The iterative bisection procedure: a useful tool for determining parameter values in data-generating processes in Monte Carlo simulations
Bibliographic record
Abstract
BACKGROUND: Data-generating processes are key to the design of Monte Carlo simulations. It is important for investigators to be able to simulate data with specific characteristics. METHODS: We described an iterative bisection procedure that can be used to determine the numeric values of parameters of a data-generating process to produce simulated samples with specified characteristics. We illustrated the application of the procedure in four different scenarios: (i) simulating binary outcome data from a logistic model such that the prevalence of the outcome is equal to a specified value; (ii) simulating binary outcome data from a logistic model based on treatment status and baseline covariates so that the simulated outcomes have a specified treatment relative risk; (iii) simulating binary outcome data from a logistic model so that the model c-statistic has a specified value; (iv) simulating time-to-event outcome data from a Cox proportional hazards model so that treatment induces a specified marginal or population-average hazard ratio. RESULTS: In each of the four scenarios the bisection procedure converged rapidly and identified parameter values that resulted in the simulated data having the desired characteristics. CONCLUSION: An iterative bisection procedure can be used to identify numeric values for parameters in data-generating processes to generate data with specified characteristics.
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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 | 0.031 | 0.650 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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; both teacher heads agree on what is shown here.
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".