bluuebunny/crossref_metadata_2025_split huggingface dataset:
Continuity Correction
Authors: Coull Brent A. 
Published: July 2005

AbstractThe term “continuity correction” has traditionally referred to an adjustment made when using a continuous distribution to approximate a discrete distribution. Corrections of this nature are common in both univariate settings, such as for inference on a single binomial proportion, and multivariate situations, such as contingency table analyses. In this entry, we briefly outline the historical development of the traditional continuity corrections and review the performance of such methods in the broader context of small‐sample strategies for categorical data. In particular, we consider the role of continuity corrections for inference on a single binomial proportion, a single 2 × 2 contingency table, and stratified 2 × 2 tables. In such settings, statistics based on the traditional continuity correction closely approximate “exact” results, yielding conservative inferences in small samples because of the discreteness of the exact distribution. We also review other more recent adjustments for discreteness. In many categorical data settings, if the nominal type I error rate of a test (or analogously the nominal confidence level for a confidence interval) need not be strictly maintained at every element of the parameter space, one can reasonably base inference on either an uncorrected score statistic or the mid‐Pvalue.
G
oodman–
K
ruskal Measures of Association
Authors: Upton G. 
Published: July 2005

Abstract
The measures of association proposed by Goodman and Kruskal between 1954 and 1972 can all be described as proportional reduction in error (PRE) measures. They describe the association between two categorical variables in terms of the increase in the probability of correctly predicting the category of one variable when information is supplied about the category of the other variable. The measures λ and τ are for use with any categorical variables, whereas the measure γ is for use when both variables are ordinal.
Logistic Regression
Authors: Lemeshow Stanley , Hosmer David W. 
Published: July 2005

Abstract
This article deals with the use of logistic regression to model data, where the response variable is binary and there are potentially numerous explanatory or predictor variables. Methods of estimating the coefficients in the model and procedures for hypothesis testing are considered. The correspondence of the coefficients of the logistic regression model to the odds ratio is noted along with methods for computing point estimates and confidence intervals for the odds ratio. Interpretation of coefficients for dichotomous, polytomous, and continuous independent variables is carefully developed. Confounding and effect modification are easily dealt with through the use of this modeling technique. All these concepts are illustrated through the analysis of low birth weight data.
McNemar Test
Authors: Lachenbruch Peter A. 
Published: July 2005

Abstract

The McNemar test is used for hypothesis testing with paired dichotomous data. The test involves only the off‐diagonal elements and results in a 1 degree of freedom χ
2
test. The dependence on only the discordant means that sample size estimation must rely on assumptions about the proportion of discordant observations. It can be shown that this test is equivalent to a paired t‐test under the assumption of equal means.
Misclassification Models
Authors: Albert Paul S. 
Published: July 2005

AbstractClassification errors in categorical data may distort the results of statistical analyses. Misclassification models have been developed in various areas of biostatistical application to account for this distortion. This article reviews selected methods that have been proposed for (i) modeling the natural history of a disease or growth process, (ii) evaluating diagnostic tests, and (iii) identifying epidemiological risk factors. We consider methods that incorporate known estimates of misclassification rates, methods that estimate misclassification rates from a subsample in which the presumably “true” classification is known, and methods in which both the true process and the misclassification rates are simultaneously modeled from misclassified data. The various methodological approaches are discussed along with their limitations, and we note an important issue for additional research.
Multinomial Distribution
Authors: Zelterman Daniel 
Published: July 2005

Abstract

The multinomial distribution is the generalization of the binomial to more than two dichotomous categorical outcomes. This multivariate discrete distribution describes the joint behavior of frequencies of each of
k
possible outcomes following
n
independent trials. The
k
individual frequencies follow a binomial distribution and are mutually negatively correlated. The probabilities of each of the
k
outcomes are usually estimated using loglinear models or Bayesian methods. Goodness‐of‐fit and exact tests assess the adequacy of the model to explain the empirical data. These topics are illustrated with an example from genetics.
Nominal Data
Authors: Wasserman Stanley 
Published: July 2005

Abstract

Nominal data arise from a specific type of
measurement
. As defined by the psychologist S.S. Stevens, measurement is the assignment of numbers to entities according to some rule. Close examination of such rules allows us to classify the various types of measurements into a small set of possibilities. Measurements are, of course, taken for many different reasons to answer many different questions, usually (but not always) on experimental units or subjects or on observational units. Measurements produce data, which take on values along some measurement scale. The measurement type(s) of data to be analyzed dictates the analyses that yield justifiable and meaningful interpretations.
Poisson Regression
Authors: Seeber Gilg U. H. 
Published: July 2005

