A Variance Estimator for Marginal Cox Regression Models Fit to Non‐Nested Multilevel Data
Bibliographic record
Abstract
In health services research, researchers often use clustered data to estimate the independent association between individual outcomes and cluster-level covariates after adjusting for individual-level characteristics. Marginal generalized linear models estimated using generalized estimating equation (GEE) methods or hierarchical (or multilevel) regression models can be used when there is a single source of clustering (e.g., patients nested within hospitals). Hierarchical regression models can also be used when there are multiple sources of clustering (e.g., patients nested within surgeons who in turn are nested within hospitals). Methods for estimating marginal regression models are less well-developed when there are multiple sources of non-nested clustering (e.g., patients are clustered both within hospitals and within in neighborhoods, but neither neighborhoods or hospitals are nested in the other). Miglioretti and Heagerty developed a GEE-type variance estimator for use when fitting marginal generalized linear models to non-nested multilevel data. We propose a variance estimator for a marginal Cox regression model fit to non-nested multilevel data that combined their approach with Lin and Wei's robust variance estimator for the Cox model. We evaluated the performance of the proposed variance estimator using an extensive set of Monte Carlo simulations. We illustrated the use of the variance estimator in a case study consisting of patients hospitalized with an acute myocardial infarction who were clustered within hospitals and who were also clustered in neighborhoods. In summary, a variance estimator motivated by that proposed by Miglioretti and Heagerty can be used with marginal Cox regression models fit to non-nested multilevel data.
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 | 0.037 | 0.125 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 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".