bluuebunny/crossref_metadata_2025_split huggingface dataset:
Mantel–Haenszel Methods
Authors: Landis J. Richard , Sharp Tonya J. , Kuritz Stephen J. , Koch Gary G. 
Published: July 2005

AbstractThis article provides an overview of generalized Mantel–Haenszel (MH) methods for the analysis of categorical data from factor–response and repeated measures study designs. These methods are illustrated using data from two different clinical research studies, investigating treatment differences within several different sets of 2 × 2 tables in a clinical trial, and within‐subject differences in an ordinal response across ordinal factor levels within a repeated measures design. The underlying multiple hypergeometric probability structure, based on a randomization model framework for hypothesis testing, is summarized for testing alternative hypotheses of 1) general association; 2) mean responses differ; and 3) linear trend in mean responses. These generalized MH methods can all be implemented directly within SAS and StatXact, with appropriate stratification and choice of scores.
Matched Pairs with Categorical Data
Authors: Davis Charles S. 
Published: July 2005

AbstractMatched pairs with categorical data arise when two measurements of the same categorical variable are obtained from each experimental unit. Such data are generally displayed in a two‐way contingency table. When the variable of interest is binary (dichotomous), marginal homogeneity can be tested using McNemar's test or the exact binomial one‐sample test. For a polytomous variable, marginal homogeneity can be tested using Stuart's test, and by tests proposed by Bhapkar and Madansky. The likelihood ratio test of marginal homogeneity conditional on the assumption of quasi‐symmetry can also be used. The hypothesis of symmetry for a polytomous variable can be tested using Bowker's test and the likelihood ratio test. For ordered categorical variables, one degree of freedom tests of marginal homogeneity can be carried out using tests analogous to those of Stuart and Bhapkar. Another approach to testing marginal homogeneity for ordered classifications is based on the conditional symmetry loglinear model.
Ordered Categorical Data
Authors: Becker Mark P. 
Published: July 2005

AbstractMany categorical variables have a natural ordering of the categories. Special methods are available for such data that are more powerful and more parsimonious than methods that ignore the ordering. This article discusses ways of modeling association for ordered categorical data and gives examples of them. These include loglinear models, related association models for two‐way tables that have row and column effects, and logit regression models for an ordinal response variable and a set of explanatory variables. The best‐known logit model, called a proportional odds model, uses the same effect parameters for each set of logits of cumulative probabilities for the ordered categorical response variable.
Overdispersion
Authors: Dean Charmaine B. 
Published: July 2005

AbstractCount data analyzed under a Poisson assumption or data in the form of proportions analyzed under a binomial assumption often exhibit overdispersion, where the empirical variance in the data is greater than that predicted by the model. This entry illustrates how overdispersion may arise and discusses the consequences of ignoring it, in particular, the underestimation of standard errors of covariate effects. Straightforward methods for ascertaining whether overdispersion is evident are presented. Simple methods for incorporating overdispersion within the framework of quasi‐likelihood estimation are reviewed as well as generalized linear mixed models, which form a broad scheme for model‐based analysis when overdispersion is present.
P
oisson Distribution
Authors: Palmgren Juni 
Published: July 2005

Abstract
A simple example involving white cell counts is used to derive how the Poisson distribution arises as the limiting distribution to the binomial distribution. The moment generating function, the normal limit and the variance‐stabilizing transform are presented as well as the conditioning argument relating the Poisson distribution to the multinomial and hypergeometric distributions. Population heterogeneity and overdispersion in relation to the Poisson distribution is discussed.
Power Divergence Methods
Authors: Imrey Peter B. 
Published: July 2005

