Ranked set sampling in finite populations with bivariate responses: An application to an osteoporosis study
Bibliographic record
Abstract
The majority of the research on rank-based sampling designs in finite populations has been concerned with univariate situations. In this article, we study design-based estimation using a bivariate ranked set sampling (BIRSS) for finite populations when we have bivariate response variables. We derive the first and second-order inclusion probabilities associated with a BIRSS design. We show that the size of a BIRSS sample is random and propose using a conditional Poisson sampling (CPS) design to rectify this problem. We then use calculated inclusion probabilities to obtain design-based estimators of correlation coefficients between the bone mineral density (BMD) levels at the baseline and followup of a longitudinal BMD study in the province of Manitoba in Canada. We also study the problem of estimating the parameters of a regression model between the followup BMD and easy to obtain auxiliary information from the underlying population. Finally, we study the problem of classifying patients as those with or without osteoporosis using BIRSS and various CPS designs. We show that BIRSS designs are very flexible and can be used to obtain more efficient design-based estimators in sample surveys when dealing with response variables that are hard to measure or expensive to obtain.
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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 | 0.060 | 0.129 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".