bluuebunny/crossref_metadata_2025_split huggingface dataset:
Bayesian Methods
Authors: Dempster A. P. 
Published: September 2014

AbstractBayesian methods are used in the analysis of statistical data to provide posterior (postdata) probabilities for hypotheses. These are calculated, by Bayes' theorem, from prior (predata) probabilities and the likelihood function obtained from the observed data. Probabilities may be “objective” or “subjective”, representing degrees of belief. The history of this approach is surveyed. It fell out of fashion during the first half of the twentieth century, under the influences of the different frequentist approaches of Fisher and Neyman, but interest was maintained by the work of Jeffreys and de Finetti and revived in the mid‐1950s through the work of Savage and others. The article discusses problems arising in contemporary work, such as the involvement of many parameters, aspects of modeling, and availability of computing methods, and summarizes arguments for and against Bayesian methods.
Hypothesis Testing, with an Historical Perspective
Authors: Salsburg David 
Published: September 2014

AbstractA significance test of a null hypothesis involves the choice of a test statistic whose null distribution is known, and a judgment as to whether, or how well, the observed value of the statistic accords with the known distribution. The article reviews the history of this approach, with emphasis on the Neyman–Pearson formulation, taking account of the behavior of the test statistic under alternative hypotheses.
Inference
Authors: Zelen M. 
Published: September 2014

AbstractStatistical inference is the process of drawing conclusions from data governed by probability laws. Conclusions are uncertain, and a principal goal is to measure the uncertainty. In practical applications, the aim may be to draw conclusions about models that may have generated the data. A central concept, in almost all approaches, is the likelihood, regarded as a function of the unknown parameters. The most widely used approach is that of the frequentist school, based on error probabilities, that is, probabilities of particular observations given hypotheses about parameters. Key concepts here are significance tests, confidence intervals, and point estimation. The likelihood school uses likelihood ratios as measures of relative support. The Bayesian school uses inverse probability, that is, probabilities of hypotheses. Bayes' theorem relates posterior probabilities (postdata) to prior probabilities (predata) via the likelihood function. Details of these approaches are given in the article.
Isotonic Inference ‐ Further Developments
Authors: Hirotsu C. 
Published: September 2014

AbstractVarious approaches to the order restricted inference other than the isotonic regression approach are developed. They include the testing procedures, the multiple comparisons approach, and the method of the confidence intervals. They have many applications in analyzing a dose–response curve, ordered categorical responses, including two‐ and higher‐way contingency tables and so on. The distribution theories of the concerned statistics are naturally complicated for the restricted parameters as compared with the unrestricted case but in some cases very efficient exact algorithms for calculating the distribution functions are obtained.
Kolmogorov‐Smirnov Test: Basic
Authors: Wilcox R. 
Published: September 2014

Abstract
This is a distribution‐free method for comparing two empirical distributions, based on the largest vertical distance between the two cumulative distribution functions. The Kolmogorov test is a special case where one distribution function is known, and hence is a test of goodness‐of‐fit. Various properties, including power, are discussed.
K
ullback
L
eibler Information
Authors: Dykstra Richard 
Published: September 2014

Abstract

The Kullback–Leibler information number,
I
(
P
‖
Q
), determined for two probability measures defined on the same measurable space often serves as a type of “distance” between the two measures.

Projections (
I
‐projections) defined in terms of minimizing the Kullback–Leibler information number over appropriate sets of probability measures are often useful for finding desirable estimators.

Kullback–Leibler information numbers also play a useful role in hypothesis testing problems.
Likelihood
Authors: Hills Michael 
Published: September 2014

Abstract
Likelihood is the probability (or probability density) of the observed data, given a probability model, regarded as a function of the unknown parameters. It needs to be defined only up to a constant of proportionality, because ratios of likelihoods are used to compare different parameter values. It is used extensively as the basis for procedures of frequentist inference, such as maximum likelihood estimation, score tests and likelihood ratio tests, and is central to Bayesian inference. Some systems of inference are based on likelihood alone.
Lognormal Distribution ‐ Basic
Authors: Ratnaparkhi M. 
Published: September 2014

AbstractThis is the distribution of a positive‐valued random variable, the natural logarithm of which follows a normal distribution with mean μ and variance σ2. A generalization to the three‐parameter lognormal distribution arises if a location parameter is introduced, giving a nonzero lower bound for the variable. Properties, estimation procedures, and applications are described.
Ordered Alternatives
Authors: Lee Y. J. 
Published: September 2014