AbstractPower divergences are measures of discrepancy between two distributions, with roots in information theory. For two multinomials with common support, the power divergence of order λ is based on the weighted sum ∑ipj(pj/qj)λof exponentiated ratios of the probabilitiespj,qjrespectively assigned to thejthpossible outcome. Note that these measures are directional rather than symmetric. The limiting logarithmic forms as λ → 0 or −1 are also considered power divergences. Asymptotically chi‐square goodness‐of‐fit statistics for count data are generally multiples of power divergences, and hence, general theoretical results and computational approaches for the power‐divergence family apply to these statistics and to estimators that minimize them. In particular, comparisons within this framework of tests and estimators based on the Pearson, Neyman, Freeman–Tukey, likelihood ratio, and discrimination information chi‐square statistics have shed considerable light on their absolute and relative performance in small sample settings, sparse contingency tables, and in the presence of outlying or zero counts. The “Cressie–Read” statistic, for which λ = 2/3, has been suggested as a possible replacement for the classical test statistics due to its good performance from several perspectives. This article defines the power divergence class of goodness‐of‐fit statistics and associated estimators, summarizes some basic comparative results, and briefly surveys the increasing use of power divergence in various statistical estimation settings.
Proportional‐Odds Model
Authors: McCullagh Peter 
Published: July 2005

AbstractThe proportional odds model is one member of the family of cumulative logistic regression models, designed for studying the effect of covariates on an ordinal responses variable. Relationships with other members of this family are described, emphasizing the effect of response aggregation. The connection with latent variable models, dispersion models, continuation‐ratio models, and log‐linear models is also discussed.
Square Contingency Table
Authors: Lipsitz Stuart R. 
Published: July 2005

AbstractThis article discusses the analysis of contingency tables for which the number of rows equals the number of columns. Three types of models for such tables are discussed: marginal models for comparing margins of the table, loglinear models for describing the joint distribution and the association patterns, and conditional models that consider the distribution of one of the categorical variables conditional on the outcome for the other one. Other topics discussed include testing marginal homogeneity and symmetry, the models of quasi‐symmetry and quasi‐independence, and modeling agreement.
Quartimax Rotation
Authors: Jackson J. Edward 
Published: July 2005

Abstract

Quartimax rotation
is a form of
orthogonal rotation
used to transform vectors associated with principal component analysis or factor analysis to
simple structure
. It is a special case of
orthomax rotation
, which maximizes the sums of squares of the coefficients across the resultant vectors for each of the original variables, as opposed to
varimax
, which maximizes the sums of squares of the coefficients within each of the resultant vectors. A numerical example is included to show a case where quartimax might be preferred to the commonly used varimax.
Accelerated Failure‐time Models
Authors: James Ian 
Published: July 2005

AbstractThe accelerated failure‐time model assumes a survival function of the formS(t) = S0(θt), whereS0is an underlying survival function and θ may depend on a number of covariates. This is equivalent to a location‐shift model for the log failure time, and in particular to a loglinear regression model when θ is loglinear. Parametric and semiparametric approaches to analyses based on these models with possibly censored failure‐time responses are reviewed. The accelerated failure‐time assumption is compared and contrasted with that of proportional hazards.
Bayesian Survival Analysis
Authors: Ibrahim Joseph G. , Chen Ming‐Hui , Sinha Debajyoti 
Published: July 2005

AbstractGreat strides in the analysis of survival data using Bayesian methods have been made in the past ten years due to advances in Bayesian computation and the feasibility of such methods. In this chapter, we review Bayesian advances in survival analysis and discuss the various semiparametric modeling techniques that are now commonly used. We review parametric and semiparametric approaches to Bayesian survival analysis, with a focus on proportional hazards models. Reference to other types of models are also given.
Counting Process Methods in Survival Analysis
Authors: Chang I‐Shou , Hsiung Chao Agnes 
Published: July 2005

AbstractA brief review of the counting process approach to generalized survival analysis is given. Examples are provided to illustrate that counting processes together with their filtration‐specific intensities are excellent modeling tools for survival analysis, where data are often incompletely observed; that the associated martingale theories are useful in proposing inference procedures, analyzing their distributional properties, and studying their efficiency; that the representation of the likelihood process in terms of its intensity offers extra convenience in the data analysis. Several examples are also given to indicate that counting process may provide good statistical model but offer limited help in the analysis.
Hazard Models Based on First‐Passage Time Distributions
Authors: Aalen Odd O. 
Published: July 2005

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.
Inverse Probability Weighting in Survival Analysis
Authors: Rotnitzky Andrea , Robins James M. 
Published: July 2005

