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What is Cox regression?

Prerequisites (assumptions)

Introduction to pre-requisites (assumptions)

Cox regression is usually labelled “Cox proportional hazards regression”. “Proportional hazards” means that the increased risk for the event (caused by an independent variable) is constant over time. The risk caused by an independent variable should not increase or decrease over time. This means the relation between an independent variable and the event should be linear.

Testing if prerequisites (assumptions) are fulfilled

The assumptions should be tested for in some way for each independent variable. The easiest way is to create a Kaplan-Meier curve for each independent variable and simply look at the graph. It will tell you if there is a reasonably linear effect of the independent variable or if the effect seems to shrink or increase by time.

There are different statistical tests to investigate this. These tests may be insufficient to discover problems in small data sets and oversensitive in large data sets. Below are two videos showing an example of how to test the main assumption using the statistical software SPSS:

Testing assumptions in the software R is described here: http://www.sthda.com/english/wiki/cox-model-assumptions

Useful links

• http://www.mwsug.org/proceedings/2006/stats/MWSUG-2006-SD08.pdf
• http://www.stat.ubc.ca/~rollin/teach/643w04/lec/node69.html
• http://www.ats.ucla.edu/stat/examples/asa/test_proportionality.htm
• https://www.sciencedirect.com/science/article/pii/S0883944111002450
• https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1445-2197.2007.04405.x
• https://www.theanalysisfactor.com/assumptions-cox-regression/

References

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