Survival Analysis

Kaplan-Meier estimation, Cox regression, hazard functions, and censoring.

Key Concepts

• •Survival function: S(t) = P(T > t) and its properties
• •Hazard function: h(t) = f(t)/S(t), the instantaneous failure rate
• •Cumulative hazard: H(t) = -ln(S(t))
• •Kaplan-Meier estimator: nonparametric survival curve estimation
• •Nelson-Aalen estimator: nonparametric cumulative hazard estimation
• •Log-rank test: comparing survival curves between groups
• •Cox proportional hazards model: semiparametric regression for survival data
• •Parametric survival models: exponential, Weibull, and log-logistic
• •Censoring types: right, left, and interval censoring
• •Truncation: left truncation (delayed entry) and its effect on estimation

Study Tips

• 1.Practice constructing Kaplan-Meier curves step by step with small datasets.
• 2.Understand the difference between censoring and truncation.
• 3.Learn to interpret hazard ratios from Cox regression models.
• 4.Work through parametric survival model fitting using maximum likelihood.
• 5.Practice problems involving both censored and truncated observations.

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