clustered data analysis

In cluster-randomized trials, conventional methods such as generalized linear mixed models (GLMMs) and generalized estimating equations (GEE) suffer from ambiguous estimands for treatment effects under model misspecification or informative cluster size. This paper proposes a model-robust standardization approach: first constructing marginal estimators simultaneously consistent for both cluster-averaged and individual-averaged treatment effects; deriving variance estimates via the jackknife and developing a formal test for informative cluster size. The method avoids specifying the intra-cluster correlation structure correctly and retains consistency under diverse forms of model misspecification. Simulation studies demonstrate substantially improved estimation accuracy and inferential reliability compared to standard GLMM and GEE approaches. An open-source R package, MRStdCRT, implements the proposed methodology.

This study addresses the variable reliability of cluster-robust inference methods in cross-sectional and panel data regressions, which often depends on data structure and model specification. The authors propose an integrated evaluation framework to systematically compare the performance of various cluster-robust variance estimators and inference procedures—including analytical and bootstrap approaches—across diverse empirical scenarios. Their analysis demonstrates that while no single method universally dominates, conducting inference through cross-validation using multiple methods substantially enhances result credibility. This framework offers applied researchers a practical guide for selecting more reliable statistical inference strategies tailored to their specific contexts, thereby strengthening the robustness of empirical conclusions and policy recommendations.

This paper addresses statistical inference challenges in difference-in-differences (DID) designs with a single treated cluster and a fixed number of control clusters. Under weak assumptions permitting arbitrary unknown intra-cluster dependence, we propose a variance-free t-test that avoids estimating the asymptotic variance. The method requires only a user-specified bound on the relative heteroskedasticity between treated and control clusters; it then constructs customized critical values—either analytically or via numerical optimization—to achieve valid inference at any desired significance level. Unlike conventional approaches, it does not rely on asymptotic normality or large numbers of clusters, thereby substantially improving inference reliability in small-sample and limited-control-group settings. Extensive simulations and empirical applications demonstrate the method’s robustness and high statistical power. A table of commonly used critical values is provided for immediate implementation by applied researchers.

Existing calibration assessment methods for multicenter clinical prediction models overlook inter-center heterogeneity in calibration, leading to potentially misleading aggregate evaluations. Method: We propose three novel calibration plot methods—CG-C, 2MA-C, and MIX-C—that explicitly incorporate clustering structure by integrating random-effects modeling with spline-based smoothing. These methods jointly estimate population-average and center-specific calibration curves. Contribution/Results: The framework enables quantification of calibration heterogeneity, robust inference for small-sample centers, and simultaneous estimation of confidence and prediction intervals. In a multicenter validation study for ovarian tumor malignancy risk prediction, MIX-C most closely approximated the true center-specific calibration curves, while 2MA-C (with splines) achieved optimal prediction interval coverage. All methods are open-source, modular, and readily deployable. Collectively, they establish a unified, robust, and interpretable statistical framework for calibration assessment in multicenter prediction modeling.

Conventional clustered robust inference fails when cluster sizes are non-negligible—e.g., following Zipf’s law—and 77% of empirical studies in the *American Economic Review* and *Econometrica* (2020–2021) violate its implicit equal-size or bounded-size assumptions. Method: This paper establishes the first necessary and sufficient condition for consistency of clustered robust estimators and proposes two new procedures: score subsampling and size-adjusted reweighting. Both methods are theoretically grounded—guaranteeing consistency and uniform size control—and practically implementable, with ready-to-use Stata packages. Results: Monte Carlo simulations demonstrate that the proposed methods strictly maintain nominal test size even where conventional approaches severely distort inference. They constitute the first truly robust and implementable inferential framework for settings with large, heterogeneous cluster sizes.

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.

Modern heterogeneity-robust difference-in-differences estimators derive their asymptotic properties under iid, cluster, or fixed-design frameworks that abstract from complex survey sampling, yet practitioners routinely apply them to nationally representative surveys with stratified cluster designs. We show that, under standard regularity conditions, the influence functions of each smooth IF-based or regression-based modern DiD estimator satisfy Binder's (1983) smoothness conditions, so the standard stratified-cluster variance formula applied to their values produces design-consistent standard errors. A Monte Carlo study with 66,000 replications shows where the design effect comes from. HC1 standard errors that treat observations as iid produce coverage as low as 34% under a baseline survey design and below 11% under informative sampling. Combining the survey-weighted point estimate with PSU-level clustering - the practitioner's cluster=psu heuristic - recovers near-nominal coverage across all scenarios. Adding strata and finite-population corrections yields incremental precision but is not required for valid coverage. Survey-weighted doubly robust estimation produces well-calibrated inference when parallel trends hold only conditionally. An NHANES illustration of the ACA dependent coverage provision shows that point estimates and standard errors change substantively - enough to reverse significance conclusions - when the survey design is accounted for. We provide diff-diff (https://github.com/igerber/diff-diff), an open-source Python package implementing design-based variance for fifteen modern DiD estimators.

This study addresses the limitations of conventional variance reduction methods in switchback experiments on online platforms, where clustered structures and temporal autocorrelation often invalidate standard assumptions. The authors develop a hierarchical simulation framework to systematically evaluate the performance of CUPED, CUPAC (a machine learning–based covariate adjustment approach), doubly robust estimators, and cluster-robust standard errors across diverse experimental conditions—including varying numbers of clusters, levels of autocorrelation, and spillover effects. Through sensitivity analyses accounting for cross-cluster interference, they quantify each method’s behavior in terms of false positive rates, confidence interval coverage, standard error reduction, statistical power, and minimum detectable effect sizes. The work culminates in a practical decision map that delineates the applicability boundaries and trade-offs of these variance reduction techniques, highlighting fundamental constraints imposed by temporal and cluster dependence.

This study addresses the inconsistency in sensitivity analyses for unmeasured confounding that arises when observational studies with clustered treatment assignment are analyzed at different levels—individual versus cluster. Focusing on linear regression models under clustered treatment, the authors propose a correction method based on Pearson’s partial eta-squared. By applying the Mundlak transformation to incorporate cluster means of covariates and parameterizing unmeasured confounding bias through partial R², the approach ensures equivalence between individual- and cluster-level sensitivity analyses. The method explicitly accounts for between-cluster variation in driving bias, thereby reconciling cross-level discrepancies and substantially enhancing the robustness and reliability of causal inference in clustered data settings.

研究评估了多种统计方法在处理仅有少数集群的随机交叉试验中的表现，发现准确建模集群-周期相关性比选择固定或随机集群截距更重要。