A comprehensive Python survival analysis workflow using statsmodels. Covers Kaplan-Meier estimation, log-rank tests, Cox proportional hazards regression, and alternative approaches like Nelson-Aalen and Accelerated Failure Time models with practical code examples.

Survival analysis (also called time-to-event analysis) models the time until an event of interest occurs. This repository provides a complete workflow for:

• Nonparametric survival estimation using Kaplan-Meier and Nelson-Aalen methods
• Comparison of survival curves with various weighted log-rank tests
• Semiparametric regression via Cox Proportional Hazards models
• Alternative approaches including Accelerated Failure Time models
• Model diagnostics and assumption checking

The main analysis is contained in the Jupyter notebook survival_and_duration_analysis.ipynb, which includes:

1. Environment Setup and Imports - All required libraries and configurations
2. Introduction to Survival Analysis - Key concepts and mathematical foundations
3. Nonparametric Methods - Kaplan-Meier estimation and visualization
4. Survival Curve Comparison - Multiple hypothesis testing approaches
5. Cox Proportional Hazards Regression - Multivariate modeling with interpretation
6. Model Diagnostics - Checking proportional hazards assumption
7. Alternative Approaches - Nelson-Aalen, AFT models, and time-varying covariates
8. References - Key academic and documentation sources

• Survival function estimation with right-censored data
• Quantile estimation with confidence intervals
• Simultaneous confidence bands
• Comparative visualization of multiple groups

• Log-rank test (default)
• Fleming-Harrington test with parameter tuning
• Gehan-Breslow test (weights early events)
• Tarone-Ware test (intermediate weighting)

• Multivariate regression with hazard ratio interpretation
• Formula interface for model specification
• Complete coefficient diagnostics with confidence intervals
• Assessment of proportional hazards assumption

• Nelson-Aalen cumulative hazard estimation
• Introduction to Accelerated Failure Time (AFT) models
• Discussion of time-varying covariates approaches

The analysis demonstrates:

• Survival quantiles: 25th percentile at 3995 days (CI: 3776-4166 days) for females
• Group comparisons: Marginal differences between sexes (p ≈ 0.05 across tests)
• Cox model findings: Age and lambda levels significantly increase hazard, while female sex is protective

statsmodels >= 0.14.0
matplotlib >= 3.7.0
numpy >= 1.24.0
pandas >= 2.0.0

Uses the flchain dataset from the R survival package, available through statsmodels.datasets.get_rdataset().

# Kaplan-Meier estimation
sf = sm.SurvfuncRight(df["futime"], df["death"])
sf.plot()

# Cox Proportional Hazards model
mod = PHReg.from_formula("futime ~ age + female + creatinine", 
                         data=data, status=data['death'])
rslt = mod.fit()

This analysis framework is applicable to:

• Medical research: Patient survival analysis
• Clinical trials: Treatment efficacy evaluation
• Engineering: Time-to-failure analysis
• Social sciences: Event history analysis
• Business: Customer churn prediction

• Survival function $S(t) = P(T > t)$
• Hazard function $\lambda(t) = \frac{f(t)}{S(t)}$
• Censoring mechanisms (right, left, interval)
• Hazard ratios and their interpretation
• Partial likelihood estimation
• Proportional hazards assumption

• Currently handles only right-censoring
• Requires careful checking of model assumptions
• Sample size considerations for quantile estimation
• Interpretation of borderline statistical significance

Potential enhancements include:

• Implementation of left and interval censoring
• Competing risks analysis
• Frailty models for clustered data
• Machine learning approaches (random survival forests, etc.)
• Bayesian survival analysis

See the notebook for complete references to:

• Therneau & Grambsch (2000) on Cox models
• Kaplan & Meier (1958) original paper
• Cox (1972) seminal work
• StatsModels official documentation

This notebook serves as an educational resource. For questions, suggestions, or improvements, please open an issue or discussion

This project is licensed under the MIT License - see the LICENSE file for details.

This notebook is designed for educational and research purposes. Real-world applications may require additional considerations and validation.