When should one adjust for measurement error in baseline variables in observational studies?
Bibliographic record
Abstract
Previously, we showed that in randomised experiments, correction for measurement error in a baseline variable induces bias in the estimated treatment effect, and conversely that ignoring measurement error avoids bias. In observational studies, non-zero baseline covariate differences between treatment groups may be anticipated. Using a graphical approach, we argue intuitively that if baseline differences are large, failing to correct for measurement error leads to a biased estimate of the treatment effect. In contrast, correction eliminates bias if the true and observed baseline differences are equal. If this equality is not satisfied, the corrected estimator is also biased, but typically less so than the uncorrected estimator. Contrasting these findings, we conclude that there must be a threshold for the true baseline difference, above which correction is worthwhile. We derive expressions for the bias of the corrected and uncorrected estimators, as functions of the correlation of the baseline variable with the study outcome, its reliability, the true baseline difference, and the sample sizes. Comparison of these expressions defines a theoretical decision threshold about whether to correct for measurement error. The results show that correction is usually preferred in large studies, and also in small studies with moderate baseline differences. If the group sample sizes are very disparate, correction is less advantageous. If the equivalent balanced sample size is less than about 25 per group, one should correct for measurement error if the true baseline difference is expected to exceed 0.2-0.3 standard deviation units. These results are illustrated with data from a cohort study of atherosclerosis.
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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 | 0.429 | 0.793 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.005 | 0.005 |
| Bibliometrics | 0.005 | 0.006 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.006 | 0.010 |
| Open science | 0.006 | 0.003 |
| Research integrity | 0.007 | 0.010 |
| Insufficient payload (model declined to judge) | 0.001 | 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; 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".