**Geek Box: Cox Regression*

**Geek Box: Cox Regression*

In cohort studies, you will commonly see what is known as a “survival analysis”, which is data that measure the time from a given starting point to the occurrence of a given specific event. For example, you could be interested in the effect of a type of knee surgery on the time to a further injury, i.e., the surgery would be the starting time point and a subsequent injury would be the event.

Survival analyses allow you to look at the probability of ‘survival’ [in this example, staying injury-free] past given time points. However, you can also compare two groups for their respective survival times. Staying with our knee surgery example, you could compare participants who underwent one type of surgery vs. another type, or one type of surgery vs. a non-surgical intervention.

Two common methods to estimate survival are the Kaplan-Meier method and the Cox proportional hazards model, also known as a Cox regression. With Kaplan-Meier analysis, both the probability of surviving to a given end time point and the cumulative proportion of participants surviving a specific time period within the overall timeframe, are calculated. Staying with our knee surgery example, if the total study period was 5yrs, Kaplan-Meier analysis would allow you to look at the probability of having further knee surgery at 1yr, 2yrs, 3yrs, etc.

The Cox proportional hazards model differs to the Kaplan-Meier method, and allows the differences in survival times between groups to be tested while including other factors. This is why it is also known as ‘Cox regression’, because it is analogous to a multiple regression model where multiple variables are entered into the model to see whether the levels of these variables predicts a change in the outcome variable.

In a Cox regression, the hazard ratios [HR] produced from the analysis do not depend on time, i.e., the hazard is ‘proportional’ between the groups being compared over time. Therefore, the difference in risk for an outcome is the difference at any given time, not a specific time like with the Kaplan-Meier method. The main attractive of Cox regression is that additional predictor variables can be included in the model.