Survival Analysis Framework

You are a statistician applying survival analysis to a business or research problem. Based on the following context, create a comprehensive survival analysis framework.

Event of Interest: [CUSTOMER CHURN/EQUIPMENT FAILURE/PATIENT OUTCOME/SUBSCRIPTION CANCELLATION/OTHER]
Time Unit: [DAYS/WEEKS/MONTHS/YEARS]
Censoring Type: [RIGHT-CENSORED/INTERVAL-CENSORED/LEFT-CENSORED]
Sample Size: [NUMBER OF SUBJECTS]
Covariates Available: [VARIABLES THAT MAY AFFECT SURVIVAL TIME]
Analysis Goal: [ESTIMATE SURVIVAL CURVES/IDENTIFY RISK FACTORS/PREDICT INDIVIDUAL SURVIVAL/COMPARE GROUPS]

Build the survival analysis across these six sections:

1. DATA PREPARATION AND CENSORING HANDLING
Prepare the dataset for survival analysis. Define the time origin, the event indicator, and the follow-up time for each subject. Explain the concept of censoring and why it is essential for unbiased estimation. Handle right-censoring where subjects are still alive or active at the end of the study period, left-censoring where the event may have occurred before observation began, and interval-censoring where the event is known to have occurred within a time range but not the exact time. Build the survival dataset in Python using lifelines library format with proper coding of event and duration columns. Address common data issues including tied event times, time-varying covariates, and subjects with zero follow-up time. Provide pandas code for constructing the analysis-ready dataset from raw event logs.

2. NON-PARAMETRIC SURVIVAL ESTIMATION
Estimate survival curves without assuming a distributional form. Implement the Kaplan-Meier estimator to plot the survival function with confidence intervals. Calculate and interpret median survival time and survival probabilities at specific time points. Use the log-rank test to compare survival curves between two or more groups with proper handling of multiple comparisons. Implement the Nelson-Aalen estimator for the cumulative hazard function. Create publication-quality survival plots using lifelines and matplotlib with risk tables showing the number at risk at each time point. Provide code for stratified analysis where groups are compared while controlling for a confounding factor.

3. COX PROPORTIONAL HAZARDS MODELING
Build a Cox proportional hazards model to identify factors that affect survival time. Implement the Cox PH model using lifelines with proper handling of categorical and continuous covariates. Interpret hazard ratios for each covariate, explaining what a hazard ratio of 1.5 means in practical terms for the specific application. Test the proportional hazards assumption using Schoenfeld residuals and scaled Schoenfeld plots, and show how to address violations through stratification or time-varying coefficients. Perform model selection using AIC, concordance index, and likelihood ratio tests. Implement variable selection using stepwise approaches or regularized Cox models with L1 penalty. Create forest plots showing hazard ratios with confidence intervals for all covariates.

4. PARAMETRIC AND MACHINE LEARNING SURVIVAL MODELS
Extend beyond Cox PH with parametric and ML approaches. Implement parametric models using Weibull, log-normal, and log-logistic distributions, explaining when each is appropriate based on the hazard shape. Compare parametric models using AIC and visual diagnostics. Build machine learning survival models using Random Survival Forests and gradient boosted survival models from scikit-survival for improved prediction accuracy when the proportional hazards assumption is violated. Implement DeepSurv or similar neural network survival models for complex non-linear covariate effects. Compare all models using the concordance index, integrated Brier score, and calibration plots.

5. PREDICTION AND RISK STRATIFICATION
Use the fitted models for individual-level predictions and risk stratification. Generate individual survival curves showing the predicted probability of surviving beyond each time point for specific covariate profiles. Create risk scores that stratify the population into low, medium, and high risk groups. Validate the risk stratification by plotting Kaplan-Meier curves within each risk group and confirming good separation. Implement time-dependent AUC to evaluate how well the model discriminates at different prediction horizons. Build a risk calculator tool where users input covariate values and receive a predicted survival curve with confidence intervals. Apply the model to identify the highest risk individuals who should receive targeted intervention.

6. ADVANCED TOPICS AND BUSINESS APPLICATION
Address advanced survival analysis scenarios and translate results into business value. Implement competing risks analysis when subjects can experience multiple types of events using the Aalen-Johansen estimator and cause-specific hazard models. Handle recurrent events where subjects can experience the same event multiple times using the Andersen-Gill or Prentice-Williams-Peterson models. Apply the survival model to business problems: for customer churn, estimate expected remaining lifetime and lifetime value. For equipment maintenance, calculate optimal replacement intervals. For clinical applications, build nomograms for patient counseling. Create a monitoring dashboard that tracks survival metrics over time and alerts when the population's survival characteristics shift significantly from the model's training period.