Lecture Slides

Welcome to the Lecture Slides section! Here, you will find the slides for each chapter MATH3085/6143. Also, here is a summary of Chapters 1-9.

📌 Note: slides may be updated throughout the course.

📊 Chapter 01: Introduction

This chapter introduces survival analysis, a set of statistical methods for time-to-event data that features unique challenges like censoring and truncation.

  • 📄 Chapter 1 (last updated on 30/09/2025)
📊 Chapter 02: Statistical Models

This chapter introduces the fundamental role of statistical models (differentiating between parametric, non-parametric, and regression approaches) to simulate the process that generates survival data.

  • 📄 Chapter 2 (last updated on 30/09/2025)
📊 Chapter 03: The Survival Distribution

This chapter introduces the core mathematical functions used to characterize a survival distribution, primarily the survival function and the hazard function.

  • 📄 Chapter 3 (last updated on 30/09/2025)
📊 Chapter 04: Distributions for Survival Models

This chapter introduces several common parametric distributions for survival modeling, including the Exponential, Weibull, Log-logistic, Lognormal, and Gompertz.

  • 📄 Chapter 4 (last updated on 02/10/2025)
📊 Chapter 05: Survival models: parameter estimation

This chapter introduces parameter estimation for parametric models using maximum likelihood estimation (MLE), a method adapted to handle right-censored data.

  • 📄 Chapter 5 (last updated on 09/10/2025)
📊 Chapter 06: Non-parametric Survival Estimation

This chapter introduces non-parametric methods for estimating the survival distribution, focusing on the widely used Kaplan-Meier (KM) product-limit estimator.

  • 📄 Chapter 6 (last updated on 20/10/2025)
📊 Chapter 07: Survival Regression Models

This chapter introduces survival regression to analyze the effect of explanatory variables, focusing on the semi-parametric Cox Proportional Hazards (PH) model and the parametric Accelerated Failure Time (AFT) model.

  • 📄 Chapter 7 (last updated on 20/10/2025)
📊 Chapter 08: Multistate Survival Models

This chapter introduces multistate models, which generalize the simple alive-dead framework to processes with multiple states by using the theory of time-homogeneous Markov processes.

  • 📄 Chapter 8 (last updated on 03/11/2025)
📊 Chapter 09: Inference for Multistate Models

This chapter introduces statistical inference for time-homogeneous multistate models by explaining how to estimate constant transition intensities from observed data using maximum likelihood.

  • 📄 Chapter 9 (last updated on 03/11/2025)
📊 Chapter 10: Modelling Human Lifetime

This chapter focuses on the specialized methods and notation required for analyzing human life expectancy. It establishes the link between standard survival modeling and classical demographic/actuarial science.