Estimating Simultaneous Confidence Intervals for Multiple Contrasts of Proportions by the Method of Variance Estimates Recovery
Bibliographic record
Abstract
Many questions in biomedical research can be addressed effectively with simultaneous confidence intervals for multiple contrasts. While procedures for normal outcome data are readily available, there is still a need for developing practical methods for binary outcomes. In this article, we construct simultaneous confidence intervals for multiple contrasts of binomial proportions using the two-step method of variance estimates recovery (Zou and Donner 2008; Zou 2008; Zou et al. 2009a). First, we obtain confidence limits about single proportions using critical values from the multivariate normal distribution that account for correlations among contrasts. Second, we set confidence limits for these contrasts using variance estimates recovered from the limits. Simulation results show this approach performs well in small to moderate sample sizes when either the Wilson or Jeffreys method is used for constructing confidence limits about a single proportion. We illustrate the procedure with 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 | 0.089 | 0.353 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.006 | 0.004 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.004 | 0.006 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.004 | 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".