AbstractPoisson regression models are regression models that assume a Poisson distribution for a count response variable. Usually they have loglinear form, modeling the log of the mean in terms of the explanatory variables. Such models are special cases of generalized linear models. A common application is in multiplicative modeling of rates, for which there are connections with Poisson process models and proportional hazards models. This article introduces these types of models, shows how to fit them using maximum likelihood, and discusses checking of model fit.
Proportions, Inferences, and Comparisons
Authors: Connor Jason T. , Imrey Peter B. 
Published: July 2005

AbstractThis article selectively reviews asymptotic, exact, and Bayesian methods for inference about one proportion, or for comparing two proportions from separate samples. For a single proportion, interval estimation is emphasized, and coverage properties of Wald, Jeffreys, Wilson, Agresti–Coull, and Clopper–Pearson (exact) confidence intervals are compared. Hypothesis testing is also discussed, primarily in the context of inverting interval estimates. For comparing proportions between two samples, we consider tests including the power‐divergence family (which incorporates all asymptotic tests commonly used); both conditional and unconditional exact tests; Bayesian tests; and several interval estimates. Some general aspects of power computation and sample size determination are discussed briefly in both contexts.
Quantal Response Models
Authors: Morgan Byron J.T. 
Published: July 2005

AbstractIn a quantal response experiment, a particular organism is selected and exposed in groups to different concentrations of a drug for a fixed time, and a discrete response is observed (such as death or survival). In the binary response case, a tolerance or threshold assumption yields a model for the probability of response at a particular dose that has the form of the cumulative distribution function of the tolerances. The median effective dose (ED50) is the dose level that results in an expected 50% response under certain model assumptions. The Spearman–Karber estimate is a nonparametric estimate of the ED50. This article also surveys parametric estimates, which can have improved precision. Parametric models are discussed, including extensions for polytomous responses and multivariate responses. Also discussed are the effect of overdispersion, and design issues such as sequential methods for finding the point at which a certain probability of response occurs.
Rasch Models
Authors: Carriquiry Alicia L. , Fienberg Stephen E. 
Published: July 2005

AbstractA fundamental component of model item response theory in psychometrics is the family of Rasch models introduced by the Danish statistician Georg Rasch. The basic Rasch model represents the log odds of the probability that an individual responds positively to theith binary test item as the sum of an individual parameter representing ability and an item parameter representing the difficulty of the item. This entry relates the Rasch model to traditional loglinear models and, in particular, models of multidimensional quasi‐symmetry. The implications of this relationship are illustrated in the context of an epidemiological example, and applications in the context of capture–recapture methods are discussed briefly.
Simpson's Paradox
Authors: Dong Jianping 
Published: July 2005

AbstractSimpson's paradox occurs when the direction of a measure of association between two variables is reversed after pooling over a covariate. For example, a treatment can be effective for both males and females, but ineffective when the data for males and females are combined. Since Simpson's original example in his 1951 paper, numerous real‐life examples of Simpson's paradox have been reported in many areas and the paradox has been generalized to many forms of association reversals. Necessary and sufficient conditions for Simpson's paradox as well as generalized forms of association reversals are given so we know, for example, when a high‐dimensional contingency table can be safely collapsed, avoiding the paradox. It is also of interest to know what the appropriate conclusion is when Simpson's paradox does occur.
Y
ates's Continuity Correction
Authors: Hilton Joan F. 
Published: July 2005

Abstract

This correction refers to the Pearson chi‐squared statistic for testing independence in a 2 × 2 contingency table. With this correction, the
P
‐value obtained from the chi‐squared distribution with df = 1 approximates the
P
‐value obtained with the hypergeometric distribution in Fisher's exact test.
R
‐ and
Q
‐Analysis
Authors: Jackson J. Edward 
Published: July 2005

