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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.
In full generality, the accelerated failure time model can be specified as [2] (|) = ()where denotes the joint effect of covariates, typically = ([+ +]). (Specifying the regression coefficients with a negative sign implies that high values of the covariates increase the survival time, but this is merely a sign convention; without a negative sign, they increase the hazard.)
The Cox regression results are interpreted as follows. Sex is encoded as a numeric vector (1: female, 2: male). The R summary for the Cox model gives the hazard ratio (HR) for the second group relative to the first group, that is, male versus female. coef = 0.662 is the estimated logarithm of the hazard ratio for males versus females.
A time-varying covariate (also called time-dependent covariate) is a term used in statistics, particularly in survival analysis. [1] It reflects the phenomenon that a covariate is not necessarily constant through the whole study Time-varying covariates are included to represent time-dependent within-individual variation to predict individual responses. [2]
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 ...
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the outcome or response variable, or a label in machine learning parlance) and one or more error-free independent variables (often called regressors, predictors, covariates, explanatory ...
The process is named after the statistician David Cox, who first published the model in 1955. [1] Cox processes are used to generate simulations of spike trains (the sequence of action potentials generated by a neuron), [2] and also in financial mathematics where they produce a "useful framework for modeling prices of financial instruments in ...
The following outline is provided as an overview of and topical guide to regression analysis: Regression analysis – use of statistical techniques for learning about the relationship between one or more dependent variables (Y) and one or more independent variables (X).