On Predicting Survival in Prostate Cancer: Using an Extended Maximum Spacing Method at the Change Point of the Semiparametric Ratio Estimator (SPRE)
Bibliographic record
Abstract
Prostate cancer is a condition of public health significance in the United States. A new method for predicting survival is derived for the domain around the change point from a semiparametric ratio estimator (SPRE) to predict survival in response to treatment for prostate cancer. Using an extended maximum spacing estimator, the geometric mean of sample spacings from a uniform distribution is derived with known endpoints given at 0 and at the value of the change point from an ordinary least squares (OLS) regression for SPRE. To determine the maximum interval on the ‘x’ axis between point estimates, the maximum spacing estimation method is derived from a continuous univariate distribution where spacing will be defined as gaps between ordered values of the distribution function. The maximum is defined as a single value in the neighborhood of the change point and spacing defined as a function of time. This maximum spacing defines the gaps between point estimates at each time-dependent predicted outcome from the change point and results in a semiparametric ratio estimator that is reliable and repeatable. Performance is discussed through a simulation of change point values for a real application in clinical medicine and, using SPRE, in personalized medicine for a single prostate cancer patient.
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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 | 0.020 | 0.073 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".