Abstract

The starting point for principal component analysis, factor analysis, or multidimensional scaling is an
nxp
data matrix representing
n
observations on
p
variables. In
R‐Analysis
, a
pxp
matrix, such as a covariance or correlation matrix, is formed from which components or factors are obtained in terms of the variables. In
Q‐Analysis
, the situation is reversed. The matrix is
nxn
and the components or factors are in terms of the observations.
N‐Analysis
, also referred to as
Singular Value Decomposition
, operates on the data matrix directly and obtains results for both the variables and observations. In
M‐Analysis
, the data matrix has been corrected for both its row and column means.
Rotation of Axes
Authors: Jackson J. Edward 
Published: July 2005

Abstract

In both
principal component analysis
and
factor analysis
, it is sometimes desirable to perform a linear transformation of the original components or factors. This operation is performed to arrive at
simple structure
where the coefficients of the vectors related to these new transformed variables are either as large as possible or close to zero. These new coefficients may be used either to aid in the interpretation of the original components or factors, or to cluster the original variables. This linear transformation amounts to a rotation of the axes related to the components or factors. The rotation may be
orthogonal
in which case the resultant new set of vectors are still at right angles to each other or
oblique
in which they are not. Loss of orthogonality may result in better interpretation of the original vector sets or clustering of the original variables. Several numerical examples are given to illustrate these procedures including one where rotation is not appropriate.
Scree Test
Authors: D'agostino Ralph B. , Russell Heidy K. 
Published: July 2005

Abstract
The scree test is a test for determining the number of factors to retain in a factor analysis or principal components analysis. The scree test involves plotting the eigenvalues in descending order of their magnitude against their factor numbers and determining where they level off. The break between the steep slope and a leveling off indicates the number of meaningful factors, different from random error. The technique is illustrated and compared with alternative techniques for determining the number of factors to retain.
Similarity, Dissimilarity, and Distance Measure
Authors: Gower John C. 
Published: July 2005

Abstract
Many coefficients exist that give measures of resemblance between a pair of cases, or samples, as opposed to association between pairs of variables; others measure resemblance between a pair of populations. Some are based on quantitative variables, some on categorical variables that may be dichotomous or ordered, and others on a mixture of both types.
Beta‐Binomial Distribution
Authors: Rosner Bernard 
Published: July 2005

Abstract
The beta‐binomial distribution results from a beta distribution mixture of binomials. It is useful for clustered binary data, for which the ordinary binomial distribution is usually inappropriate because different observations are correlated rather than independent. Models using this distribution permit the mean to depend on explanatory variables. An implicit assumption of the distribution is that subunits are exchangeable within a cluster. Generalizations of it allow for data structures with multiple levels of nesting.
A
alen–
J
ohansen Estimator
Authors: Borgan Ørnulf 
Published: July 2005

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.
Censored Data
Authors: Andersen Per Kragh 
Published: July 2005

AbstractThe concepts of independent right censoring and noninformative right censoring in survival analysis are defined. Dependent censoring is a kind of selection bias and adds to biased inference for the survival time distribution. Informative censoring typically leads to inefficient inference. Examples are presented and relations between right censoring and competing risks are discussed. Other kinds of censoring, including interval censoring are touched upon.
Cox Regression Model
Authors: Sasieni Peter 
Published: July 2005

AbstractIn 1972, D.R. Cox proposed the semiparametric modelfor the hazard at timetfor an individual with covariatesz. Here, the hazard is the instantaneous conditional probability of failure attgiven that failure has not happened beforet.The Cox model has had enormous influence in the theory and practice of biostatistics, and this article surveys its definition, history, basic use, estimators and algorithms, asymptotic properties, use of time‐dependent covariates, model checking, and alternatives and extensions.
Grouped Survival Times
Authors: Zhang Mei‐Jie 
Published: July 2005

AbstractThe grouped survival data consists of occurrence and exposure data over given time intervals and possible covariate strata. Grouping data from such large sample sizes into tabular presentations (life tables) often provides a convenient format for presenting and summarizing life information. Grouped survival data can involve censored data (right censoring, left censoring, or double censoring) and/or truncated data. Moreover, the exact censoring or truncation times may be unknown for grouped data. In this article, we provide the literature on analyzing grouped survival data, and discuss the estimating procedure for the hazard function and survival function under nonparametric or parametric models, test statistics for comparing the survival probabilities among different population groups, and large sample properties for these estimators and test statistics.
Influence Function in Survival Analysis
Authors: Reid N. 
Published: July 2005

