# *Geek Box: Kaplan-Meier “Survival Analysis” and Cox Proportional Hazard Ratios

#### *Geek Box: Kaplan-Meier “Survival Analysis” and Cox Proportional Hazard Ratios

In cohort studies, you will commonly see what is known as a “survival analysis”, which is data that measure the time from the beginning of a study to the occurrence of a 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 specified 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 sham surgery.

Two common methods to estimate survival are the Kaplan-Meier method and the Cox proportional hazards model, also known as a Cox regression. These methods produce what is known as the “hazard ratio”, or HR, and should be presented with 95% confidence intervals around the estimated HR. With Kaplan-Meier analysis, both the probability of surviving over a total specified time period [e.g., 5-years], and the cumulative proportion of participants surviving a specific time within the overall timeframe [e.g., each year within the 5-year overall period], 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 as it 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 predict a change in the outcome. To continue with our knee surgery example, we might want to know whether type of activity [running vs. resistance training] or type of rehabilitation [active vs. passive] influence the association between type of surgery [the exposure] and risk of a further knee injury [the outcome].

In a Cox regression, the HR’s 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 in order to account for potential confounders.