Statistical Methods for Analyzing Clustered Data

Clustered data arise when observations are organised into groups—such as patients within hospitals, students within schools or repeated measures on the same subject—so that measurements within a group are correlated. Classical regression techniques that assume independent observations can yield misleading standard errors and biased inference in this context. Two principal frameworks have been developed: cluster-specific models, which use random effects to capture within-cluster correlation and yield conditional estimates for a typical cluster member; and marginal or population-average models, which directly specify the average response across clusters, most commonly via generalised estimating equations. Hybrid approaches and extensions address complications such as informative cluster size, where the number of observations per cluster is related to the outcome, and confounding by cluster-level covariates. Resampling techniques, notably cluster and hierarchical bootstrap procedures, have emerged to quantify uncertainty without relying on strict distributional assumptions. Bayesian hierarchical models offer an alternative by placing priors on random effects and integrating over uncertainty. Recent advances include composite likelihood methods for high-dimensional clusters, semiparametric approaches that relax distributional assumptions on random effects, and robust rank-based tests that adjust for covariate effects and informative cluster size. These tools underpin applications ranging from risk prediction in multicentre clinical studies to diagnostic test evaluation and ecological monitoring, thereby supporting reliable inference in the presence of complex dependence structures.

Research from Nature Portfolio

No recent Nature Portfolio content available.

Statistical Methods for Analyzing Clustered Data publication trend

The graph below shows the total number of articles in statistical methods for analyzing clustered data across all publications each year (not limited to Nature Index journals).

Technical terms

Clustered data: Observations organised into groups in which measurements within each group are correlated.

Random effects: Latent variables introduced into regression models to capture extra variability due to clusters, yielding cluster-specific inference.

Marginal inference: Estimation of average population effects across clusters, typically via generalised estimating equations.

Generalised estimating equations (GEE): A semi-parametric method for estimating average response relationships in correlated data without specifying the full joint distribution.

Informative cluster size: A situation where the number of observations per cluster is associated with the outcome, potentially biasing standard methods.

Bootstrap methods: Resampling techniques that approximate the sampling distribution of a statistic by repeatedly drawing samples, adapted to respect cluster structure.

Covariate-induced group size (IICGS): The dependence between subgroup sample sizes within a cluster and subgroup outcomes, distinct from overall cluster-size informativeness.

References

1. Nonparametric bootstrap methods for interval estimation of the area under the ROC curve with correlated diagnostic test data: application to whole-virus ELISA testing in swine. Frontiers in Veterinary Science (2023).
2. Testing Informativeness of Covariate-Induced Group Sizes in Clustered Data. Mathematics (2024).
3. Review of methods for handling confounding by cluster and informative cluster size in clustered data. Statistics in Medicine (2014).
4. Risk prediction in multicentre studies when there is confounding by cluster or informative cluster size. BMC Medical Research Methodology (2021).
5. Robust Testing of Paired Outcomes Incorporating Covariate Effects in Clustered Data with Informative Cluster Size. Stats (2022).