AbstractThe influence function of a statistic is a type of derivative that indicates how perturbations in the data affect the statistic. If the influence function is bounded, then the effect of outliers on the statistic is limited. Influence functions can be used in deriving the limiting distribution of a statistic, and can also be used to develop diagnostics for regression models. This latter application has been useful in proportional hazards regression.
Interim Analysis of Censored Data
Authors: Tsiatis A. A. 
Published: July 2005

AbstractMany clinical trials of chronic diseases are monitored periodically and interim analyses are performed, both for reasons of “safety”, that is, to monitor possible side effects, and to avoid continuing a trial from which no more convincing evidence can be expected. The adequate handling of this monitoring requires close collaboration between the Data and Safety Monitoring Committee and statistical expertise.Statistical methods have been developed for respecting basic rules of hypothesis testing when multiple views are involved. Usually some form ofgrouped sequentialapproach fits best to the practical situation. A complication is that often the entry of study subjects isstaggeredover time, so that time on trial does not correspond to calendar time.
Interval Censoring
Authors: Sun Jianguo 
Published: July 2005

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.
L
exis Diagram
Authors: Keiding Niels 
Published: July 2005

Abstract
A Lexis diagram is a (time, age) coordinate system, representing individual lives by line segments of unit slope, joining (time, age) of birth and death. The diagram is an important descriptive tool in epidemiology and demography and it also has several applications in survival analysis and analytical epidemiology as a tool for several classes of statistical models.
Measurement Error in Survival Analysis
Authors: Prentice Ross L. 
Published: July 2005

AbstractThis entry describes various approaches to estimating the regression coefficient in the Cox failure time regression model when some of the regression variables are poorly measured. Regression parameter estimation may be considered if there is a validation subsample within which the “true” regression variable is available, or if there is a reliability subsample within which multiple estimates of the regression variable having independent measurement errors are available. The former context is closely connected to corresponding missing data estimation problems. Simplead hocestimators are reviewed, along with effective but inconsistent regression calibration estimators, and more complex nonparametric maximum likelihood and augmented inverse probability weighted estimators. With only a reliability sample available, estimation procedures include regression calibration and an extended risk set regression calibration approach, along with corrected score estimation procedures. Some comments on procedures for measurement error accommodation in an additive hazards model are also provided. This rapidly developing measurement error research area has implications for the analysis of follow‐up studies in a number of important application areas.
Phase‐Type Distributions in Survival Analysis
Authors: Aalen Odd O. 
Published: July 2005

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.
Sample Size Determination in Survival Analysis
Authors: Collett D. 
Published: July 2005

Abstract
This article outlines how the sample size for a study can be determined when the response variable is a survival time. This is a two‐stage process in which the number of events required to meet prespecified power requirements is first determined. The occurrence of censoring generally means that not everyone recruited to a study will experience the end point, and so the next step is to calculate the number of individuals who need to be recruited to give the required number of events. This number will depend on parameters such as the anticipated recruitment rate and the follow‐up period. The procedure is illustrated using a numerical example.
Survival Analysis, Overview
Authors: Andersen Per Kragh , Keiding Niels 
Published: July 2005

AbstractSurvival analysis is the generic name for analysis of time‐to‐event data. The distinguishing feature of such data is the presence of right‐censored observations. Thus, for some subjects, instead of observing the real time to the event, only a lower limit for this time, the right‐censoring time, is known. This kind of incomplete data calls for special statistical techniques for the analysis. This article reviews such methods with cross‐references to other articles dealing with special techniques.
Survival Distributions and Their Characteristics
Authors: Klein John P. 
Published: July 2005

Abstract
The four basic functions that characterize the probability distribution of the time to an event are presented. These functions, the survival function, the density or mass function, the hazard rate, and the mean residual life function are presented, and the relationship between the functions is discussed. Classes of distributions that reflect aging properties are presented. These classes include the increasing hazard rate (IHR) class, the increasing hazard rate on the average class (IHRA), the decreasing mean residual life (DMRL) class, the new better than used (NBU) class, the new better than used in expectation class (NBUE) and the harmonic new better than used in expectation class (HNBUE).
Total Time on Test
Authors: Andersen Per Kragh , Keiding Niels 
Published: July 2005

Abstract
In survival analysis, the exponential distribution plays an important role as a null hypothesis. One classical technique from reliability analysis for testing this hypothesis is based on the total time on test concept. It is explained, in the framework of counting processes, how a number of graphical and numerical test procedures may be based on this concept. These procedures are illustrated using data from a clinical trial in liver cirrhosis.