A bootstrap semiparametric homogeneity test for the distributions of multigroup proportional data, with applications to analysis of quality of life outcomes in clinical trials
Bibliographic record
Abstract
This article is concerned about the test for the difference in the distributions of multigroup proportional data, which is motivated by the problem of comparing the distributions of quality of life (QoL) outcomes among different treatment groups in clinical trials. The proportional data, such as QoL outcomes assessed by answers to questions on a questionnaire, are bounded in a closed interval such as [0,1] with continuous observations in (0,1) and, in addition, excess observations taking the boundary values 0 and/or 1. Common statistical procedures used in practice, such as t- and rank-based tests, may not be very powerful since they ignore the specific feature of the proportional data. In this article, we propose a three-component mixture model for the proportional data and a density ratio model for the distributions of continuous observations in (0,1). A semiparametric test statistic for the homogeneity of distributions of multigroup proportional data is derived based on the empirical likelihood ratio principle and shown to be asymptotically distributed as a chi-squared random variable under null hypothesis. A nonparametric bootstrap procedure is proposed to further improve the performance of the semiparametric test. Simulation studies are performed to evaluate the empirical type I error and power of the proposed test procedure and compare it with likelihood ratio tests (LRTs) under parametric distribution assumptions, rank-based Kruskal-Wallis test, and Wald-type test. The proposed test procedure is also applied to the analysis of QoL outcomes from a clinical trial on colorectal cancer that motivated our study.
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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 | 0.061 | 0.259 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.005 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".