Survival Analysis: Censored Data and Hazards

Module: Machine Learning | Difficulty: Advanced

Survival Function

Hazard Function

Cox Proportional Hazards

Kaplan-Meier Estimator

where = deaths at time , = at risk.

Censored Data

import numpy as np
from lifelines import CoxPHFitter

class CoxModel:
    def __init__(self):
        self.cph = CoxPHFitter()
    def fit(self, df, duration_col, event_col):
        self.cph.fit(df, duration_col=duration_col, event_col=event_col)
    def predict_survival(self, X):
        return self.cph.predict_survival_function(X)
    def predict_partial_hazard(self, X):
        return self.cph.predict_partial_hazard(X)

Research Insight: Random survival forests outperform Cox regression when the proportional hazards assumption is violated. The key advantage is that they can capture non-linear effects and interactions automatically.