Sample Size Estimation for Random-effects Models
Bibliographic record
Abstract
Panel study designs are common in environmental epidemiology, whereby repeated measurements are collected from a panel of subjects to evaluate short-term within-subject changes in response variables over time. In planning such studies, questions of how many subjects to include and how many different exposure conditions to measure are commonly asked at the design stage. In practice, these choices are constrained by budget, logistics, and participant burden and must be carefully balanced against statistical considerations of precision and power. In this article, we provide intuitive sample size formulae for the precision of regression coefficients derived from panel studies and show how they can be applied in planning such studies. We show that there are five determinants of the precision with which regression coefficients can be estimated: (1) the residual variance of the responses; (2) the variance of the slopes; (3) the number of subjects; (4) the number of measurements/subject; and (5) the within-subject range of the exposure values "X" at which the responses are measured. The planning of such studies would be greatly improved if investigators regularly reported all of the variance components in fitted random-effects models: currently, literature values for the relevant variance parameters are often not readily available and must be estimated through pilot studies or subjective estimates of "reasonable values."
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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 | 0.192 | 0.562 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.005 | 0.003 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.008 | 0.004 |
| Research integrity | 0.006 | 0.007 |
| Insufficient payload (model declined to judge) | 0.006 | 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".