Methods to Analyze Time-to-Event Data: The Cox Regression Analysis

Abstract

The Cox model is a regression technique for performing survival analyses in epidemiological and clinical research. This model estimates the hazard ratio (HR) of a given endpoint associated with a specific risk factor, which can be either a continuous variable like age and C-reactive protein level or a categorical variable like gender and diabetes mellitus. When the risk factor is a continuous variable, the Cox model provides the HR of the study endpoint associated with a predefined unit of increase in the independent variable (e.g., for every 1-year increase in age, 2 mg/L increase in C-reactive protein). A fundamental assumption underlying the application of the Cox model is proportional hazards; in other words, the effects of different variables on survival are constant over time and additive over a particular scale. The Cox regression model, when applied to etiological studies, also allows an adjustment for potential confounders; in an exposure-outcome pathway, a confounder is a variable which is associated with the exposure, is not an effect of the exposure, does not lie in the causal pathway between the exposure and the outcome, and represents a risk factor for the outcome.