• 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

  • our programs
    • Membership
    • Online Workshops
    • Free Webinars
    • Consulting Services
  • statistical resources
  • blog
  • about
    • Our Team
    • Our Core Values
    • Our Privacy Policy
    • Employment
    • Collaborate with Us
  • contact
  • login

Cox Regression

What Is a Hazard Function in Survival Analysis?

by Karen Grace-Martin 

One of the key concepts in Survival Analysis is the Hazard Function.

But like a lot of concepts in Survival Analysis, the concept of “hazard” is similar, but not exactly the same as, its meaning in everyday English. Since it’s so important, though, let’s take a look. [Read more…] about What Is a Hazard Function in Survival Analysis?

Tagged With: Cox Regression, discrete, Event History Analysis, hazard function, Survival Analysis

Related Posts

  • Interpreting the Shapes of Hazard Functions in Survival Analysis
  • Six Types of Survival Analysis and Challenges in Learning Them
  • What is Survival Analysis and When Can It Be Used?
  • Member Training: Cox Regression

The Proportional Hazard Assumption in Cox Regression

by guest contributer  2 Comments

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.

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.

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
  • Interpreting the Shapes of Hazard Functions in Survival Analysis

Member Training: Types of Regression Models and When to Use Them

by Karen Grace-Martin  Leave a Comment

Linear, Logistic, Tobit, Cox, Poisson, Zero Inflated… The list of regression models goes on and on before you even get to things like ANCOVA or Linear Mixed Models.

In this webinar, we will explore types of regression models, how they differ, how they’re the same, and most importantly, when to use each one.


Note: This training is an exclusive benefit to members of the Statistically Speaking Membership Program and part of the Stat’s Amore Trainings Series. Each Stat’s Amore Training is approximately 90 minutes long.

Not a Member? Join!

About the Instructor

Karen Grace-Martin helps statistics practitioners gain an intuitive understanding of how statistics is applied to real data in research studies.

She has guided and trained researchers through their statistical analysis for over 15 years as a statistical consultant at Cornell University and through The Analysis Factor. She has master’s degrees in both applied statistics and social psychology and is an expert in SPSS and SAS.

Not a Member Yet?
It’s never too early to set yourself up for successful analysis with support and training from expert statisticians. Just head over and sign up for Statistically Speaking.

You'll get access to this training webinar, 100+ other stats trainings, a pathway to work through the trainings that you need — plus the expert guidance you need to build statistical skill with live Q&A sessions and an ask-a-mentor forum.

Tagged With: ancova, Cox Regression, linear mixed model, linear regression, logistic regression, Poisson Regression, Tobit Regression, Zero Inflated

Related Posts

  • When Linear Models Don’t Fit Your Data, Now What?
  • Member Training: Using Excel to Graph Predicted Values from Regression Models
  • Member Training: Hierarchical Regressions
  • How to Combine Complicated Models with Tricky Effects

How to Combine Complicated Models with Tricky Effects

by Karen Grace-Martin  4 Comments

Need to dummy code in a Cox regression model?

Interpret interactions in a logistic regression?

Add a quadratic term to a multilevel model?

quadratic interaction plotThis is where statistical analysis starts to feel really hard. You’re combining two difficult issues into one.

You’re dealing with both a complicated modeling technique at Stage 3 (survival analysis, logistic regression, multilevel modeling) and tricky effects in the model (dummy coding, interactions, and quadratic terms).

The only way to figure it all out in a situation like that is to break it down into parts.  [Read more…] about How to Combine Complicated Models with Tricky Effects

Tagged With: Cox Regression, dummy coding, interaction, logistic regression, multilevel model, quadratic terms, Survival Analysis

Related Posts

  • Member Training: Types of Regression Models and When to Use Them
  • When NOT to Center a Predictor Variable in Regression
  • Member Training: Goodness of Fit Statistics
  • Interpreting Regression Coefficients in Models other than Ordinary Linear Regression

Primary Sidebar

This Month’s Statistically Speaking Live Training

  • Member Training: Moderated Mediation, Not Mediated Moderation

Upcoming Workshops

    No Events

Upcoming Free Webinars

TBA

Quick links

Our Programs Statistical Resources Blog/News About Contact Log in

Contact

Upcoming

Free Webinars Membership Trainings Workshops

Privacy Policy

Search

Copyright © 2008–2023 The Analysis Factor, LLC.
All rights reserved.

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