PROPORTIONAL HAZARD MODEL Meaning and
Definition
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A Proportional Hazard Model, also known as a Cox model or Cox proportional hazard model, is a statistical method used to analyze survival or time-to-event data. It is a type of regression model that helps determine the effects of explanatory variables on the hazard rate or the risk of an event occurring at a given time.
In this model, the hazard rate represents the instantaneous risk of an event happening, considering both the time since the start of the study and the subject's characteristics. The proportional hazard assumption states that the hazard function for any two individuals at a given time is proportional and remains constant over time.
The Proportional Hazard Model estimates the hazard function by comparing the hazards of multiple individuals based on their predictor variables. It provides a hazard ratio, which describes how the hazard changes with respect to a one-unit change in a particular predictor variable while holding other factors constant.
To estimate the hazard, the model uses a partial likelihood method. The likelihood function only considers individuals who have experienced the event or are still at risk at a given time, letting it handle censored data effectively. The model's coefficients can be interpreted as the logarithm of the hazard ratio, providing valuable insights into the impact of predictors on the risk of an event occurring.
Proportional Hazard Models have widespread applications in medical research, epidemiology, and survival analysis, where the focus is often on estimating the effects of various factors on the timing of an event or the risk of its occurrence.
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