A Comparison of Variance Estimators for Logistic Regression Models Estimated Using Generalized Estimating Equations (<scp>GEE</scp>) in the Context of Observational Health Services Research
Bibliographic record
Abstract
In observational health services research, researchers often use clustered data to estimate the independent association between individual outcomes and several cluster-level covariates after adjusting for individual-level characteristics. Generalized estimating equations are a popular method for estimating generalized linear models using clustered data. The conventional Liang-Zeger variance estimator is known to result in estimated standard errors that are biased low when the number of clusters in small. Alternative variance estimators have been proposed for use when the number of clusters is low. Previous studies focused on these alternative variance estimators in the context of cluster randomized trials, which are often characterized by a small number of clusters and by an outcomes regression model that often consists of a single cluster-level variable (the treatment/exposure variable). We addressed the following questions: (i) which estimator is preferred for estimating the standard errors of cluster-level covariates for logistic regression models with multiple binary and continuous cluster-level variables in addition to subject-level variables; (ii) in such settings, how many clusters are required for the Liang-Zeger variance estimator to have acceptable performance for estimating the standard errors of cluster-level covariates. We suggest that when estimating standard errors: (i) when the number of clusters is < 15 use the Kauermann-Carroll estimator; (ii) when the number of clusters is between 15 and 40 use the Fay-Graubard estimator; (iii) when the number of clusters exceeds 40, use the Liang-Zeger estimator or the Fay-Graubard estimator. When estimating confidence intervals, we suggest using the Mancl-DeRouen estimator with a t-distribution.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.141 | 0.404 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.004 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".