• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
The Analysis Factor

The Analysis Factor

Statistical Consulting, Resources, and Statistics Workshops for Researchers

  • Home
  • About
    • Our Programs
    • Our Team
    • Our Core Values
    • Our Privacy Policy
    • Employment
    • Guest Instructors
  • Membership
    • Statistically Speaking Membership Program
    • Login
  • Workshops
    • Online Workshops
    • Login
  • Consulting
    • Statistical Consulting Services
    • Login
  • Free Webinars
  • Contact
  • Login

The Proportional Hazard Assumption in Cox Regression

by guest 1 Comment

by Steve Simon, PhD

The Cox regression model has a fairly minimal set of assumptions, but how do you check those assumptions and what happens if those assumptions are not satisfied?

Non-proportional hazards

The proportional hazards assumption is so important to Cox regression that we often include it in the name (the Cox proportional hazards model). What it essentially means is that the ratio of the hazards for any two individuals is constant over time. They’re proportional. It involves logarithms and it’s a strange concept, so in this article, we’re going to show you how to tell if you don’t have it.

There are several graphical methods for spotting this violation, but the simplest is an examination of the Kaplan-Meier curves.

If the curves cross, as shown below, then you have a problem.

Figure 1. Graph of crossing survival curves

Likewise, if one curve levels off while the other drops to zero, you have a problem.

Figure 2. Kaplan-Meier curve with only one curve leveling off

You can think of non-proportional hazards as an interaction of your independent variable with time. It means that you have to do more work in interpreting your model. If you ignore this problem, you may also experience a serious loss in power.

If you have evidence of non-proportional hazards, don’t despair. There are several fairly simple modifications to the Cox regression model that will work for you.

Nonlinear covariate relationships

The Cox model assumes that each variable makes a linear contribution to the model, but sometimes the relationship may be more complex.

You can diagnose this problem graphically using residual plots. The residual in a Cox regression model is not as simple to compute as the residual in linear regression, but you look for the same sort of pattern as in linear regression.

If you have a nonlinear relationship, you have several options that parallel your choices in a linear regression model.

Lack of independence

Lack of independence is not something that you have to wait to diagnose until your data is collected. Often it is something you are aware from the start because certain features of the design, such as centers in a multi-center study, are likely to produce correlated outcomes. These are the same issues that hound you with a linear regression model in a multi-center study.

There are several ways to account for lack of independence, but this is one problem you don’t want to ignore. An invalid model will ruin all your confidence intervals and p-values.

Introduction to Survival Analysis
Learn the key tools necessary to learn Survival Analysis in this brief introduction to censoring, graphing, and tests used in analyzing time-to-event data.

Tagged With: Cox Regression, curves, hazards, independence, Kaplan-Meier curve, model, multi-center study, nonlinear, proportional, residual plot

Related Posts

  • What Is a Hazard Function in Survival Analysis?
  • Six Types of Survival Analysis and Challenges in Learning Them
  • Member Training: An Introduction to Kaplan-Meier Curves
  • Parametric or Semi-Parametric Models in Survival Analysis?

Reader Interactions

Comments

  1. Carol says

    November 12, 2019 at 5:23 pm

    Do you have a reference for this? I have only ever found references for using the log minus log plots to check this assumption but this is even more simple and makes complete sense. Thanks!

    “There are several graphical methods for spotting this violation, but the simplest is an examination of the Kaplan-Meier curves.”

    Reply

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Please note that, due to the large number of comments submitted, any questions on problems related to a personal study/project will not be answered. We suggest joining Statistically Speaking, where you have access to a private forum and more resources 24/7.

Primary Sidebar

This Month’s Statistically Speaking Live Training

  • February Member Training: Choosing the Best Statistical Analysis

Upcoming Workshops

  • Logistic Regression for Binary, Ordinal, and Multinomial Outcomes (May 2021)
  • Introduction to Generalized Linear Mixed Models (May 2021)

Read Our Book



Data Analysis with SPSS
(4th Edition)

by Stephen Sweet and
Karen Grace-Martin

Statistical Resources by Topic

  • Fundamental Statistics
  • Effect Size Statistics, Power, and Sample Size Calculations
  • Analysis of Variance and Covariance
  • Linear Regression
  • Complex Surveys & Sampling
  • Count Regression Models
  • Logistic Regression
  • Missing Data
  • Mixed and Multilevel Models
  • Principal Component Analysis and Factor Analysis
  • Structural Equation Modeling
  • Survival Analysis and Event History Analysis
  • Data Analysis Practice and Skills
  • R
  • SPSS
  • Stata

Copyright © 2008–2021 The Analysis Factor, LLC. All rights reserved.
877-272-8096   Contact Us

The Analysis Factor uses cookies to ensure that we give you the best experience of our website. If you continue we assume that you consent to receive cookies on all websites from The Analysis Factor.
Continue Privacy Policy
Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.
Necessary
Always Enabled

Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.

Non-necessary

Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.

SAVE & ACCEPT