Optimising the two‐stage randomised trial design when some participants are indifferent in their treatment preferences
Bibliographic record
Abstract
Outcomes in a clinical trial can be affected by any underlying preferences that its participants have for the treatments under comparison and by whether they actually receive their preferred treatment. These effects cannot be evaluated in standard trial designs but are estimable in the alternative two-stage randomised trial design, in which some patients can choose their treatment, while the rest are randomly assigned. We have previously shown that, when all two-stage trial participants have a preferred treatment, the preference effects can be evaluated, in addition to the usual direct effect of treatment. We also determined criteria by which to optimise how many participants should be given a choice of treatment vs being randomised. More recently, we extended our methodology to allow for participants who are unable or unwilling to express a treatment preference if they are assigned to the choice group. In this paper, we show how to optimise the two-stage design when some participants are undecided about their treatment. We demonstrate that the undecided group should be regarded as distinct in the analysis, to obtain valid estimates of the preference effects. We derive the optimal proportion of participants who should be offered a choice of treatment, which in many cases will be close to 50%. More generally, the optima depend on the preference rates for treatments and the proportion of undecided participants, and the parameters of primary interest. We discuss some advantages and disadvantages of the two-stage trial design in this situation and describe a practical example.
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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 | 0.369 | 0.411 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.006 | 0.006 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.007 | 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; 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".