Parametric and nonparametric methods for confidence intervals and sample size planning for win probability in parallel‐group randomized trials with Likert item and Likert scale data
Bibliographic record
Abstract
Data on the Likert scale are ubiquitous in medical research, including randomized trials. Statistical analysis of such data may be conducted using the means of raw scores or the rank information of the scores. In the context of parallel-group randomized trials, we quantify treatment effects by the probability that a subject in the treatment group has a better score than (or a win over) a subject in the control group. Asymptotic parametric and nonparametric confidence intervals for this win probability and associated sample size formulas are derived for studies with only follow-up scores, and those with both baseline and follow-up measurements. We assessed the performance of both the parametric and nonparametric approaches using simulation studies based on real studies with Likert item and Likert scale data. The simulation results demonstrate that even without baseline adjustment, the parametric methods did not perform well, in terms of bias, interval coverage percentage, balance of tail error, and assurance of achieving a pre-specified precision. In contrast, the nonparametric approach performed very well for both the unadjusted and adjusted win probability. We illustrate the methods with two examples: one using Likert item data and the other using Like scale data. We conclude that non-parametric methods are preferable for two-group randomization trials with Likert data. Illustrative SAS code for the nonparametric approach using existing procedures is provided.
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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 | 0.400 | 0.758 |
| Meta-epidemiology (narrow) | 0.005 | 0.003 |
| Meta-epidemiology (broad) | 0.009 | 0.012 |
| Bibliometrics | 0.013 | 0.011 |
| Science and technology studies | 0.002 | 0.009 |
| Scholarly communication | 0.006 | 0.009 |
| Open science | 0.010 | 0.006 |
| Research integrity | 0.009 | 0.017 |
| Insufficient payload (model declined to judge) | 0.017 | 0.003 |
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".