Logistic Regression & AUC

Logistic regression models the probability of a binary outcome. Licklider handles Odds Ratio reporting with 95% CI, model calibration checks, and ROC-AUC calculation — and enforces the disclosure that logistic regression describes association, not prediction accuracy in isolation from AUC.

STEP 1 — The Scenario

Researcher Profile

A clinical researcher developing a simple diagnostic score to predict 30-day readmission after cardiac surgery. The dataset contains n=200 patients, with predictors including age, EF (ejection fraction), creatinine, and diabetes status.

Research Question

"Which clinical variables independently predict 30-day readmission, and how well does the model discriminate between readmitted and non-readmitted patients (AUC-ROC)?"

Dataset

• n=200 patients; 38 readmitted (19%), 162 not readmitted
• Outcome: 30-day readmission (binary: 1=yes, 0=no)
• Predictors: Age (continuous), EF% (continuous), Creatinine mg/dL (continuous), Diabetes (binary)

STEP 2 — Licklider Analysis Path

1. Data Upload & Outcome Type Detection

Licklider detects a binary outcome (0/1 coded). The Outcome Type Lock (2.1.3) step confirms: outcome type = binary, analysis purpose = confirmatory (pre-specified predictors) or exploratory (data-driven selection).

2. Class Balance Check

Licklider reports the outcome distribution: 19% positive class. Moderate imbalance flagged — results are calibrated and Youden's J threshold is calculated. The guard warns if class imbalance is severe (<10% minority) and recommends SMOTE or weighted regression.

3. Logistic Regression Fitting

Multivariable logistic regression: Readmission ~ Age + EF + Creatinine + Diabetes. For each predictor: OR, 95% CI (Wald or likelihood-ratio based), z-value, and p-value are reported. The Hosmer-Lemeshow goodness-of-fit test is run to check model calibration.

4. Multicollinearity Check

VIF is calculated for all continuous predictors. VIF >5 triggers a warning. If EF and creatinine are correlated, Licklider suggests removing one or computing a composite.

5. ROC-AUC Calculation

The ROC curve is plotted. AUC is calculated with DeLong 95% CI. Youden's J optimal threshold is identified and reported (sensitivity, specificity, PPV, NPV at threshold).

6. Figure Generation

ROC curve with AUC and 95% CI annotated. Diagonal reference line (AUC=0.5) included. A forest plot of ORs with 95% CI is generated as a companion figure.

STEP 3 — Guards & Disclosures Activated

Proportion OLS Prevention (4.4.4)

If the outcome column contains values between 0 and 1 (e.g., proportion readmitted per hospital), OLS is blocked and logistic or beta regression is enforced. For binary 0/1 outcomes, logistic regression is the required model.

Covariate Selection Audit (4.6.3)

Licklider asks: "Were these predictors pre-specified in a protocol, or selected based on univariate screening?" If the latter, the report is labeled exploratory and stepwise model building is flagged as inflating Type I error.

Regression Diagnostics Guard (4.7.1)

Hosmer-Lemeshow test result is disclosed. If p<0.05 (poor calibration), the guard warns that model predictions may not be reliable for clinical deployment without re-calibration.

Causal Language Detection (3.1.5)

If the auto-generated text uses "creatinine causes readmission," the causal language guard replaces it with "higher creatinine was independently associated with increased readmission odds."

Effect Size Reporting (4.1.2)

OR and 95% CI are required for every predictor. Nagelkerke's R² is reported as an overall model effect size measure.

STEP 4 — Export Package

• Figures: ROC curve (main) + Forest plot of ORs (companion) — 300 dpi TIFF/PDF
• Statistical Report: OR table (all predictors, 95% CI, p-values); AUC + DeLong CI; Hosmer-Lemeshow p; Nagelkerke R²; threshold performance metrics (sensitivity, specificity, PPV, NPV); VIF table
• Methods Text: "Multivariable logistic regression was used to model 30-day readmission. Odds ratios and 95% CIs are reported. Model discrimination was assessed using AUC-ROC with DeLong 95% CI. Model calibration was assessed using the Hosmer-Lemeshow test. Results reflect associations; no causal claims are implied. n=200."
• Figure Legend: ROC curve — AUC annotation, CI method, optimal threshold, n
• Preprocessing Audit Log: Outcome distribution; missing data; VIF summary