Survival Analysis

Overview

Survival data, survivor and hazard functions. Nonparametric method: estimating median and percentile survival and confidence intervals. Comparing two groups of survival data, the log-rank and Wilcoxon tests. Comparison of k-groups. The Cox proportional hazard model, baseline hazard, hazard ratio, including variates and factors, maximum likelihood, treatment of ties. Confidence intervals for the Cox model regression parameters and hypothesis testing. Estimating the baseline hazard. Model building, Wald tests, likelihood ratio tests and nested models.

Learning Objectives

On completion of the module, it is intended that students will be able to: demonstrate an understanding of survival analysis, the special features of survival data, skewed survival distribution and censoring and how to handle censored real data; demonstrate an understanding for the survival, hazard and cumulative hazard functions and how they relate and use the nonparametric procedures of life-tables and Kaplan-Meier to estimate the survival curve, hazard and survival percentiles, the survival median and confidence intervals; demonstrate how to treat more than one group of survival data and use log-rank and Wilcoxon tests for comparing up to k groups of survival data; demonstrate an understanding of the Cox proportional hazards model, using the baseline hazard function and hazard ratio, along with considering variates and factors and using maximum likelihood for the Cox model; calculate confidence intervals for the Cox model regression parameters, to implement hypothesis testing, to deal with ties in the data, to estimate the baseline hazard, use Wald and likelihood ratio tests to build models and formulate nested models; demonstrate an awareness of parametric models, time-dependent variables, non-proportional hazards, and accelerated-failure-time models.

Skills

The effective use of appropriate statistical software to analyse survival data.

Assessment

None.