Proportional hazards models, also known as Cox regression models, are statistical models used in survival analysis to study the relationship between covariates and the time to an event of interest. This type of model allows researchers to analyze how different factors impact the risk or hazard of an event occurring over time.
In a proportional hazards model, it is assumed that the ratio of hazards (or risks) between any two individuals remains constant over time. This means that the hazard function for each individual is proportional to a baseline hazard function, which represents the hazard in the absence of any covariates. The model estimates the effect of covariates on the hazard by determining the hazard ratio (HR), which represents the multiplicative change in the hazard for a unit change in the covariate.
The covariates in a proportional hazards model can include individual characteristics, environmental factors, or treatment interventions, among others. These covariates are often categorized as either time-independent or time-dependent. Time-independent covariates are fixed characteristics that do not change over time, such as age or sex. Time-dependent covariates can vary over time, such as changes in treatment or exposure status.
Proportional hazards models provide a valuable tool in survival analysis as they allow researchers to examine the impact of different factors on the time to an event while adjusting for the effects of other covariates. They are widely used in various fields, including medical research, epidemiology, and social sciences, to explore the timing and risk factors associated with events such as diseases, mortality, or failure in engineering or business settings.
