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Proportional Hazard Model

Proportional Hazard Model:

Proportional hazard model is a generic term for models (particularly survival models in medicine) that have the form

 

L(t | x1, x2, ¼, xn) = h(t) exp(b1 x1 + ¼+ bn xn),

where L is the hazard function or hazard rate, {xi} are covariates, {bi} are coefficients of the model - effects of the corresponding covariates, and h(t) gives the effect of duration on the hazard rate.

In a proportional hazard model, the effect of an independent variable on the hazard rate is assumed to be multiplicative. For example, the variable "smoking" in a model might have the effect of increasing the hazard rate 30%.

Examples of proportional hazard model are exponential, Weibull, and Gompertz models given respectively by

 

h(t) = 1;
h(t) = exp(g ln(t));
h(t) = exp(gt).

Cox proposed an ingenious principle for estimating all proportional hazard models without knowing the function h(t) or even the base hazard rate h0(t). Using this principle one estimates the effects {bi} of the covariates {xi}, but not the effect of duration h(t).

This is known as the Cox Proportional Hazard Model.

 

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Courses Using This Term

Biostatistics 2 – For Medical Science and Public Health
This course will teach you clinical trial designs including randomized controlled trials, ROC curves, CI and tests for relative risk and odds ratio, and an introduction to survival analysis.
Survival Analysis
This course will teach you the various methods used for modeling and evaluating survival data or time-to event data.
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