The
Studies,
In Full

A risk model in front of a clinician must have literal probabilities, and it must know when to defer. Does isotonic recalibration plus selective prediction deliver that on a small real cohort, and what does abstention buy per case deferred?

303 real patients from the Cleveland Clinic: 13 clinical features from age and chest pain type through fluoroscopy vessel count. Outcome is angiographically confirmed coronary disease, prevalence 46 percent. Six missing values, median imputed.

L2 regularized logistic regression solved by Newton's method. Isotonic calibration by pool adjacent violators, fit on a held out quarter of each training fold so it never sees test data. Abstention inside a widening band around 0.5. Bootstrap confidence intervals, 2000 resamples.

Recalibration backfired: with roughly 55 calibration points per fold, the isotonic step function overfit and calibration error doubled. The raw logistic model was already nearly calibrated. Meanwhile abstention worked exactly as designed: declining the most uncertain 43 percent of cases lifted accuracy on the answered cases from 82 to 95 percent. We kept both findings.

Discrimination is not benefit. Across the range of threshold probabilities a clinician might hold, does acting on the model beat the two default strategies, biopsy everyone and biopsy no one? That is the question decision curve analysis answers, and the one AUC cannot.

569 real fine needle aspirate samples from the Wisconsin Diagnostic Breast Cancer study: 30 morphometric features of cell nuclei as mean, standard error and worst value. 37 percent malignant.

Regularized logistic regression, every number out of fold. Net benefit at threshold t weighs true positives against false positives at the odds t over one minus t, the standard formulation in which the threshold itself encodes how a clinician trades a missed cancer against an unnecessary biopsy.

The model dominates both defaults at every plotted threshold. At a working threshold of ten percent, the margin over biopsying everyone is 5.8 net true positives per hundred patients. The heaviest coefficients are worst texture, radius error, worst radius and worst concave points: large, irregular, deeply concave nuclei, which is precisely the pathologist's account of malignancy. The model's reasoning is open and it agrees with the field.

How much prognostic signal do sex and ECOG performance status carry in advanced lung cancer, and can survival machinery written from scratch, Kaplan Meier, the log rank test, Cox proportional hazards, be shown correct against the field's reference implementation?

228 real patients from the North Central Cancer Treatment Group trial, 164 deaths observed, the remainder censored. One patient dropped for missing performance status.

Kaplan Meier with Greenwood variance. Two group log rank. Cox proportional hazards fit by Newton's method on the Breslow partial likelihood, standard errors from the inverse information matrix, discrimination by Harrell's concordance.

The hazard ratios reproduce the published reference values to two decimals: 0.58 for female sex, 1.59 per ECOG point, age contributing little once performance status is in the model. Median survival 270 days for men against 426 for women. The agreement is the finding: an auditable implementation, validated externally, which is the exact property the wider Quantix Bio suite claims.

Solubility gates oral bioavailability, which makes predicting it the first question asked of any drug candidate. How much of Delaney's landmark ESOL model can a fully transparent ridge regression on five descriptors recover, and which descriptors carry the signal?

1,128 small molecules with experimentally measured aqueous log solubility, with molecular weight, hydrogen bond donors, ring count, rotatable bonds and polar surface area precomputed.

Ridge regression, ten fold cross validation, every metric out of fold, compared against the ESOL reference predictions shipped with the dataset and against a predict the mean baseline.

Five interpretable numbers recover most of the reference model: 1.19 log units of error against ESOL's 0.91, from a baseline of 2.10. The physics reads correctly, heavier and more ring laden molecules dissolve worse, polar surface dissolves better. The remaining 0.28 log units localize precisely what the missing lipophilicity term is worth, since logP requires atom level structure our descriptor set does not carry.

Can a mechanistic SIR model, integrated with a hand written Runge Kutta solver and fitted by least squares, recover the transmission dynamics of a real and essentially completely observed outbreak, and what reproduction number does it imply?

In January 1978, influenza A swept a boys' boarding school in northern England. 763 boys, a closed population, and an infirmary that counted every bed every day for fourteen days. Among the cleanest outbreak records in existence.

The SIR ordinary differential equations, integrated by fourth order Runge Kutta at 0.05 day steps from a single infectious boy. Transmission and recovery rates fitted by least squares over a refined grid. Final attack rate from the final size equation.

Two fitted parameters reproduce the entire epidemic within seventeen boys RMS on a peak of 298, giving a reproduction number of 3.77 and an infectious period of 2.26 days, matching published analyses of this outbreak. The counterfactual runs make "flatten the curve" a computation: a forty percent transmission reduction roughly halves the peak and delays it by days.

Ward early warning systems fail in practice through alarm fatigue: staff silence what cries wolf. The evaluation that matters is therefore not AUC but the operating curve of warning hours against false alerts per patient day. How does a trend aware model compare to a standard threshold score on that curve?

Every vital sign trajectory here is generated by the study's own code, because simulation is the only setting where the true deterioration time is known exactly and lead time can be measured without label noise. No clinical performance is claimed and none should be inferred. The deliverable is the evaluation method, which transfers to real wards; the numbers do not.

400 train and 400 test simulated patients, 72 hours of hourly vitals, fifteen percent deteriorating toward a sepsis like pattern. A NEWS2 style aggregate score against logistic regression on current vitals plus four hour slopes, both swept across their thresholds; each threshold yields median lead time, detection fraction, and false alert episodes per patient day.

At matched alarm burden, the trend aware model reaches similar warning time at roughly half the false alerts per day. The general lesson stands regardless of the simulator: comparing alert systems at one threshold is meaningless, and the denominator staff actually experience is per patient day.