AbstractSurvival studies usually incorporate high‐dimensional covariate data, but interest may focus on low‐dimensional characteristics of the survival distribution. Inverse probability weighted augmented estimation (AIPW) provides a robust approach, largely insensitive to model misspecification. The method was originally introduced to deal with coarsened (incompletely observed) data, and is discussed here with and without the assumption of random coarsening.
Length Bias
Authors: Wang Mei‐Cheng 
Published: July 2005

AbstractLength bias occurs when the sampling scheme implies that the probability of observing a positive‐valued random variable is proportional to the value of the valuable. Length bias is well documented in renewal theory, but is also important in epidemiology. Examples include prevalent cohort studies (where left truncation is an important remedy), other sampling schemes originating from cross‐sectional samples, and screening for chronical diseases.Comments are given on necessary modification of methods from nonparametric survival analysis.
Life Table
Authors: Hoem Jan M. 
Published: July 2005

Abstract
A life table is a traditional representation of estimates related to grouped survival times, sometimes called the “actuarial” method. Besides the survivor function, it usually contains estimates of residual life expectancy. There are also so‐called multiple‐decrement tables relevant for competing risks.
The history of the life table is long and well documented. Many special terms have been attached to the life table during its service in demography and actuarial mathematics.
Marker Processes
Authors: Kalbfleisch John D. 
Published: July 2005

AbstractIn longitudinal studies in survival analysis, repeated measures are often taken of more or less specific health measures. Suchmarker processesmay serve as (a) time‐dependent covariates for improving estimation of a survival distribution, (b) surrogate for survival in a comparative trial, (c) providing information on time of onset of disease, when this is not directly observable.
Parametric Models in Survival Analysis
Authors: Lawless J. F. 
Published: July 2005

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.
Product‐integration
Authors: Gill Richard D. 
Published: July 2005

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.
Rank Regression
Authors: Cuzick Jack 
Published: July 2005

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 ɛ is the error term, usually taken to have mean zero. If ɛ has the extreme‐value distributionthe well‐known proportional hazards model results. Other choices of ɛ 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.
Structural Nested Failure Time Models
Authors: Robins James M. 
Published: July 2005

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).
Survival Analysis, Software
Authors: Klein John P. , Zhang Mei‐Jie 
Published: July 2005

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.
Time‐Dependent Covariate
Authors: Andersen Per Kragh 
Published: July 2005

AbstractModels for survival data are often specified from the hazard function thereby allowing regression models to include covariates that change with time. This article reviews different types of time‐dependent covariates in survival analysis. Potential problems in connection with estimation of the survival function in models with time‐dependent covariates are discussed. Estimation in Cox's multiplicative regression model and other regression models with time‐dependent covariates, including additive models, are reviewed.
Truncated Survival Times
Authors: De Gruttola Victor , Liao Q. 
Published: July 2005

AbstractTruncation of survival data arises when observation can only occur if the failure time (survival time) lies within a certain interval (l,r) wherelorrmay be infinite. When the failure time is outside the truncation interval, no information about the subject is available, so the subject is “sampled from a conditional distribution”. This feature distinguishes truncation from censoring. Left truncation (delayed entry) is relatively easily handled by minor modification of hazard‐based survival analysis methods. Right truncation has been extensively studied in connection with latency times from HIV infection to onset of clinical AIDS.
Turnbull Estimator
Authors: Frydman H. 
Published: July 2005

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.
W
eibull Distribution
Authors: Klein John P. , Andersen Per Kragh , Keiding Niels 
Published: July 2005

Abstract

Properties and derivations of the Weibull distribution are discussed. The Weibull distribution is shown to arise as a limiting distribution of the minimum of
n
independent random variables. A derivation based on a model for carcinogenesis is presented. The Weibull distribution is shown to fall in both the proportional hazards and accelerated failure‐time class of models.
Autocorrelation Function
Authors: Rabe‐Hesketh Sophia 
Published: July 2005

