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The term Cox regression model (omitting proportional hazards) is sometimes used to describe the extension of the Cox model to include time-dependent factors. However, this usage is potentially ambiguous since the Cox proportional hazards model can itself be described as a regression model.
Cox's 1958 paper [18] and further publications in the 1960s addressed the case of binary logistic regression. [19] The proportional hazards model, which is widely used in the analysis of survival data, was developed by him in 1972. [20] [21] An example of the use of the proportional hazards model is in survival analysis in medical research. The ...
For quantitative predictor variables, an alternative method is Cox proportional hazards regression analysis. Cox PH models work also with categorical predictor variables, which are encoded as {0,1} indicator or dummy variables. The log-rank test is a special case of a Cox PH analysis, and can be performed using Cox PH software.
Extensions of the Cox proportional hazard models are popular models in social sciences and medical science to assess associations between variables and risk of recurrence, or to predict recurrent event outcomes. Many extensions of survival models based on the Cox proportional hazards approach have been proposed to handle recurrent event data.
The hazard ratio is the effect on this hazard rate of a difference, such as group membership (for example, treatment or control, male or female), as estimated by regression models that treat the logarithm of the HR as a function of a baseline hazard () and a linear combination of explanatory variables:
The logrank test statistic compares estimates of the hazard functions of the two groups at each observed event time. It is constructed by computing the observed and expected number of events in one of the groups at each observed event time and then adding these to obtain an overall summary across all-time points where there is an event.
In statistics, the one in ten rule is a rule of thumb for how many predictor parameters can be estimated from data when doing regression analysis (in particular proportional hazards models in survival analysis and logistic regression) while keeping the risk of overfitting and finding spurious correlations low. The rule states that one ...
A well-known example of a semiparametric model is the Cox proportional hazards model. [3] If we are interested in studying the time T {\displaystyle T} to an event such as death due to cancer or failure of a light bulb, the Cox model specifies the following distribution function for T {\displaystyle T} :