Bias due to Aggregation of Individual Covariates in the Cox Regression Model
Bibliographic record
Abstract
The impact of covariate aggregation, well studied in relation to linear regression, is less clear in the Cox model. In this paper, the authors use real-life epidemiologic data to illustrate how aggregating individual covariate values may lead to important underestimation of the exposure effect. The issue is then systematically assessed through simulations, with six alternative covariate representations. It is shown that aggregation of important predictors results in a systematic bias toward the null in the Cox model estimate of the exposure effect, even if exposure and predictors are not correlated. The underestimation bias increases with increasing strength of the covariate effect and decreasing censoring and, for a strong predictor and moderate censoring, may exceed 20%, with less than 80% coverage of the 95% confidence interval. However, covariate aggregation always induces smaller bias than covariate omission does, even if the two phenomena are shown to be related. The impact of covariate aggregation, but not omission, is independent of the covariate-exposure correlation. Simulations involving time-dependent aggregates demonstrate that bias results from failure of the baseline covariate mean to account for nonrandom changes over time in the risk sets and suggest a simple approach that may reduce the bias if individual data are available but have to be aggregated.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.017 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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; a candidate call from one teacher head, 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".