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Kaplan–Meier Estimator
The Kaplan–Meier estimator, also known as the product limit estimator, is a non-parametric statistic used to estimate the survival function from lifetime data. In medical research, it is often used to measure the fraction of patients living for a certain amount of time after treatment. In other fields, Kaplan–Meier estimators may be used to measure the length of time people remain unemployed after a job loss, the time-to-failure of machine parts, or how long fleshy fruits remain on plants before they are removed by frugivores. The estimator is named after Edward L. Kaplan and Paul Meier, who each submitted similar manuscripts to the ''Journal of the American Statistical Association''. The journal editor, John Tukey, convinced them to combine their work into one paper, which has been cited almost 61,000 times since its publication in 1958. The estimator of the survival function S(t) (the probability that life is longer than t) is given by: : \widehat S(t) = \prod\limits_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Km Plot
KM, Km, or km may stand for: Postnominal *Knight of the Sovereign Military Order of Malta, a chivalric order Businesses *KM Group, a multimedia group based in Kent *Kennis Music, a record label *Kia Motors, an automobile manufacturer *Kmart (former stock symbol "KM") *Konica Minolta, a manufacturer of electronics *Air Malta (IATA code KM) Organisations * Knight of Malta (other), a Christian order of knighthood *Kriegsmarine, name of the German navy during the Nazi regime *Koninklijke Marine, Dutch name of the Royal Netherlands Navy Places *Kamenz (district), Germany (license plate indication) *Messenia, Greece (license plate indication) *KM Junction, West Virginia *Comoros, country (ISO 3166-1 code KM) *Kysucké Nové Mesto, town in Slovakia (district code KM) *Kosovska Mitrovica, town in Serbia *Kosovo and Metohija, an autonomous province in Serbia (ISO 3166-2 code RS-KM) Science, technology, and mathematics *Kilometre (km), SI unit of distance *.km, Internet top-leve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hazard Function
Failure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. It is usually denoted by the Greek letter λ (lambda) and is often used in reliability engineering. The failure rate of a system usually depends on time, with the rate varying over the life cycle of the system. For example, an automobile's failure rate in its fifth year of service may be many times greater than its failure rate during its first year of service. One does not expect to replace an exhaust pipe, overhaul the brakes, or have major transmission problems in a new vehicle. In practice, the mean time between failures (MTBF, 1/λ) is often reported instead of the failure rate. This is valid and useful if the failure rate may be assumed constant – often used for complex units / systems, electronics – and is a general agreement in some reliability standards (Military and Aerospace). It does in this case ''only'' relate to the flat region of the ba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R (programming Language)
R is a programming language for statistical computing and graphics supported by the R Core Team and the R Foundation for Statistical Computing. Created by statisticians Ross Ihaka and Robert Gentleman, R is used among data miners, bioinformaticians and statisticians for data analysis and developing statistical software. Users have created packages to augment the functions of the R language. According to user surveys and studies of scholarly literature databases, R is one of the most commonly used programming languages used in data mining. R ranks 12th in the TIOBE index, a measure of programming language popularity, in which the language peaked in 8th place in August 2020. The official R software environment is an open-source free software environment within the GNU package, available under the GNU General Public License. It is written primarily in C, Fortran, and R itself (partially self-hosting). Precompiled executables are provided for various operating systems. R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SAS (software)
SAS (previously "Statistical Analysis System") is a statistical software suite developed by SAS Institute for data management, advanced analytics, multivariate analysis, business intelligence, criminal investigation, and predictive analytics. SAS was developed at North Carolina State University from 1966 until 1976, when SAS Institute was incorporated. SAS was further developed in the 1980s and 1990s with the addition of new statistical procedures, additional components and the introduction of JMP. A point-and-click interface was added in version 9 in 2004. A social media analytics product was added in 2010. Technical overview and terminology SAS is a software suite that can mine, alter, manage and retrieve data from a variety of sources and perform statistical analysis on it. SAS provides a graphical point-and-click user interface for non-technical users and more through the SAS language. SAS programs have DATA steps, which retrieve and manipulate data, and PROC steps, whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematica
Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages. It was conceived by Stephen Wolfram, and is developed by Wolfram Research of Champaign, Illinois. The Wolfram Language is the programming language used in ''Mathematica''. Mathematica 1.0 was released on June 23, 1988 in Champaign, Illinois and Santa Clara, California. __TOC__ Notebook interface Wolfram Mathematica (called ''Mathematica'' by some of its users) is split into two parts: the kernel and the front end. The kernel interprets expressions (Wolfram Language code) and returns result expressions, which can then be displayed by the front end. The origin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 time ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Log Rank Test
The logrank test, or log-rank test, is a hypothesis test to compare the survival distributions of two samples. It is a nonparametric test and appropriate to use when the data are right skewed and censored (technically, the censoring must be non-informative). It is widely used in clinical trials to establish the efficacy of a new treatment in comparison with a control treatment when the measurement is the time to event (such as the time from initial treatment to a heart attack). The test is sometimes called the Mantel–Cox test. The logrank test can also be viewed as a time-stratified Cochran–Mantel–Haenszel test. The test was first proposed by Nathan Mantel and was named the ''logrank test'' by Richard and Julian Peto. Definition 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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martingale Central Limit Theorem
In probability theory, the central limit theorem says that, under certain conditions, the sum of many independent identically-distributed random variables, when scaled appropriately, converges in distribution to a standard normal distribution. The martingale central limit theorem generalizes this result for random variables to martingales, which are stochastic processes where the change in the value of the process from time ''t'' to time ''t'' + 1 has expectation zero, even conditioned on previous outcomes. Statement Here is a simple version of the martingale central limit theorem: Let X_1, X_2, \dots\, be a martingale with bounded increments; that is, suppose :\operatorname _ - X_t \vert X_1,\dots, X_t0\,, and :, X_ - X_t, \le k almost surely In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (or Lebesgue measure 1). In other words, the set of possible exceptions may be non-empty, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delta Method
In statistics, the delta method is a result concerning the approximate probability distribution for a function of an asymptotically normal statistical estimator from knowledge of the limiting variance of that estimator. History The delta method was derived from propagation of error, and the idea behind was known in the early 19th century. Its statistical application can be traced as far back as 1928 by T. L. Kelley. A formal description of the method was presented by J. L. Doob in 1935. Robert Dorfman also described a version of it in 1938. Univariate delta method While the delta method generalizes easily to a multivariate setting, careful motivation of the technique is more easily demonstrated in univariate terms. Roughly, if there is a sequence of random variables satisfying :, where ''θ'' and ''σ''2 are finite valued constants and \xrightarrow denotes convergence in distribution, then : for any function ''g'' satisfying the property that exists and is non-zero value ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Distribution
In probability theory and statistics, the binomial distribution with parameters ''n'' and ''p'' is the discrete probability distribution of the number of successes in a sequence of ''n'' independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: ''success'' (with probability ''p'') or ''failure'' (with probability q=1-p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., ''n'' = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance. The binomial distribution is frequently used to model the number of successes in a sample of size ''n'' drawn with replacement from a population of size ''N''. If the sampling is carried out without replacement, the draws are not independent and so the resulting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HMSO
The Office of Public Sector Information (OPSI) is the body responsible for the operation of His Majesty's Stationery Office (HMSO) and of other public information services of the United Kingdom. The OPSI is part of the National Archives of the United Kingdom and is responsible for Crown copyright. The OPSI announced on 21 June 2006 that it was merging with the National Archives. The merger took place in October 2006. The OPSI continues to discharge its roles and responsibilities from within the structure of the National Archives. Controller of HMSO and Director of OPSI The Controller of HMSO is also the Director of OPSI. HMSO continues to operate from within the expanded remit of OPSI. The Controller of HMSO also holds the offices of Kings's Printer of Acts of Parliament, King's Printer for Scotland and Government Printer for Northern Ireland. By virtue of holding these offices OPSI publishes, through HMSO, the '' London Gazette'', ''Edinburgh Gazette'', ''Belfast Gazette'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \sigma^2, s^2, \operatorname(X), V(X), or \mathbb(X). An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
