Contents

1. Introduction to survival analysis

• Survival data: Concepts of censoring and truncation, definition of the concepts of study time and patient time, examples, etc.
• Survival function, hazard function, and cumulative hazard function. Mean residual life.
• Classical distributions of survival random variables: Exponential, Weibull, Gompertz, log-logistic, log-normal, etc.

2. Likelihood and log-likelihood functions for survival data

• The Random censoring model and the concept of non-informative censoring.
• Construction of the likelihood and log-likelihood functions under different scenarios of censoring and/or truncation in survival data.

3. Non-parametric inference for right-censored survival data

• Estimation of the survival function (Kaplan-Meier) and the cumulative hazard function (Nelson-Aalen).
• Confidence intervals for survival and hazard functions: Greenwood’s formula and log and log-log transformations.
• Point estimates and confidence intervals for the median survival time and other percentiles.
• Comparison of two survival curves: Log-Rank and Wilcoxon tests.

4. Parametric models for survival time: PH and AFT models

• Proportional hazards (PH) models: The exponential regression model.
• Accelerated failure time (AFT) models: The Weibull regression model.

5. The semi-parametric Cox proportional hazards model

• General description of the model.
• Estimation of the Cox regression model: Concept of partial likelihood.
• Confidence intervals, hypothesis testing, and comparison of alternative models.
• Interpretation of parameter estimates in the model.
• Goodness-of-fit techniques in the Cox regression model.