Package multgee: A Generalized Estimating Equations Solver for Multinomial Responses

Anestis Touloumis|arXiv (Cornell University)|Oct 20, 2014

Advanced Causal Inference Techniques22 citations

TL;DR

This paper introduces the R package multgee, which implements a novel generalized estimating equations (GEE) approach for correlated multinomial responses using marginalized local odds ratios. Unlike existing software, it supports both ordinal and nominal responses with flexible association structures, improving estimation efficiency and avoiding convergence issues common in traditional GEE methods for multinomial data.

ABSTRACT

The R package multgee implements the local odds ratios generalized estimating equations (GEE) approach proposed by Touloumis et al. (2013), a GEE approach for correlated multinomial responses that circumvents theoretical and practical limitations of the GEE method. A main strength of multgee is that it provides GEE routines for both ordinal (ordLORgee) and nominal (nomLORgee) responses, while relevant softwares in R and SAS are restricted to ordinal responses under a marginal cumulative link model specification. In addition, multgee offers a marginal adjacent categories logit model for ordinal responses and a marginal baseline category logit model for nominal. Further, utility functions are available to ease the local odds ratios structure selection (intrinsic.pars) and to perform a Wald type goodness-of-fit test between two nested GEE models (waldts). We demonstrate the application of multgee through a clinical trial with clustered ordinal multinomial responses.

Motivation & Objective

• To address the limitations of existing GEE methods for correlated multinomial responses, particularly their restriction to ordinal data and sensitivity to association structure misspecification.
• To develop a unified GEE framework that applies to both ordinal and nominal multinomial responses by using marginalized local odds ratios as a nuisance parameter.
• To provide practical R functions for model fitting, goodness-of-fit testing, and local odds ratios structure selection, enhancing usability and reliability.
• To overcome convergence problems in existing GEE implementations by decoupling the marginal model from the association structure through a stable parameterization.
• To enable robust inference for clustered or repeated multinomial outcomes in clinical and longitudinal studies where response categories are not necessarily ordered.

Proposed method

• Proposes a GEE approach that models the association structure via marginalized local odds ratios, treating them as a nuisance parameter independent of the marginal model.
• Employs the family of association models (Goodman, 1985) to define parsimonious and interpretable local odds ratios structures, such as 'uniform' and 'time.exch'.
• Implements two core functions: ordLORgee for ordinal responses (using cumulative or adjacent categories logit models) and nomLORgee for nominal responses (using baseline category logit model).
• Introduces utility functions: intrinsic.pars for selecting local odds ratios structures based on rule-of-thumb criteria, waldts for Wald-type goodness-of-fit testing between nested models, and matrixLOR for constructing desired local odds ratios tables.
• Uses the 'sandwich' estimator for robust standard errors and applies a Wald test to assess significance of regression coefficients.
• Applies a small constant (add) to handle sparse contingency tables and improve convergence, especially with complex structures.

Experimental results

Research questions

• RQ1 Can a GEE approach for multinomial responses be developed that is robust to association structure misspecification and applicable to both ordinal and nominal outcomes?
• RQ2 How does the use of marginalized local odds ratios as a nuisance parameter improve the stability and efficiency of GEE estimation compared to existing methods?
• RQ3 What local odds ratios structures (e.g., uniform, time.exch) are most effective for achieving convergence and efficient estimation in practice?
• RQ4 How can goodness-of-fit be assessed between nested GEE models for multinomial responses when standard likelihood ratio tests are not available?
• RQ5 What practical guidelines can be derived for selecting marginal models and association structures in real-world clustered multinomial data analysis?

Key findings

• The local odds ratios GEE approach significantly improves estimation efficiency compared to the independence 'working' correlation structure, with efficiency gains observed in simulations.
• The multgee package successfully implements GEE for both ordinal and nominal multinomial responses, overcoming a key limitation of existing R and SAS software that restricts to ordinal responses under cumulative link models.
• The 'uniform' structure for local odds ratios yielded an estimated value of 2.257 in the clinical trial example, indicating consistent association across response categories and time points.
• The p-value for the null model (testing no covariate effects) was <0.0001, indicating strong evidence against the null hypothesis and significant covariate effects in the model.
• The Wald-type goodness-of-fit test comparing nested models yielded a p-value of 0.1384, suggesting no significant improvement from adding sex and age to the model at conventional levels.
• Convergence issues were observed with complex local odds ratios structures or sparse tables, but these were mitigated by simplifying the structure or increasing the add constant in contingency tables.