Discrete Distribution Based on Compound Sum to Model Dental Caries Count Data
Bibliographic record
Abstract
Methods for analysing dental caries and associated risk indicators have evolved considerably in recent decades. The use of zero-inflated or hurdle models is increasing so as to take account of the decayed, missing, and filled teeth (DMFT) distribution, which is positively skewed and has a high proportion of zero scores. However, there is a need to develop new statistical models that involve pragmatic biological considerations on dental caries in epidemiological surveys. In this paper, we show that the zero-inflated and the hurdle models can both be expressed as a compound sum. Using the same compound sum, we then present the generalized negative binomial (GNB) distribution for dental caries count data, and provide a numerical application using the data of the EPIPAP study. The GNB model generates the best score functions while handling the lifetime dental caries disease process better. In conclusion, the GNB model suits the nature of some count data, in particular when structural zeros are unlikely to occur and when several latent spells can lead to new countable events. For these reasons, the use of the GNB distribution appears to be relevant for the modelling of dental caries count 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 | 0.010 | 0.025 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 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".