stat-logistic-regression

Skill: Logistic Regression

Use When

• User wants to model the probability of a binary outcome (disease/healthy, expressed/not expressed, responder/non-responder)
• User needs odds ratios and their confidence intervals for each predictor
• User wants to evaluate model discrimination with AUC-ROC and calibration
• Common in medical, epidemiological, and genomics classification tasks

Inputs

• Required:
  • Data table (CSV or TSV) with a binary outcome column (0/1 or two-level factor) and one or more predictor columns
  • Outcome variable name
  • Predictor variable name(s)
• Optional:
  • Regularization: none (default), l1 (Lasso), or l2 (Ridge)
  • Test set fraction for performance evaluation (default: 0.2)
  • Output directory (default: ./logit_output)

Workflow

1. Read data; validate that outcome column is binary; encode predictors as needed.
2. Split data into training and test sets (stratified by outcome).
3. Fit logistic regression on training set:
   • If regularization=none: unpenalized MLE fit for inferential reporting.
   • If regularization=l1 or l2: cross-validated penalized fit for prediction-focused modeling.
4. Report coefficients:
   • Unpenalized model: log-odds estimate, standard error, z-statistic, p-value, odds ratio, 95% CI.
   • Penalized model: shrunken coefficients and odds ratios; do not report classical p-values/z-statistics from penalized fit.
5. Evaluate on test set: compute AUC-ROC, plot ROC curve, compute confusion matrix at 0.5 threshold (accuracy, sensitivity, specificity, PPV, NPV).
6. Compute Hosmer-Lemeshow goodness-of-fit test for calibration for the unpenalized model; for penalized models, report calibration curve and Brier score.
7. If regularization is used: report optimal lambda from cross-validation and non-zero coefficients at optimal lambda.
8. Save the executable analysis script (analysis_code.py or analysis_code.R) and software version manifest (session_info.txt) used to produce results.
9. Write coefficient table(s), performance metrics (TSV), ROC curve plot (PDF), and calibration plot (PDF) to output directory.

Output Contract

• Coefficient table (TSV, unpenalized): term, log_odds, std_error, z_statistic, p_value, odds_ratio, ci_lower_or, ci_upper_or
• Coefficient table (TSV, penalized): term, log_odds, odds_ratio, selected_at_lambda
• Performance metrics (TSV): auc, accuracy, sensitivity, specificity, ppv, npv, hl_test_p_or_na, brier_score
• ROC curve (PDF)
• Confusion matrix (printed to stdout)
• Reproducibility artifacts: analysis_code.py or analysis_code.R, plus session_info.txt

Limits

• Assumes independence of observations; does not account for clustering or repeated measures.
• Requires sufficient events per variable (EPV ≥ 10 recommended) to avoid overfitting.
• Class imbalance can inflate accuracy; examine sensitivity/specificity and AUC.
• Penalized models are prediction-oriented; classical inferential statistics (standard errors/p-values) are not directly interpretable from penalized coefficients.
• Common failure: outcome column with more than two levels — binarize before running.