Evidence of Absence: Bayesian Way to Reveal True Zeros Among Occupational Exposures
Bibliographic record
Abstract
OBJECTIVES: Workplace exposure measurements typically contain some observations below limit of detection. The current paradigm for exposure data interpretation relies on the lognormal distribution, where censored observation are assumed to be present but not quantifiable. However, there are setting were such assumptions are untenable and true zero exposures cannot be ruled out. This issue can be non-trivial because decisions about compliance depend on the adequacy of the lognormal model. METHODS: We adapted previously described statistical models for mixture of true zeros and lognormal distribution to function within Bayesian procedure that overcomes historical limitations that precluded them from being used in practice. We compared the performance of the new models and the traditional lognormal model in simulation. Their implementation is illustrated in diverse datasets. RESULTS: The approach we propose involves estimating the proportion of true zeroes, and the geometric mean and standard deviation of the lognormal component of the mixture. This can be implemented in practice either based on the truncated lognormal model fit to the observed data, or on the censored Bernoulli-lognormal mixture model, which has the advantage of allowing for multiple censoring points. Both models can be implemented via a free online application. In simulations, when none of the censored values were zeros, all estimation procedures led to similar risk assessment. However, when all or most of the censored values were zeros, the traditional approach that assumes lognormal distribution performed noticeably worse than newly proposed methods, typically overestimating noncompliance. Application to real data suggests that we cannot rule out presence of true zero exposures in typical measurement series gathered by occupational hygienists. CONCLUSIONS: Forcing the usual lognormal model to data containing a large proportion of censored values can bias risk assessment if a substantial part of the censored points are true zeroes. The Bernoulli-lognormal model is a suitable and accessible model that can account for such challenging data, and leads to unbiased risk assessments regardless of the presence of true zeros in the data.
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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 | 0.016 | 0.107 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.005 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 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".