Abstract

The correlation between two random variables that are part of a time series is usually known as the
autocorrelation
. A series of such correlations can be found according to the time separation or lag of the two variables. A plot of these correlations against the lag, sometimes known as a correlogram, is often an important tool in identifying a suitable model for the series.
Intervention Analysis in Time Series
Authors: Helfenstein Ulrich 
Published: July 2005

Abstract
When data are collected in the form of dependent time series data, important questions are concerned with “changes” in the series. Changes may be “man made” or they may arise “naturally”: How efficient was a preventive program to decrease the monthly number of accidents? How did the pattern of morbidity change after an environmental accident? Notifications of diseases or accidents and so on, are often collected in regular intervals. ARIMA models allow the stochastic dependence of consecutive data to be modeled flexibly. Intervention analysis is an extension of ARIMA modeling allowing the study of the structure of changes of ARIMA processes. Since the series may be nonstationary, large changes of the series could occur even when no intervention takes place. Intervention analysis may allow an investigator to distinguish between what can be expected due to nonstationarity alone and what cannot. Analogous questions of “change” may arise when studying time series data recorded in an individual patient. This article reviews basic concepts of intervention analysis. The methods are illustrated by medical applications.
Linear Mixed Effects Models for Longitudinal Data
Authors: Pinheiro José C. 
Published: July 2005

AbstractLinear mixed‐effects (LME) models have become a popular tool for analyzing longitudinal data that arise in areas as diverse as clinical trials, epidemiology, agriculture, economics, and geophysics. The increasing popularity of these models is explained by the flexibility they offer in modeling the within‐subject correlation often present in longitudinal data, by the handling of both balanced and unbalanced data, and by the availability of reliable and efficient software for fitting them. This paper describes a general LME model for longitudinal Gaussian data, presenting the model definition and its underlying assumptions. Maximum likelihood and restricted maximum likelihood estimation methods are discussed, as well as asymptotic inference methods. Available software for fitting and analyzing LME models are briefly reviewed. The model and methods are illustrated through an example from a longitudinal growth study.
N
yquist Frequency
Authors: Janacek G. J. 
Published: July 2005

Abstract
If we sample a signal observed over time at intervals, perhaps by digitizing an analog signal, then we naturally expect some loss of information. If the observed signal has cyclic components, then the sampling may induce some distortion in the effects we see in the sampled results.

There are some cyclic effects that are not observable, at least directly, and these are ones with high frequencies (or short periods). The frequency beyond which cyclic effects are unobservable is called the
Nyquist or folding frequency
. This frequency is related to the sampling rate
Δt
and is in fact 1/2
Δt
cycles per unit time.
Random Coefficient Repeated Measures Model
Authors: Goldstein Harvey 
Published: July 2005

Abstract
Biostatistical data often have a hierarchical structure. Typically, these structures are naturally occurring ones: animal populations are characterized by individuals nested within parents, themselves often nested within groups or herds that may also be nested within spatial entities. In other cases, the structure may result from research designs, as in multicenter clinical trials. Other examples are repeated measure designs, where measurements are “nested” within individual subjects and multivariate response data, where measurements are “nested” within individuals. In addition to nesting relationships among data units, we may also have cross‐classifications. For example, an individual cow may be nested within a herd of cattle, but also be the offspring of parent stock where any parent may contribute to several herds: individual cows are thus cross‐classified by parents as well as nested within their herds. A further complexity is also often present whereby individual units at one level of a data hierarchy may be nested within more than one higher‐level unit as in spatial data.
The article describes models for all these kinds of data structures, increasing in complexity as they move from simple hierarchies with continuously distributed responses, to cross‐classifications and multivariate data and to discrete responses. Various extensions and special cases will also be considered. The emphasis is on model specification with a brief section on estimation.
Structural Time Series Models
Authors: Harvey A. , Koopman S. J. 
Published: July 2005

AbstractStructural time series models are set up in terms of components, such as trends and cycles, which have a direct interpretation. Their statistical treatment is based on the state space form and the Kalman filter. Signal extraction is carried out by smoothing algorithms. Models may be constructed for multivariate series, and explanatory and intervention variables may be included. Nonlinear and non‐Gaussian models are handled using simulation techniques.