AbstractOrdered alternatives occur naturally in many experimental and observational studies. The dose‐response study is a typical one. The age‐related response is another one. Tendency to lie may increase with the age. The more the alcohol that is consumed during the pregnancy the higher is the risk of congenital malformation. There are numerous other examples of this nature. The independent variable that induces ordered response could be quantitative or ordinal (ordered categorical). The response variable observed for the ordered alternatives can be continuous counts, ordinal, dichotomous (success or failure), or even multinomial. Data may be collected in blocks or per dose group. Methods appropriate for dichotomous outcomes, Poisson counts, multinomial outcomes, and nonparametric data are reviewed. A reference for nonparametric methods appropriate for blocked data with missing observations is also given but not reviewed.
Power, Sensitivity and Alignment
Authors: Muller K. E. 
Published: September 2014

Abstract
In the Neyman–Pearson approach to the theory of hypothesis testing, power is the probability of rejecting the null hypothesis when an alternative hypothesis is true.
It therefore depends on the specific alternative, and may lead to the selection of a test statistic that provides satisfactory power. In particular, one might choose a uniformly most powerful unbiased test (unbiasedness here indicating minimum power at the null hypothesis). Power considerations are often used in the determination of sample size.
Rank Correlation
Authors: Kraemer Helena Chmura 
Published: September 2014

Abstract
When observations on two variables are made on each of a number of units, the association between the variables is often measured by the Pearson product‐moment correlation coefficient. This is inappropriate if the variables are ordinal or when their distributions are far from normal. Rank correlation coefficients are based on the ranks of the observations. Spearman's coefficient is obtained by using the ranks in the usual formula for the product‐moment coefficient. Kendall's tau coefficient is expressed through comparisons between all pairs of units, noting, for each pair, whether the two variables order the units in the same or the opposite direction. Methods of inference are outlined.
Restricted Maximum Likelihood: Introduction
Authors: Cook Nancy R. 
Published: September 2014

AbstractRestricted maximum likelihood estimation (REML) aims to maximize likelihood over a restricted parameter space. In a general linear model with multivariate normal error distribution, REML leads to unbiased estimators. Transformation of the data enables the log‐ likelihood to be split so that variances are estimated from error contrasts. There is a connection with Bayesian methods. The method has been applied to a random‐coefficients model for longitudinal data, and to situations where the parameters satisfy order restrictions.
Scedasticity
Authors: Morrison Donald F. 
Published: September 2014

Abstract

Homoscedasticity is the condition under which a series of observations have the same degree of variation. Heteroscedasticity is its negation. Homoscedasticity is assumed in the standard models for least squares linear regression, the two‐sample
t
test and the analysis of variance, and the effects of heteroscedasticity in these situations are discussed here.
Simultaneous Inference
Authors: Geller Nancy L. , O'Brien Peter C. 
Published: September 2014

Abstract
This covers statistical procedures to assess either more than one parameter or one parameter repeatedly during the course of a study. It includes multiple comparisons, multiple endpoints, sequential methods, and longitudinal data analysis. A common approach is to control the per‐family error rate (expected number of false positive conclusions per study) or the experimentwise error rate (probability of at least one false positive). Examples are given, with particular reference to problems of data monitoring of clinical trials.
Uniform Distribution: Definitions and Properties
Authors: Deng Lih‐yuan 
Published: September 2014

Abstract
A discrete uniform distribution has constant probability for each integer within a stated range. A continuous uniform distribution has constant probability density within a stated range. The continuous uniform distribution in the range (0, 1) has connections with the probability integral transformation, and with the exponential, logistic, and beta distributions. Some characterizations of functions of two independent random variables are given.
U

‐Statistics
Authors: Janssen Paul 
Published: September 2014

Abstract

A U‐statistic, calculated from a random sample of size
n
, is an average of a symmetric function of
m
sample values, calculated for all
m
‐tuples in the sample. Examples are the sample variance, the Cramér‐von Mises statistic of goodness of fit, and the Kaplan–Meier and Nelson–Aalen estimators in survival analysis. Asymptotic properties are described.
Youden Squares and Row–Column Designs
Authors: Gupta Sudhir 
Published: September 2014

AbstractOften several other factors potentially contribute to the variability of the observed response in addition to the treatments or factors under investigation. For example, gender, age, and center may also affect the blood pressure of patients in a placebo‐controlled hypertensive clinical trial. The technique of blocking is used to control the experimental error variation due to these types of extraneous sources. Two sources can be controlled using a Youden square or a row–column design, the rows and columns comprising two different systems of blocking. This article provides the details for the least squares analysis of these designs. Designs having variance balance, supplemented balance, row‐orthogonality, adjusted‐orthogonality, designs for factorial experiments, and computer algorithms for constructing designs are also briefly discussed.
A
alen–
J
ohansen Estimator
Authors: Borgan Ørnulf 
Published: September 2014

