Exposure Estimation in the Presence of Nondetectable Values: Another Look
Bibliographic record
Abstract
A common problem faced by industrial hygienists is the selection of a valid way of dealing with those samples reported to contain nondetectable values of the contaminant. In 1990, Hornung and Reed compared a maximum likelihood estimation (MLE) statistical method and two methods involving the limit of detection, L. The MLE method was shown to produce unbiased estimates of both the mean and standard deviation under a variety of conditions. That method, however, was complicated, requiring difficult mathematical calculations. Two simpler alternatives involved the substitution of L/2 or L/square root of 2 for each nondetectable value. The L/square root of 2 method was recommended when the data were not highly skewed. Although the MLE method produces the best estimates of the mean and standard deviation of an industrial hygiene data set containing values below the detection limit, it was not practical to recommend this method in 1990. However, with advances in desktop computing in the past decade the MLE method is now easily implemented in commonly available spreadsheet software. This article demonstrates how this method may be implemented using spreadsheet software.
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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 | 0.041 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.001 | 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".