Proportional hazards model

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Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes before some event occurs to one or more covariates that may be covariateis not restricted to binary predictors; in the case of a continuous covariate , it is typically assumed that the hazard responds logarithmically; each unit increase in results in proportional scaling of the hazard. The Cox partial likelihood, shown below, is obtained by using Breslow's estimate of the baseline hazard function, plugging it into the full likelihood and then observing that the result is a product of two factors. The first factor is the partial likelihood shown below, in which the baseline hazard has "canceled out". The second factor is free of the regression coefficients and depends on the data only through the censoring pattern. The effect of covariates estimated by any proportional hazards model can thus be reported as hazard ratios.

Sir David Cox observed that if the proportional hazards assumption holds (or, is assumed to hold) then it is possible to estimate the effect parameter(s) without any consideration of the hazard function. This approach to survival data is called application of the Cox proportional hazards model,[2] sometimes abbreviated to Cox model or to proportional hazards model. However, Cox also noted that biological interpretation of the proportional hazards assumption can be quite tricky.[3] [4]

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关键词：proportional Proportion Hazards hazard model continuous restricted increase obtained survival