the Cox proportional hazards model (Cox Regression Model)

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Presentation transcript:

the Cox proportional hazards model (Cox Regression Model)

Cox Regression h(t), represents how the risk changes with time, and exp represents the effect of covariates (or factors/features) identifying significant prognostic factors most commonly used

Cox Regression To estimate the coefficients, β, Cox (1972) proposes a partial likelihood function based on a conditional probability of failure Statistical Methods for Survival Data Analysis, Third Edition, A JOHN WILEY & SONS, INC., PUBLICATION By solving the regression problem, we get: Regression Coefficient (>0 bad, <0 good, =0 no effect) Standard Error p-Value

A Example If we consider standard Error Age (1.12, 6.75) The estimated risk of dying for patients at least 50 years of age is exp(1.01)=2.75 times higher than that for patients younger than 50. Patients with 100% cellularity have a 42% higher risk of dying than patients with less than 100% cellularity. If we consider standard Error Age (1.12, 6.75) Cellularity (0.60, 3.35)

Thanks