A local-EM algorithm for spatio-temporal disease mapping with aggregated data
Bibliographic record
Abstract
Spatial data on disease incidence locations are often aggregated to regional counts to preserve privacy, and spatio-temporal modelling of such can be problematic when there are boundary changes over the study period. Here an inhomogeneous Poisson process with intensity depending on variations in population (known a priori) and a smoothly varying relative risk is estimated with a local-Expectation–Maximization (or local-EM) algorithm. Using incidence data for male bladder cancer in Nova Scotia, Canada, the question of whether the data are consistent with spatially varying but temporally constant relative risk is examined. Areas where there is evidence that relative risk is substantially greater than 1 are identified with the intention of assessing the possible presence of environmental risk factors. This paper extends existing work by incorporating a temporally varying risk surface and an explicit data structure which contains a mixture of point locations and locations aggregated to non-nested areas. This added flexibility allows the modelling of data amalgamated from different sources and collected over many years. While local-EM leads naturally to an Expectation–Maximization–Smoothing algorithm, the extension to mixtures of aggregations leads to a modified algorithm that includes an additive term at every iteration to account for observed point locations.
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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 | 0.006 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.003 |
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".