Cox Model

Cox Proportional Hazards model

Authors

Affiliations

Nate Yomogida, B.S., SPT

Doctor of Physical Therapy

B.S. in Kinesiology

Chloë Kerstein, B.S., SPT

Doctor of Physical Therapy

B.A. in Neuroscience

The Cox model is a “refinement” of linear regression¹ that calculates a hazard function for (risk of the outcome occurring at a given time) as a function of predictor variables (x) while accounting for participants that have not yet experienced the outcome (y)

¹

Indication

Use the Cox model when the outcome (y) you want to study is “time-to-event,” such as “time-to-death” or “time-to-failure” and how the variables (x) impact this outcome¹.

Strengths

• The Cox model does not make assumptions about the distribution of the predictor variables (can handle “non-parametric” data)¹.
• The outcome does not have to occur for every individual for the model to work¹.

Output

The output of the cox model is coefficients which can be transformed (exponentiated) into a hazard ratio¹. that is the expected multiplicative change in the hazard of the outcome per one-unit change in the predictor. Thus, the value of each predictor to the overall risk of the outcome is readily calculated.

References

1.

Rigatti SJ. Random Forest. Journal of Insurance Medicine (New York, NY). 2017;47(1):31-39. doi:10.17849/insm-47-01-31-39.1