Constrained Optimization for Decision Making in Health Care Using Python: A Tutorial
Bibliographic record
Abstract
Constrained optimization can be used to make decisions aimed at maximizing some quantity in the face of fixed limits, such as resource allocation problems in health where tradeoffs between alternatives are inherent, and has been applied in a variety of health-related applications. This tutorial guides the reader through the process of mathematically formulating a constrained optimization problem, providing intuitive explanations for each component within the problem. We discuss how constrained optimization problems can be implemented using software and provide instructions on how to set up a solution environment using Python and the Gurobi solver engine. We present 2 examples from the existing literature that illustrate different constrained optimization problems in health and provide the reader with Python code used to solve these problems as well as a discussion of results and sensitivity analyses. This tutorial can be used to help readers formulate constrained optimization problems in their own application domains. Highlights This tutorial provides a user-friendly guide to mathematically formulating constrained optimization problems and implementing them using Python. Two examples are presented to illustrate how constrained optimization is used in health applications, with accompanying Python code provided.
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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 | 0.017 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".