How to Understand the 95% Confidence Interval Around the Relative Risk, Odds Ratio, and Hazard Ratio
Bibliographic record
Abstract
Statistics such as the mean difference (MD), standardized mean difference (SMD), relative risk (RR), odds ratio (OR), hazard ratio (HR), and others are meant to be examined along with their 95% confidence intervals (CIs), and their significance can be understood by viewing these CIs as compatibility intervals. The 95% CIs around the MD and SMD are easily understood because they are expressed along a linear scale. The 95% CIs around the RR, OR, and HR are harder to understand because they are expressed along an exponential scale; however, when the numbers are log-transformed, they are linearized, and understanding becomes easy. Another approach to understanding the CIs around the RR, OR, or HR is to examine the reciprocal of the lower limit of the CI; however, because the reciprocal also lies along an exponential scale, this method is inferior to the log-transformation method. These approaches may seem daunting, but the difficulty is an illusion because log transformation or reciprocal transformation takes only a few seconds when a statistical calculator is opened. All terms and concepts are explained with extreme simplification and with the help of examples.
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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 | 0.065 | 0.392 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.007 | 0.003 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.009 | 0.015 |
| Open science | 0.005 | 0.002 |
| Research integrity | 0.007 | 0.016 |
| Insufficient payload (model declined to judge) | 0.019 | 0.016 |
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".