Proportional hazards models are a sub-class of survival models in statistics, in which the effect of a treatment under study has a multiplicative effect on the subject's hazard rate. For example, a drug may halve one's immediate probability of stroke. This is in contrast to additive hazards models, wherein a treatment may increase one's hazard by a fixed amount which is independent of other covariates.

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  • Proportional hazards models are a sub-class of survival models in statistics, in which the effect of a treatment under study has a multiplicative effect on the subject's hazard rate. For example, a drug may halve one's immediate probability of stroke. This is in contrast to additive hazards models, wherein a treatment may increase one's hazard by a fixed amount which is independent of other covariates. For the purposes of this article, consider survival models to consist of two parts: the underlying hazard function, often denoted <math>\Lambda_0(t)</math>, describing how hazard (risk) changes over time at baseline levels of covariates; and the effect parameters, describing how the hazard varies in response to explanatory covariates. A typical medical example would include as covariates, treatment assignment as well as patient characteristics to reduce variability and/or control for confounding. The proportional hazards assumption is the assumption that covariates multiply hazard. In the simplest case of stationary coefficients, for example, a treatment with a drug may, say, halve a subject's hazard at any given time <math>t</math>, while the baseline hazard may vary. Note however, that the covariate is not restricted to binary predictors; in the case of a continuous covariate <math>x</math>, the hazard responds logarithmically; each unit increase in <math>x</math> results in proportional scaling of the hazard. Typically under the fully-general Cox model, the baseline hazard is "integrated out", or heuristically removed from consideration, and the remaining partial likelihood is maximized. 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, sometimes abbreviated to Cox model or to proportional hazards model. The Cox model may be specialized if a reason exists to assume that the baseline hazard follows a parametric form. In this case, the baseline hazard <math>\Lambda_0(t)</math> is replaced by a parametric density; typically one can then just maximize the full likelihood which greatly simplifies model-fitting and provides interpretability, at the cost of flexibility. For example, assuming the hazard function to be the Weibull hazard function gives the Weibull proportional hazards model (in which the survival times follow a Weibull distribution which is rescaled by the covariates). Incidentally, the Weibull distribution for the baseline hazard is the only assumption under which a model satisfies both the proportional hazards, and accelerated failure time models.
  • Die Cox-Regression ist ein Regressionsmodell aus der mathematischen Statistik. Es wird zur Modellierung von Überlebenszeiten in der Survival Analysis benutzt und basiert auf dem Konzept der Hazardrate. Benannt wurde die Cox-Regression nach dem britischen Statistiker David Cox.
  • Modele proporcjonalnego hazardu to gałąź statystycznej analizy przeżycia, pozwalającej na przewidywanie czasu do wystąpienia jakiegoś zdarzenia, np. śmierci, znalezienia pracy, lub awarii urządzenia.
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  • Proportional hazards models are a sub-class of survival models in statistics, in which the effect of a treatment under study has a multiplicative effect on the subject's hazard rate. For example, a drug may halve one's immediate probability of stroke. This is in contrast to additive hazards models, wherein a treatment may increase one's hazard by a fixed amount which is independent of other covariates.
  • Die Cox-Regression ist ein Regressionsmodell aus der mathematischen Statistik. Es wird zur Modellierung von Überlebenszeiten in der Survival Analysis benutzt und basiert auf dem Konzept der Hazardrate. Benannt wurde die Cox-Regression nach dem britischen Statistiker David Cox.
  • Modele proporcjonalnego hazardu to gałąź statystycznej analizy przeżycia, pozwalającej na przewidywanie czasu do wystąpienia jakiegoś zdarzenia, np. śmierci, znalezienia pracy, lub awarii urządzenia.
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  • Proportional hazards models
  • Cox-Regression
  • Modele proporcjonalnego hazardu
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