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 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 | 0.001 | 0.014 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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".