Estimating the number needed to treat (NNT) index when the data are subject to error
Bibliographic record
Abstract
The number needed to treat (NNT) index has been proposed as a clinically useful measure to assess the results of randomized trials and other clinical studies. In its usual form, NNT indicates the expected number of patients who must be treated with an experimental therapy in order to prevent one adverse event, compared to the expected event rates under the control therapy. It can be formulated as a function of the proportions of patients who respond to treatment by more than a certain amount, the clinically important difference. We may also wish to evaluate two group studies comparing treatment and control responses, and to consider net benefit from treatment (by also allowing for individuals who deteriorate as well as those who respond positively). In this paper, we investigate the effect on NNT caused by measurement errors in continuous outcome measures. Such errors can lead to bias in the estimated proportions of subjects with clinically important responses, and hence bias the associated values of NNT. General expressions for the bias are derived, and enumerated for typical scenarios. For many situations, reliability of 80 per cent or more in the observations is required to restrict the bias to tolerable levels.
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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 | 0.283 | 0.634 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.010 | 0.005 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.008 | 0.007 |
| Insufficient payload (model declined to judge) | 0.002 | 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; the direct Gemma label and the distilled Codex classifier 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".