Abstract
The Aalen–Johansen estimator is a matrix version of the Kaplan–Meier estimator, which can be used to estimate the transition probability matrix of a Markov process with a finite number of states. The estimator is first presented for the competing risks model and the Markov illness–death model for a chronic disease. For these two simple Markov processes, the elements of the Aalen–Johansen estimator take an explicit form. Then a general finite state Markov process, modeling the life histories of individuals from a homogeneous population, is considered. It is described how the Aalen–Johansen estimator may be obtained as the product‐integral of the matrix of Nelson–Aalen estimators for the cumulative transition intensities. Finally, it is briefly indicated how the product‐integral formulation of the Aalen–Johansen estimator is useful for the study of its statistical properties.
Compliance and Survival Analysis
Authors: Goetghebeur Els 
Published: September 2014

Abstract
Partial compliance with assigned treatment can act as both cause and effect of survival experiences in randomized clinical trials. Structural failure time models have been developed for causal inference on the effect of resulting exposure patterns on survival time. In this setting, we review randomization based estimation methods that protect the standard α level. We also point to alternative methods relying on the assumption of no unmeasured time‐dependent confounders.
Hazard Models Based on First‐Passage Time Distributions
Authors: Aalen Odd O. 
Published: September 2014

AbstractWhen considering the occurrence of events in survival analysis, it is natural to think of them as being due to some underlying process crossing a limit. Myocardial infarction, for instance, occurs when occlusion of blood vessels in the heart reaches a certain level. The idea of viewing the event as due to the passage of a process beyond a limit may be formalized within standard models like Markov chains or Wiener processes. Although these models are highly idealized, they may still yield useful insights. The concept of quasi‐stationarity is of use in this context.
Interval Censoring: Overview
Authors: Sun Jianguo 
Published: September 2014

AbstractIn interval censoring, a random variable is known only to lie in an interval. In survival or failure‐time data, this may arise, for instance, when a critical change has occurred sometime between a patient's successive visits to a clinic. The survival distribution may be estimated by nonparametric maximum likelihood. Attention is given to the estimation of parameters in regression models and to the comparison of survival functions.
Kaplan–Meier Estimator
Authors: Borgan Ørnulf 
Published: September 2014

AbstractIt is described how the Kaplan–Meier estimator can be used to provide a nonparametric estimate of the survival distribution from right‐ censored data. Problems with estimating the survival distribution with left‐truncated data are considered, and it is pointed out that for such data, it may be more useful to estimate conditional survival distributions. Estimation of the median and mean survival times is discussed, and it is described how the Kaplan–Meier estimator may be derived by the redistribute‐to‐the‐right algorithm and how it is the unique self‐consistent estimator for right‐censored survival data. It is shown how the Kaplan–Meier estimator can be given as the product‐integral of the Nelson–Aalen estimator for the cumulative hazard rate, and it is indicated how the product‐integral formulation is helpful in the study the of statistical properties of the estimator. Finally, the construction of confidence bands for the survival distribution is considered.
Parametric Models in Survival Analysis
Authors: Lawless J. F. 
Published: September 2014

AbstractSurvival analysis deals with the analysis of times to events, or lifetimes. Parametric models are used to represent the distributions of lifetimes, and their relationship to explanatory variables, or covariates. This entry reviews common parametric models such as the exponential, Weibull, and lognormal distributions, and associated methods of inference. Parametric regression analysis using linear models for log lifetimes (accelerated failure time models) is described and illustrated. Parametric proportional hazards models and models for competing risks or multiple lifetimes are discussed briefly.
Phase‐Type Distributions in Survival Analysis
Authors: Aalen Odd O. 
Published: September 2014

Abstract
Consider a finite‐state, time‐continuous, homogeneous Markov chain with an absorbing state. The time to absorption in such a state is said to have a phase‐type distribution. Markov models are useful because they may incorporate an understanding of how a phenomenon, for example, a disease, moves through different stages. Densities and hazard rates of phase‐type distributions can be calculated from standard Markov chain theory. Hazard rates are usually asymptotically constant due to quasi‐stationarity; that is, conditional on nonabsorption, the distribution on the transient space converges to a limiting distribution. Quasi‐stationarity can also give an explanation of the various shapes of hazard rates that may occur.
Product‐integration
Authors: Gill Richard D. 
Published: September 2014

AbstractProduct integration is a mathematical theory doing for products, what integration does for sums. It lies behind the relationship between hazard rates and densities, unifying both the discrete time and the continuous time cases. It comes into its own when studying Markov processes and event history analysis, since when multiplying matrices, the time order of the matrices makes a difference to the result. The theory becomes a powerful tool, which takes full account of these potential problems.
Quality of Life and Survival Analysis
Authors: Olschewski Manfred 
Published: September 2014

