fit generalized estimating equations

This study addresses bias in marginal population parameter estimation for non-normal, bivariate correlated data—particularly in longitudinal settings. We systematically compare the performance of generalized joint regression models (GJRM), generalized linear mixed models (GLMM), and generalized estimating equations (GEE). Through Monte Carlo simulations and analysis of real-world physician visit data, we first demonstrate that GLMM yields substantial bias in marginal parameter estimates under non-identity link functions and skewed response distributions. In contrast, GJRM—when the copula is correctly specified—exhibits unbiased marginal estimation, robust standard errors, and superior model fit. GJRM maintains consistency of marginal estimates and validity of statistical inference across diverse non-normal distributions (e.g., Poisson, negative binomial, Beta), outperforming GLMM, GEE, and generalized linear models (GLM). These findings establish GJRM as a more reliable methodological choice for analyzing such complex correlated data.

This study addresses the substantial bias in generalized estimating equations (GEE) when the number of independent clusters is small. Viewing GEE as an M-estimator for clustered data, the authors derive a corrected estimating equation that achieves first-order bias reduction while accounting for the dependence of the working covariance on mean parameters. Innovatively, they formulate the bias-corrected GEE estimator under a pairwise odds-ratio parameterization, circumventing the stringent compatibility constraints imposed by traditional correlation-based parameterizations on marginal means and thereby enhancing suitability for small-sample settings. Six new estimators implemented in the R package geer demonstrate markedly reduced bias across various scenarios, while preserving efficiency and confidence interval coverage comparable to standard GEE. The practical utility of the proposed approach is further validated through application to clinical trial data analysis.

This study addresses the instability of conventional generalized estimating equations (GEE) in separation scenarios—such as small samples, sparse data, or rare events—where non-convergence or extreme estimates commonly occur, particularly under non-independent working correlation structures. To overcome these limitations, the authors propose a penalized GEE framework that integrates Jeffreys’ prior penalty with a marginalized odds ratio parameterization, effectively circumventing the breakdown of traditional correlation parameters at extreme probabilities and guaranteeing finite estimates. The approach accommodates multiple link functions, including logit, probit, clog-log, and cauchit, and introduces both a one-step algorithm (OPGEE) and a hybrid variant (HPGEE) to enhance computational efficiency. Simulation studies and an analysis of a respiratory disease trial demonstrate that the proposed method substantially outperforms standard GEE under separation while maintaining comparable performance in regular settings. The methodology is implemented in the R package geer.

Conventional generalized estimating equations (GEE) suffer from low estimation efficiency in small-to-moderate samples when analyzing pure-tone audiometry data, where complex within-cluster correlation structures—particularly interaural dependence—violate standard working correlation assumptions. Method: This paper introduces a novel second-order GEE framework that jointly estimates regression coefficients and correlation structure parameters—specifically modeling interaural correlation parametrically—thereby improving statistical efficiency for ear-level covariate effects, especially under moderate-to-strong within-cluster dependence. Contribution/Results: Simulation studies and analysis of real data from the Conservation of Hearing Study demonstrate that the proposed method achieves superior efficiency gains for ear-level exposure effect estimation compared to independence-, exchangeable-, and unstructured-GEE approaches. It robustly identifies a statistically significant association between dietary adherence and hearing loss. The core innovation lies in establishing an estimable and interpretable correlation structure modeling framework, advancing precise analysis of high-dimensional repeated-measures data in auditory epidemiology.

Existing R tools lack systematic support for crossover design data—particularly those involving longitudinal within-period measurements and carryover effects. This paper introduces CrossCarry, the first open-source R package specifically designed for modeling crossover trials. It accommodates exponential-family responses, arbitrary-order designs, and scenarios with or without washout periods. Methodologically: (1) it extends the generalized estimating equations (GEE) framework by jointly modeling within-period correlation structures and between-period carryover dependencies—a novel integration; (2) it incorporates B-spline–based nonparametric components to flexibly estimate both temporal trends and carryover effects; and (3) it enables unified, flexible modeling of treatment, time, and carryover effects. Empirical evaluations demonstrate that CrossCarry substantially improves statistical power and estimation accuracy for treatment and carryover effects under challenging conditions—including skewed responses and weak washout.

