Survival Analysis

Introduction

Survival Models

Models time to happening of an event

Example:

  1. Time to death after heart attack
  2. Time to get job after Graduation
  3. Time to default in payment after taking loan.
  4. Time to adopt new technology after knowing it.

Why can’t we use linear regression?

Requirements

Event and Time

Anomalies in Survival Analysis

Censoring and Survival function

Causes of censored data:

Censoring and it may arise in the following ways:

  1. a patient has not (yet) experienced the relevant outcome, such as relapse or death, by the time of the close of the study;
  2. a patient is lost to follow-up during the study period;
  3. a patient experiences a different event that makes further follow-up impossible.
  4. Right censoring occurs when a subject leaves the study before an event occurs, or the study ends before the event has occurred. For example, we consider patients in a clinical trial to study the effect of treatments on stroke occurrence. The study ends after 5 years. Those patients who have had no strokes by the end of the year are censored. If the patient leaves the study at time te; then the event occurs in ( te, infinite).
  5. Left censoring is when the event of interest has already occurred before enrolment. This is very rarely encountered.

Definitions

Survival And Hazard function

Kaplan Meier estimate of the survival function

       

       

       

Log-Rank Test

Cox proportional hazards (PH) regression analysis

By using R