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Proportional Hazards Models
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 associated with that quantity of time. In a proportional hazards model, the unique effect of a unit increase in a covariate is multiplicative with respect to the hazard rate. For example, taking a drug may halve one's hazard rate for a stroke occurring, or, changing the material from which a manufactured component is constructed may double its hazard rate for failure. Other types of survival models such as accelerated failure time models do not exhibit proportional hazards. The accelerated failure time model describes a situation where the biological or mechanical life history of an event is accelerated (or decelerated). Background Survival models can be viewed as consisting of two parts: the underlying baseline hazard function, often denoted \lambda_0(t), describing how the risk of event per ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Survival Analysis
Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysis in engineering, duration analysis or duration modelling in economics, and event history analysis in sociology. Survival analysis attempts to answer certain questions, such as what is the proportion of a population which will survive past a certain time? Of those that survive, at what rate will they die or fail? Can multiple causes of death or failure be taken into account? How do particular circumstances or characteristics increase or decrease the probability of survival? To answer such questions, it is necessary to define "lifetime". In the case of biological survival, death is unambiguous, but for mechanical reliability, failure may not be well-defined, for there may well be mechanical systems in which failure is partial, a matter of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time-varying Covariate
A time-varying covariate (also called time-dependent covariate) is a term used in statistics, particularly in survival analysis. 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. For instance, if one wishes to examine the link between area of residence and cancer, this would be complicated by the fact that study subjects move from one area to another. The area of residency could then be introduced in the statistical model A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form ... as a time-varying covariate. In survival analysis, this would be done by splitting each study subject into several observations, one for each area ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Journal Of Statistics
The ''Electronic Journal of Statistics'' is an open access peer-reviewed scientific journal published by the Institute of Mathematical Statistics and the Bernoulli Society. It covers all aspects of statistics (theoretical, computational, and applied) and the editor-in-chief is Domenico Marinucci. According to the ''Journal Citation Reports'', the journal has a 2013 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... of 1.024. By 2017, the impact factor was recorded as 1.529. References External links * {{Official website, http://www.imstat.org/journals-and-publications/electronic-journal-of-statistics/ Statistics journals English-language journals Publications established in 2007 Creative Commons Attribution-licensed journals Institute of Mathematical Statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Statistics
The ''Annals of Statistics'' is a peer-reviewed statistics journal published by the Institute of Mathematical Statistics. It was started in 1973 as a continuation in part of the ''Annals of Mathematical Statistics (1930)'', which was split into the ''Annals of Statistics'' and the ''Annals of Probability''. The journal CiteScore is 5.8, and its SCImago Journal Rank is 5.877, both from 2020. Articles older than 3 years are available on JSTOR, and all articles since 2004 are freely available on the arXiv. Editorial board The following persons have been editors of the journal: * Ingram Olkin (1972–1973) * I. Richard Savage (1974–1976) * Rupert Miller (1977–1979) * David V. Hinkley (1980–1982) * Michael D. Perlman (1983–1985) * Willem van Zwet (1986–1988) * Arthur Cohen (1988–1991) * Michael Woodroofe (1992–1994) * Larry Brown and John Rice (1995–1997) * Hans-Rudolf Künsch and James O. Berger (1998–2000) * John Marden and Jon A. Wellner (2001–2003) * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
L1-norm
In mathematics, the spaces are function spaces defined using a natural generalization of the -norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue , although according to the Bourbaki group they were first introduced by Frigyes Riesz . spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Because of their key role in the mathematical analysis of measure and probability spaces, Lebesgue spaces are used also in the theoretical discussion of problems in physics, statistics, economics, finance, engineering, and other disciplines. Applications Statistics In statistics, measures of central tendency and statistical dispersion, such as the mean, median, and standard deviation, are defined in terms of metrics, and measures of central tendency can be characterized as solutions to variational problems. In penalized regression, "L1 penalty" and "L2 penalty" refer to penali ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lasso (statistics)
