Quantile Regression for Area Disease Counts: Bayesian Estimation using Generalized Poisson Regression
Bibliographic record
Abstract
Generalized linear models based on Poisson regression are commonly applied to count data for area morbidity outcomes, focused on modelling the conditional mean of the response as a function of a set of risk factors. Mean regression models may be sensitive to outliers and provide no information on other distributional features of the response. We consider instead a Poisson lognormal hierarchical approach to quantile regression of spatially configured count data, allowing for observed risk factors and spatially correlated unobserved risk factors. This technique has the advantage that a profile of the relative outcome risk across quantiles can be obtained, including estimates of uncertainty (e.g. the uncertainty attaching to 2.5% or 5% relative risk quantiles). An application involves counts of emergency hospitalisations for self-harm for 6791 small areas in England. Known risk factors are area deprivation, a measure of social fragmentation and a measure of rural status. It is shown that impact of these predictors varies between quantiles, and that hierarchical quantile regression generally produces narrower risk intervals, except for outlier areas, and leads to a higher number of areas being classed as high risk.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.029 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 teacher head, 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".