Semiparametric Inference for Two-Phase Studies with Ordinal Outcomes
Bibliographic record
Abstract
Background: The two-phase design is an increasingly used approach in health research. In Phase 1, broad data are collected on a large sample size, and in Phase 2, the correlation of auxiliary variables with an expensive variable is used to select a small but more informative sample. Objectives: Previous research on two-phase design has primarily focused on binary, continuous, and time-to-event outcomes. Recognizing the lack of research on ordinal outcomes, we propose a novel approach for three logit models with proportional odds: cumulative logit (CL), adjacent category (AC), and stopping ratio (SR). Additionally, we examine the validity of our method through four simulation scenarios with various outcome distributions. Methods: We have developed a semiparametric maximum likelihood model to incorporate Phase 1 data. An expectation-maximization (EM) algorithm was used to obtain the estimates while the Louis method was employed to calculate the covariance matrix. We compare the results estimated by our method with those obtained using only Phase 2 data under both simple random sampling and balanced outcome-dependent sampling (ODS). Results: In all experiments, balanced ODS led to reduced bias and higher relative efficiency, and the advantage was more noticeable with higher variability in sampling probability between the outcome categories. The EM method led to improved results in balanced ODS for the CL and SR models, but it was not as effective for the AC model. Conclusions: These findings suggest the efficacy of our method in incorporating Phase 1 data to enhance the quality of statistical estimates when used with balanced ODS.
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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 | 0.080 | 0.246 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.004 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 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; 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".