Variance estimation in tests of clustered categorical data with informative cluster size

Stat Methods Med Res, 2020 · DOI: 10.1177/0962280220928572 · Published: November 1, 2020

Simple Explanation

This paper addresses the problem of analyzing clustered data where the size of the cluster is related to the outcome of interest, a situation called informative cluster size (ICS). Classical tests don't work well in this situation. The authors focus on categorical data, where outcomes fall into categories. The authors develop new statistical tests that adjust for ICS when dealing with categorical data. These tests are based on reweighting the data to account for the bias introduced by ICS. They also compare different ways of estimating the variance of these tests. Through simulations, the authors show that the choice of variance estimation method significantly impacts the performance of these tests. They find that variance estimators constructed under the null hypothesis perform best.

Study Duration

Not specified

Participants

175 individuals with spinal cord injuries

Evidence Level

Simulation study and application to a real-world dataset

Key Findings

1
Cluster-weighted tests based on variance estimators constructed under the null hypothesis maintain size closest to nominal.
2
The choice of variance estimation technique can have a profound impact on the performance of cluster-weighted tests for categorical data.
3
The cluster-weighted test using the null sandwich variance estimator exhibited consistently higher power.

Research Summary

This paper develops cluster-weighted estimators of marginal proportions that remain unbiased under informativeness, and derives analogues of three popular tests for clustered categorical data: the one-sample proportion, goodness of fit, and independence chi square tests. The authors construct these tests using several variance estimators and demonstrate substantial differences in the performance of cluster-weighted tests based on variance estimation technique. The proposed tests are illustrated through an application to a data set of functional measures from patients with spinal cord injuries participating in a rehabilitation program.

Practical Implications

Improved Analysis of Clustered Categorical Data

The developed tests provide more accurate statistical inference for clustered categorical data when informative cluster size is present, reducing potential bias.

Guidance on Variance Estimation

The study highlights the importance of variance estimation techniques, suggesting that estimators constructed under the null hypothesis are preferable for cluster-weighted tests.

Application in Biomedical Research

The methods can be applied to various biomedical research areas where clustered categorical data with informative cluster size is common, such as dental studies and longitudinal patient data.

Study Limitations

1
The methods are asymptotic in nature and require a sufficiently large number of clusters (approximately 30 or more).
2
The tests may be inappropriate under within-cluster group size informativeness, requiring alternative weighting methods.
3
The application corresponds to an analysis of a typical member from a typical cluster, in which the cluster is the primary unit of interest; other marginal analyses may be more appropriate in some cases.

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