This study addresses the challenge of reliably estimating the variance of standardized treatment effects in randomized trials with rare binary outcomes or small sample sizes, where existing methods often inflate Type I error rates. The authors propose an influence function–based leave-one-out cross-validation (IF-LOO) variance estimator within the g-computation framework for covariate adjustment. This approach provides, for the first time, a closed-form variance estimator for the standardized average treatment effect that exhibits favorable finite-sample properties, combining computational efficiency with theoretical rigor. Simulation studies demonstrate that IF-LOO effectively controls Type I error in settings with rare events and limited sample sizes, substantially outperforming current methods while remaining readily implementable in clinical trial statistical practice.

This study addresses marginal parameter estimation in settings with missing data, such as two-phase studies, by proposing Marginal Generalized Raking (MGR)—the first extension of the generalized raking framework to marginal inference. Leveraging influence function theory, MGR efficiently incorporates auxiliary information and substantially improves estimation efficiency over naive approaches that simply marginalize conditional generalized raking estimators, while preserving robustness. The method integrates augmented inverse probability weighting with parametric working models, and its theoretical advantages are corroborated through both simulation studies and empirical analysis of an HIV observational cohort. Results demonstrate that MGR achieves superior finite-sample performance, thereby advancing the theory of marginal inference under generalized raking for incompletely observed data.

This study addresses the sensitivity of causal effect estimation to model misspecification in longitudinal cluster-randomized and quasi-experimental designs. Within an M-estimation framework, it demonstrates that fixed-effects models yield consistent and asymptotically normal estimates of nonparametrically defined treatment effects, provided the treatment effect structure is correctly specified—even when other model components are arbitrarily misspecified. The work establishes, for the first time, that fixed-effects models are valid for estimating superpopulation marginal effects and reveals their robustness to partial misspecification of the treatment effect structure across diverse longitudinal settings. Through theoretical analysis, simulations, and reanalyses of empirical data, the paper further shows that fixed-effects models outperform mixed-effects models in robustness and reliability when time-invariant confounding exists at the cluster or individual level.

This study addresses the challenge of regression with high-dimensional responses and covariates when the responses are influenced by both observed covariates and unobserved latent variables, a setting where conventional multivariate regression methods fail to provide effective modeling. The authors propose a generalized latent variable model that accommodates mixed-type high-dimensional responses and allows for flexible dependence structures between covariates and latent factors. By decomposing the non-convex estimation problem into a sequence of convex subproblems through alternating optimization, and integrating debiased estimation with asymptotic normality analysis, the work achieves, for the first time, valid statistical inference on covariate effects within a high-dimensional generalized latent variable framework. The proposed estimator enjoys statistical consistency and guaranteed error bounds, while the debiased version exhibits asymptotic normality, as demonstrated empirically in an application to PISA data for assessing educational equity.

This work addresses key limitations of traditional Bayesian profile regression in handling hierarchical or longitudinal data, its inability to effectively model interactions between latent profile clusters and covariates, and its reduced statistical efficiency under highly correlated covariate structures. To overcome these challenges, the authors integrate generalized linear mixed models (GLMMs) into the Bayesian profile regression framework, incorporating random effects to accommodate multilevel and longitudinal designs. The latent clusters derived from profile clustering are explicitly included as predictors in the outcome model, enabling direct modeling of cluster–covariate interactions. This approach substantially extends the applicability of profile regression and enhances both modeling efficiency and predictive performance for complex dependency structures. An open-source R package implementing this method combines Bayesian inference, GLMMs, and profile clustering, supporting continuous or binary outcomes and mixed-type covariates, with broad utility in epidemiology, social sciences, and clinical research.