<i>Z</i>‐scores and the birthweight paradox
Bibliographic record
Abstract
Investigators have long puzzled over the observation that low-birthweight babies of smokers tend to fare better than low-birthweight babies of non-smokers. Similar observations have been made with regard to factors other than smoking status, including socio-economic status, race and parity. Use of standardised birthweights, or birthweight z-scores, has been proposed as an approach to resolve the crossing of the curves that is the hallmark of the so-called birthweight paradox. In this paper, we utilise directed acyclic graphs, analytical proofs and an extensive simulation study to consider the use of z-scores of birthweight and their effect on statistical analysis. We illustrate the causal questions implied by inclusion of birthweight in statistical models, and illustrate the utility of models that include birthweight or z-scores to address those questions. Both analytically and through a simulation study we show that neither birthweight nor z-score adjustment may be used for effect decomposition. The z-score approach yields an unbiased estimate of the total effect, even when collider-stratification would adversely impact estimates from birthweight-adjusted models; however, the total effect could have been estimated more directly with an unadjusted model. The use of z-scores does not add additional information beyond the use of unadjusted models. Thus, the ability of z-scores to successfully resolve the paradoxical crossing of mortality curves is due to an alteration in the causal parameter being estimated (total effect), rather than adjustment for confounding or effect decomposition or other factors.
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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 | 0.028 | 0.088 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| 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".