In statistics and machine learning, lasso (least absolute shrinkage and selection operator; also Lasso or LASSO) is a regression analysis method that performs both variable selection and regularization in order to enhance the prediction accuracy and interpretability of the resulting statistical model. It was originally introduced in geophysics, and later by Robert Tibshirani, who coined the term. Lasso was originally formulated for linear regression models. This simple case reveals a substantial amount about the estimator. These include its relationship to ridge regression and best subset selection and the connections between lasso coefficient estimates and so-called soft thresholding. It also reveals that (like standard linear regression) the coefficient estimates do not need to be unique if covariates are collinear. Though originally defined for linear regression, lasso regularization is easily extended to other statistical models including generalized linear models, general ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Linear Model
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a ''link function'' and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression. They proposed an iteratively reweighted least squares method for maximum likelihood estimation (MLE) of the model parameters. MLE remains popular and is the default method on many statistical computing packages. Other approaches, including Bayesian regression and least squares fitting to variance stabilized responses, have been developed. Intuition Ordinary linear regression predicts the expected value of a given unknown quanti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Regression
In statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable ''Y'' has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. A Poisson regression model is sometimes known as a log-linear model, especially when used to model contingency tables. Negative binomial regression is a popular generalization of Poisson regression because it loosens the highly restrictive assumption that the variance is equal to the mean made by the Poisson model. The traditional negative binomial regression model is based on the Poisson-gamma mixture distribution. This model is popular because it models the Poisson heterogeneity with a gamma distribution. Poisson regression models are generalized linear models with the logarithm as the (canonical) link function, and the Poisson distribution function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics In Medicine (journal)
'' Statistics in Medicine'' is a peer-reviewed statistics journal published by Wiley. Established in 1982, the journal publishes articles on medical statistics. The journal is indexed by '' Mathematical Reviews'' and SCOPUS. According to the '' Journal Citation Reports'', the journal has a 2021 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... of 2.497. References External links * Mathematics journals Publications established in 1982 English-language journals Wiley (publisher) academic journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiparametric Model
In statistics, a semiparametric model is a statistical model that has parametric and nonparametric components. A statistical model is a parameterized family of distributions: \ indexed by a parameter \theta. * A parametric model is a model in which the indexing parameter \theta is a vector in k-dimensional Euclidean space, for some nonnegative integer k.. Thus, \theta is finite-dimensional, and \Theta \subseteq \mathbb^k. * With a nonparametric model, the set of possible values of the parameter \theta is a subset of some space V, which is not necessarily finite-dimensional. For example, we might consider the set of all distributions with mean 0. Such spaces are vector spaces with topological structure, but may not be finite-dimensional as vector spaces. Thus, \Theta \subseteq V for some possibly infinite-dimensional space V. * With a semiparametric model, the parameter has both a finite-dimensional component and an infinite-dimensional component (often a real-valued function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weibull Distribution
In probability theory and statistics, the Weibull distribution is a continuous probability distribution. It is named after Swedish mathematician Waloddi Weibull, who described it in detail in 1951, although it was first identified by Maurice René Fréchet and first applied by to describe a particle size distribution. Definition Standard parameterization The probability density function of a Weibull random variable is : f(x;\lambda,k) = \begin \frac\left(\frac\right)^e^, & x\geq0 ,\\ 0, & x 0 is the ''shape parameter'' and λ > 0 is the ''scale parameter'' of the distribution. Its complementary cumulative distribution function is a stretched exponential function. The Weibull distribution is related to a number of other probability distributions; in particular, it interpolates between the exponential distribution (''k'' = 1) and the Rayleigh distribution (''k'' = 2 and \lambda = \sqrt\sigma ). If the quantity ''X'' is a "time-to-failure", the Weibull distribution gives a d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least Squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting. When the problem has substantial uncertainties in the independent variable (the ''x'' variable), then simple regression and least-squares methods have problems; in such cases, the methodology required for fitting errors-in-variables models may be considered instead of that for least squares. Least squares problems fall into two categories: linear or ordinary least squares and nonlinear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regress ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
