Kaplan-Meier curve

The Proportional Hazard Assumption in Cox Regression

August 20th, 2018 by

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.


Six Types of Survival Analysis and Challenges in Learning Them

August 6th, 2018 by

Survival analysis isn’t just a single model.

It’s a whole set of tests, graphs, and models that are all used in slightly different data and study design situations. Choosing the most appropriate model can be challenging.

In this article I will describe the most common types of tests and models in survival analysis, how they differ, and some challenges to learning them.


Member Training: Cox Regression

September 1st, 2016 by
When you have data measuring the time to an event, you can examine the relationship between various predictor variables and the time to the event using a Cox proportional hazards model.

In this webinar, you will see what a hazard function is and describe the interpretations of increasing, decreasing, and constant hazard. Then you will examine the log rank test, a simple test closely tied to the Kaplan-Meier curve, and the Cox proportional hazards model.

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.



Member Training: An Introduction to Kaplan-Meier Curves

March 29th, 2016 by

Survival data models provide interpretation of data representing the time until an event occurs. In many situations, the event is death, but it can also represent the time to other bad events such as cancer relapse or failure of a medical device. It can also be used to denote time to positive events such as pregnancy. Often patients are lost to follow-up prior to death, but you can still use the information about them while they were in your study to better estimate the survival probability over time.

This is done using the Kaplan-Meier curve, an approach developed by (more…)