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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".
Cox's theorem, named after the physicist Richard Threlkeld Cox, is a derivation of the laws of probability theory from a certain set of postulates. [ 1 ] [ 2 ] This derivation justifies the so-called "logical" interpretation of probability, as the laws of probability derived by Cox's theorem are applicable to any proposition.
In the mathematical subfield of numerical analysis, de Boor's algorithm [1] is a polynomial-time and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of de Casteljau's algorithm for Bézier curves.
In mathematical finance, the Cox–Ingersoll–Ross (CIR) model describes the evolution of interest rates. It is a type of "one factor model" (short-rate model) as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives.
For instance, the from the Cox-model or the log-rank test might then be used to assess the significance of any differences observed in these survival curves. [ 9 ] Conventionally, probabilities lower than 0.05 are considered significant and researchers provide a 95% confidence interval for the hazard ratio, e.g. derived from the standard ...
R 2 N, proposed by Nico Nagelkerke in a highly cited Biometrika paper, [4] provides a correction to the Cox and Snell R 2 so that the maximum value is equal to 1. Nevertheless, the Cox and Snell and likelihood ratio R 2 s show greater agreement with each other than either does with the Nagelkerke R 2. [1]
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.)
In arithmetic geometry, the Cox–Zucker machine is an algorithm created by David A. Cox and Steven Zucker.This algorithm determines whether a given set of sections [further explanation needed] provides a basis (up to torsion) for the Mordell–Weil group of an elliptic surface E → S, where S is isomorphic to the projective line.