odds-ratio parameterized gee

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.

In cluster-randomized trials (CRTs) with few clusters (<30–40), conventional inference for hazard ratios (HRs) and risk differences (RDs) often inflates Type I error rates. To address this, we systematically evaluate the finite-sample performance of generalized estimating equations (GEE) with binomial, Poisson, and Gaussian working models, combined with bias-corrected standard errors—including Kauermann–Carroll (KC), Morel–Bokossa–Neuhaus (MBN), Morel–Dai (MD), and average (AVG)—and t-distribution–based inference. Our study fills a critical methodological gap in robust HR/RD estimation for small- to moderate-cluster CRTs. It demonstrates substantial improvements in Type I error control and statistical power under challenging conditions: rare outcomes, small cluster sizes, high intracluster correlation, and highly variable cluster sizes. The findings yield directly implementable, evidence-based analytical recommendations for practitioners conducting CRTs with limited numbers of clusters.

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 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 the substantial bias exhibited by the G-computation estimator in high-dimensional settings within small-sample randomized controlled trials (RCTs) involving multiple covariates. By leveraging a proportional asymptotic framework to elucidate the underlying bias-generating mechanism, this work proposes effective bias-correction strategies tailored for high-dimensional, small-sample scenarios. These strategies integrate cross-fitting, leave-one-out techniques, and Monte Carlo simulations. Furthermore, the paper systematically evaluates the performance of various correction methods, establishing both a theoretical foundation and practical guidelines for the robust application of G-computation in modern RCTs.

This study addresses the lack of a unified robust inference framework for generalized causal effects—such as the Mann-Whitney parameter or causal net benefit—under non-Gaussian or multivariate outcomes. The authors develop a design-based regression adjustment and variance estimation framework that defines effect sizes through pairwise contrast functions. Innovatively integrating U-statistics with finite-population asymptotic theory, they propose a model-assisted (rather than model-dependent) estimation approach and demonstrate that covariate adjustment does not universally yield efficiency gains under nonlinear contrasts. To resolve the inconsistency of existing robust variance estimators in this setting, they further introduce a fully two-way clustered robust variance estimator. Theoretical analysis establishes the consistency and asymptotic normality of the proposed estimators, which remain valid even under misspecification of the working model.

In covariate-adaptive randomization (CAR) trials with high-dimensional covariates (p = o(n)), model-free adjustment for covariates remains challenging for unbiased average treatment effect (ATE) estimation. Method: We propose an unbiased ATE estimator based on second-order U-statistics. Our approach innovatively extends coupling techniques to the U-statistic framework and employs an m-out leave-out analysis of the inverse Gram matrix. It simultaneously achieves controllable bias, minimal assumptions, and efficiency gains under both CAR and superpopulation settings. Contribution/Results: Theoretically, the estimator is asymptotically unbiased and delivers deterministic efficiency gains over standard estimators. Synthetic and semi-synthetic experiments demonstrate substantial finite-sample improvements over state-of-the-art methods. Crucially, our method breaks the classical bias–efficiency trade-off inherent in ordinary least squares (OLS) under high-dimensional CAR, establishing a new paradigm for efficient, assumption-light causal inference without structural modeling constraints.

本文针对具有信息性集群大小的集群随机试验中治疗效果估计问题，提出了一种简单且稳健的方法：通过饱和集群大小模型与g-计算来准确估计个体和集群平均治疗效果。