An Efficient Way to Find Optimal Crossover Designs Using CVX for Precision Medicine
Bibliographic record
Abstract
Crossover designs play an increasingly important role in precision medicine. We show the search of an optimal crossover design can be formulated as a convex optimization problem and convex optimization tools, such as CVX, can be directly used to search for an optimal crossover design. We first demonstrate how to transform crossover design problems into convex optimization problems and show CVX can effortlessly find optimal crossover designs that coincide with a few theoretical crossover optimal designs in the literature. The proposed approach is especially useful when it becomes problematic to construct optimal designs analytically for complicated models. We then apply CVX to find crossover designs for models with auto-correlated error structures or when the information matrices may be singular and analytical answers are unavailable. We also construct N-of-1 trials frequently used in precision medicine to estimate treatment effects on the individuals or to estimate average treatment effects, including finding dual-objective optimal crossover designs.
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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 | 0.016 | 0.050 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 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".