Revisiting sample size planning for receiver operating characteristic studies: A confidence interval approach with precision and assurance
Bibliographic record
Abstract
Estimation of areas under receiver operating characteristic curves and their differences is a key task in diagnostic studies. Here we develop closed-form sample size formulas for such studies with a focus on estimation rather than hypothesis testing, by explicitly incorporating pre-specified precision and assurance, with precision denoted by the lower limit of confidence interval and assurance denoted by the probability of achieving that lower limit. For sample size estimation purposes, we introduce a normality-based variance function for valid estimation allowing for unequal variances of observations in the disease and non-disease groups. Simulation results demonstrate that the proposed formulas produce empirical assurance probability close to the pre-specified assurance probability and empirical coverage probability close to the nominal level. Compared with a frequently used existing variance function, the proposed function provides more accurate and efficient sample size estimates. For an illustration of the proposed formulas, we present real-world worked examples. To facilitate implementation, we have developed an online calculator openly available at https://dishu.page/calculator/.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.101 | 0.960 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.002 |
| 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; both teacher heads 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".