Cox Proportional Hazards Models, also known as Cox regression, is a statistical method used in survival analysis to analyze the relationship between predictor variables and the time to occurrence of an event. This model was developed by statistician David Cox in 1972 and is widely used in biomedical research and other fields where studying time-to-event data is of interest.
In survival analysis, the event of interest can be any event that has a duration, such as the time to death, disease recurrence, or failure of a mechanical system. The Cox Proportional Hazards model aims to estimate the hazard function, which represents the probability of the event occurring at a given time, based on the values of the predictor variables. It assumes that the hazard function follows a specific form that can be influenced by covariates.
The main assumption of the Cox Proportional Hazards Models is that the effects of the predictor variables on the hazard function are constant over time, meaning that the hazard ratios remain constant throughout the study period. This assumption is known as the proportional hazards assumption.
The model estimates the hazard ratios, which represent the relative change in risk of the event occurring for a unit change in the predictor variable, while holding other variables constant. It provides valuable information about the strength and direction of the relationships between the predictors and the event of interest.
Cox Proportional Hazards Models are widely used due to their flexibility, the ability to handle censored observations (where the event has not occurred by the end of the study), and their ability to incorporate multiple predictor variables simultaneously. They are implemented using software packages like R, SAS, and SPSS and play a crucial role in survival analysis and medical research.
