Top Banner
06/12/22 1 Survival Analysis
16

Survival Analysis

Jan 21, 2016

Download

Documents

quinta

Survival Analysis. Introduction. Abbreviated Outline. Descriptive overview of survival analysis Terminology and notation Goals of survival analysis. - PowerPoint PPT Presentation
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Survival Analysis

04/21/231 Survival Analysis

Page 2: Survival Analysis

Survival Analysis

Introduction

Page 3: Survival Analysis

Abbreviated Outline

Descriptive overview of survival analysis

Terminology and notation

Goals of survival analysis

04/21/233 Survival Analysis

Page 4: Survival Analysis

Survival analysis is a collection of statistical procedures for data analysis for which the outcome variable of interest is time until an event occurs.

The event of interest is typically referred to as a failure.

The time to the event is referred to as survival time (or failure time in reliability analysis)

When more than one event is considered, the statistical problem is characterized as a competing risk problem.

04/21/234 Survival Analysis

Page 5: Survival Analysis

Examples

Engineering: the lifetime of a light bulb; the time from start to burned out

Social science: the survival time of a marriage ; the time from start to the end of marriage due to annulment, divorce or death

Public health: the time to local or regional recurrence since the

first radiation course for the breast cancer patient the time to death due to AIDS or ALDS-related

complications after a confirmed diagnosis of HIV

04/21/23Survival Analysis5

Page 6: Survival Analysis

3 elements to determine the survival time

1. Time origin or starting point

2. Ending event of interest

3. Measurement scale

It is usually in time such as days or months; but can be otherwise such as in dollars: the cost from admission to discharge.

04/21/236 Survival Analysis

Page 7: Survival Analysis

04/21/23 7Survival Analysis

Page 8: Survival Analysis

Survival Distributions

Y: the actual survival time of an individual; Y > 0

4 functions characterize the distributions of Y: the cumulative distribution function, the survival function, the hazard function, and the mean residual life function

04/21/238 Survival Analysis

Page 9: Survival Analysis

CDF of Y

04/21/239 Survival Analysis

Page 10: Survival Analysis

Survival Function of Y

04/21/2310 Survival Analysis

Page 11: Survival Analysis

About Survival Function

The survival function S is monotone nonincreasing over its support [0,infinity).

S(0)=1 and S(infinity)=0.

A steep curve represents shorter survival, while a gradual curve represents longer survival.

04/21/2311 Survival Analysis

Page 12: Survival Analysis

Hazard Function of Y

04/21/2312 Survival Analysis

Page 13: Survival Analysis

About Hazard Function

The hazard function, h(y), gives the instantaneous rate at time y for experiencing the event of interest, given that the event has not occurred prior to time y.

At time y, h(y) > 0 and has no upper bound.

An analogy: the concept of velocity What does it mean that your car’s

speedometer shows 70 mph? Would you really travel exactly 70 miles in the next hour?

04/21/2313 Survival Analysis

Page 14: Survival Analysis

About Hazard Function

Increasing hazard rates may arise when there is natural aging or wear.

Decreasing hazard rates are less common but find occasional use when there is an early likelihood of failure (such as after surgery).

04/21/2314 Survival Analysis

Page 15: Survival Analysis

The Mean Residual Life Function

04/21/2315 Survival Analysis

Page 16: Survival Analysis

Goals of Survival Analysis To estimate and interpret survival and/or

hazard functions from survival data. To compare survival and /or hazard

functions. The hazard function is usually more

informative about the underlying mechanism of failure than the survival function.

To assess the relationship of explanatory variables to survival time.

04/21/2316 Survival Analysis