State‐space size considerations for disease‐progression models
Bibliographic record
Abstract
Markov models of disease progression are widely used to model transitions in patients' health state over time. Usually, patients' health status may be classified according to a set of ordered health states. Modelers lump together similar health states into a finite and usually small, number of health states that form the basis of a Markov chain disease-progression model. This increases the number of observations used to estimate each parameter in the transition probability matrix. However, lumping together observably distinct health states also obscures distinctions among them and may reduce the predictive power of the model. Moreover, as we demonstrate, precision in estimating the model parameters does not necessarily improve as the number of states in the model declines. This paper explores the tradeoff between lumping error introduced by grouping distinct health states and sampling error that arises when there are insufficient patient data to precisely estimate the transition probability matrix.
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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 | 0.031 | 0.138 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.006 | 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".