# Module Overview

### Industrial Statistics: Survival Analysis

This module introduces the techniques of survival analysis and proportional hazards modelling. These techniques are used in diverse areas such as medicine, engineering (reliability analysis), actuarial science, sociology (event history analysis) and business / economics (duration analysis / time-to-event analysis).

The module introduces the student to the special features of survival data such as censoring and positive skew in the distribution of survival times. Fundamental concepts of survival analysis will be introduced including the survivor function, the hazard function and the hazard ratio. The course will build from some nonparametric techniques such as the Kaplan-Meier estimate of the survival curve to parametric and non-parametric (i.e., Cox) proportional hazards models – some of the most flexible and widely used tools for the analysis of survival data.

MATH 4821

##### ECTS Credits

5

*Curricular information is subject to change

Introduction to survival data:

Features of survival data, distribution of survival times, survivor function, hazard function, cumulative hazard function.

Nonparametric procedures:

Estimating the survivor function: life-table, Kaplan-Meier, Nelson-Aalen, confidence intervals. Estimating the hazard function, estimating median and percentile survival and confidence intervals. Comparing two groups of survival data, the log-rank and Wilcoxon tests. Comparison of k-groups of survival data.

Parametric procedures:

Exponential, Weibull and log-normal models. Estimating survivor and hazard functions. Likelihood methods for estimating parameters from censored data. Including covariates and factors and hypothesis testing. Model building, Wald tests, likelihood ratio tests and nested models.

The Cox model:

The Cox proportional hazard model, baseline hazard function, hazard ratio, including covariates and factors, maximum likelihood for the Cox model. Treatment of ties in the Cox model. Confidence intervals for the Cox model regression parameters and hypothesis testing. Estimating the baseline hazard.

Lectures supported by tutorials and computer lab. sessions.

Module Content & Assessment
Assessment Breakdown %
Formal Examination75
Other Assessment(s)25