Abstract

In clinical research, where time to a specific endpoint like, for example, death is of interest, methods of survival analysis are usually applied. In recent years, such research is more and more accompanied by the inclusion of the patients subjective assessment of treatment circumscribed by the term
health‐related quality of life
(HQoL). In the analysis of HQoL, methods of longitudinal analysis of variance are adequate. In this chapter, we put emphasis on statistical analysis methods that allow a joint analysis of both quantity and quality of survival. The major approach here is defined by quality‐adjusted survival (QAS) times. Conceptually, this means that the survival time of a patient is weighted according to his/her subjective assessment of that time. Advantages and limitations of such a joint analysis are discussed in relation to the separate analyses of the components.
Rank Regression
Authors: Cuzick Jack 
Published: September 2014

AbstractIn rank regression, the ranks of the dependent variable are regressed on a set of covariates. A formal specification iswheregis any strictly increasing transformation of the dependent variablet,zis a vector of covariates,βare the corresponding regression coefficients and ϵ is the error term, usually taken to have mean zero. If ϵ has the extreme‐value distributionthe well‐known proportional hazards model results. Other choices of ϵ lead to other important models, including frailty models.A different use of the term “rank regression” refers to models based on ranks of residuals in censored regression models, an early example being the Buckley–James approach.
Staggered Entry
Authors: Slud E. V. 
Published: September 2014

AbstractClinical trials and epidemiologic studies, which measure duration until some endpoint of interest, often follow subjects who may arrive at random or “staggered” times and may remain under observation until occurrence either of the endpoint or censoring/withdrawal. An important theme of statistical methodological development over the past three decades has been to understand how to handle such data. Building on earlier ideas (Lexis Diagrams, life tables), the treatment of staggered data has required sophisticated mathematical treatment (counting processes, martingales, repeated significance tests), but has practical impact in the interim analysis and early stopping of survival experiments.
Structural Nested Failure Time Models
Authors: Robins James M. 
Published: September 2014

AbstractStructural nested failure time models are causal models for the effect of a time‐dependent treatment or exposure on a survival time outcome in the presence of time‐dependent confounders. A time‐dependent confounder is a repeatedly measured covariate, which acts as a confounder for future exposure measurements but is on the causal path between earlier exposure measurements and ultimate response (i.e. here it acts as intermediate variable). Standard epidemiologic methodology fails if time‐dependent confounders are present.Under the essential condition ofno unmeasured confounders(the mathematical definition of which is a central issue) these models allow for unbiased causal inference, generalizing Robins'sg‐computation algorithm. The models use as building blocks time‐dependent accelerated failure time models.Important applications are intricate endogenous (feedback) selection effects in occupational epidemiology (healthy worker effect) and clinical epidemiology (AIDS treatment).
Software for Survival Analysis
Authors: Klein John P. , Zhang Mei‐Jie 
Published: September 2014

AbstractStatistical software for survival analysis is discussed. We examine the abilities of five major software packages, BMDP, SAS, SPSS, S‐PLUS, and STATA to perform basic calculations for censored data. Packages are compared based on their performance in computing summary statistics, in hypothesis testing, in performing Cox semiparametric regression modeling, and in performing parametric regression modeling.
Turnbull Estimator
Authors: Frydman H. 
Published: September 2014

AbstractThe Turnbull estimator is a nonparametric maximum likelihood estimator of a one‐dimensional distribution based onNindependent, arbitrarily censored and/or truncated observations (including interval censoring). Turnbull's algorithm is based on Efron's idea of self‐consistency. Asymptotic properties of the estimator depend essentially on the particular patterns of censoring and truncation.
Data Quality in Vital and Health Statistics
Authors: Swerdlow A. J. 
Published: September 2014

Abstract
In this chapter, the importance of data quality in the design and interpretation of analyses of routinely collected vital and health data is discussed. Issues considered include: the quality of information in underlying data sources; completeness of data collection; duplication; late registrations and alterations; validity and precision of data collection; coding, bridge‐coding, and assignment of underlying cause; data processing and editing; quality of denominators; and numerator/denominator discrepancies. Separate consideration is given to particular issues for analysis of clusters and other rare events, and record linkage. While not intrinsically interesting, data quality is worth considerable attention if analyses of routinely collected data are to be correctly interpreted.
Gestational Age
Authors: Macfarlane Alison 
Published: September 2014

Abstract
The World Health Organization defines the duration of a pregnancy as the time since the first day of the last normal menstrual period. This can be problematic if women conceive soon after stopping oral contraception or have irregular periods; so ultrasound estimates are increasingly used in countries where it is in common use. The World Health Organization also subdivides gestational ages into preterm, term and postterm.