Data Algorithms

Chapter 19. Cox Regression

In medical statistics, survival analysis describes the effect on survival times of a continuous variable (such as gene expression). Cox proportional hazards regression is a very important and popular regression algorithm used in survival analysis; its simplicity and lack of assumptions about survival distribution provide the relative risk for a unit change in the variable. For example, a unit change in the expression of a specific gene gives a twofold increase in relative risk. A simple example of Cox regression is: do men and women have different risks of developing brain cancer based on their consumption of alcoholic beverages? By constructing a Cox regression model with alcohol usage (ounces consumed per day) and gender entered as covariates, you can test hypotheses regarding the effects of gender and alcohol on time to onset for brain cancer.

A Cox regression model is a statistical technique used to explore the relationship between the survival of a patient and several explanatory variables such as time and censor. The Cox regression model was developed by statistics professor Sir David Cox. One important characteristic of Cox regression is that it estimates relative rather than absolute risk, and it does not assume any knowledge of absolute risk. By definition, Cox regression that implements the proportional hazards model is designed for the analysis of the time until an event occurs or the time between events. Cox regression uses one or more predictor ...