Bias factor, maximum bias and the E-value: insight and extended applications
Bibliographic record
Abstract
BACKGROUND: Unmeasured confounding can bias the relationship between exposure and outcome. Sensitivity analyses generate bias-adjusted measures but these are not much used; this may change with the availability of the E-value (for evidence for causality in observational studies), appealing for its ease of calculation. However, as currently proposed, the E-value has some practical limitations that may reduce its use. METHODS: We first provide some insight into the relationship between two established measures for unmeasured confounding: 'the bias factor' and the maximum value this bias factor can take ('the B bias'). These measures are the statistical foundation for the E-value. We use them to develop new E-value formulas for situations when it is not currently applicable such as e.g. when, not unusually, a negative relation between unmeasured confounder and outcome and a positive one with exposure are postulated. We also provide E-values on the odds ratio scale because, currently, even when using the odds ratio as the study measure in the calculation of E-value, the result is to be interpreted as a relative risk, which is somewhat inconvenient. RESULTS: The additional formulas for the E-value measure make it applicable in all possible scenarios defined by the combined directions between unmeasured confounder and both the exposure and outcome. In addition, E-value measures can now be interpreted as odds ratios if the observed results are reported on the same scale. CONCLUSIONS: The E-value is part of newer sensitivity analyses methods for unmeasured confounding. We provide insight into its structure, underscoring its advantages and limitations, and expand its applications.
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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 | 0.114 | 0.395 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.004 |
| Bibliometrics | 0.008 | 0.008 |
| Science and technology studies | 0.001 | 0.009 |
| Scholarly communication | 0.006 | 0.011 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.005 | 0.010 |
| Insufficient payload (model declined to judge) | 0.008 | 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".