The effect of number of clusters and magnitude of within‐cluster homogeneity in outcomes on the performance of four variance estimators for a marginal multivariable Cox regression model fit to clustered data in the context of observational research
Bibliographic record
Abstract
Researchers often estimate the association between the hazard of a time-to-event outcome and the characteristics of individuals and the clusters in which individuals are nested. Lin and Wei's robust variance estimator is often used with a Cox regression model fit to clustered data. Recently, alternative variance estimators have been proposed: the Fay-Graubard estimator, the Kauermann-Carroll estimator, and the Mancl-DeRouen estimator. Using Monte Carlo simulations, we found that, when fitting a marginal Cox regression model with both individual-level and cluster-level covariates: (i) in the presence of weak to moderate within-cluster homogeneity of outcomes, the Lin-Wei variance estimator can result in estimates of the SE with moderate bias when the number of clusters is fewer than 20-30, while in the presence of strong within-cluster homogeneity, it can result in biased estimation even when the number of clusters is as large as 100; (ii) when the number of clusters was less than approximately 20, the Fay-Graubard variance estimator tended to result in estimates of SE with the lowest bias; (iii) when the number of clusters exceeded approximately 20, the Mancl-DeRouen estimator tended to result in estimated standard errors with the lowest bias; (iv) the Mancl-DeRouen estimator used with a t-distribution tended to result in 95% confidence that had the best performance of the estimators; (v) when the magnitude of within-cluster homogeneity in outcomes was strong or very strong, all methods resulted in confidence intervals with lower than advertised coverage rates even when the number of clusters was very large.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.278 | 0.610 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.004 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.004 | 0.003 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
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".