How can two biological variables have opposing secular trends, yet be positively related? A demonstration using timing of puberty and adult height
Bibliographic record
Abstract
Timing of puberty and adult height have opposing secular trends yet are positively associated in individuals. We demonstrate this using data from a single sample and discuss possible statistical and epidemiological reasons behind it. The sample comprised 365 females from Fels Longitudinal Study born 1929-1992. We used Super-Imposition by Translation and Rotation (SITAR) to estimate individual age at peak height velocity (PHV) and PHV from serial height data (8149 observations between 5 and 24 years). General linear regression was used to investigate the association between height and age at PHV, and secular trends in height, age at PHV and PHV. Although adult height increased 0.42 (95% CI: 0.08, 0.77) cm per decade, and age at PHV decreased 1.14 (-3.74, 1.45) weeks per decade, adult height increased by 2.44 (1.78, 3.10) cm per year higher age at PHV. We found tentative evidence of the positive association between age at PHV and adult height strengthened 0.25 (-0.09, 0.59) cm each decade. Secular trends in related variables may differ if the between-individual and between-cohort associations are different. To understand if a secular trend in one variable has contributed to a trend in another, each needs to be modelled over time, together with the changing association between them.
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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 | 0.012 | 0.029 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".