bluuebunny/crossref_metadata_2025 huggingface dataset:
Ascertainment
Authors: Hodge S. E.
Published: July 2005

For most disorders of genetic interest, families are not selected for study at random but rather because they are segregating for the disorder. This biases the estimate of the segregation ratio if not properly allowed for in the analysis. The classical ascertainment model assumes families are ascertained if they contain at least one proband, an affected person who at any time was detected independently of the other members of the family. Ascertainment can be complete (“truncate selection”), multiple, or single; in the last situation, the probability of that a sibship will be ascertained is proportional to the number of affected sibs it contains. In practice, this independent “proband” model may not be appropriate and other models have been proposed. However, some situations still remain difficult or intractable.
Candidate Gene
Authors: Elston Robert C.
Published: July 2005

The “candidate gene” approach presupposes that we have reason to believe that a particular metabolic pathway underlies a disease. We then try to confirm or refute this belief by seeking a disease–marker association or linkage, where the marker is the causative gene, in linkage disequilibrium with the causative gene, or tightly linked but in equilibrium with it.
Eugenics
Authors: Pelias Mary Z.
Published: July 2005

The Eugenics Movement was born in England in the late nineteenth century and rapidly found ardent followers in England, the United States, and Germany. The goal of eugenics was to describe and improve the genetic endowment of man. Investigations in eugenics included studies of physical traits and criminality, social traits and pathology, mental traits, and racial and ethnic traits. Many of these studies were later discounted as pseudoscience, strongly influenced by ethnocentric biases of the investigators. The pursuit of eugenic goals eventually led to legal sterilizations, restrictive immigration laws, and to obscene violations of human rights and barbarous excesses of racism and genocide in Nazi Germany. Today, eugenic principles are no longer imposed by law, but they remain alive in the choices that humans make about transmitting their genes to their offspring.
Genetic Risk Ratios
Authors: Kopciuk K. A. , Bull Shelley B.
Published: July 2005

Genetic risk ratios measure the association between known or putative genetic factors and the occurrence of a particular disease. These risk quantifiers are expressed as relative risks (RRs) or odds ratios (ORs). Risk ratios for relatives, such as measures of familial aggregation or recurrence risk in relatives, use family disease history to assess the evidence for an inherited genetic basis for the disease. Allelic, genotype, and haplotype risk ratios evaluate the association of a disease with a measured candidate gene or with one or more genetic markers. Risk ratios estimated under a case–control design may be population‐based or family‐based depending on the type of control group.
Genotype
Authors: Elston Robert C.
Published: July 2005

The genotype of an organism is its genetic make‐up, as opposed to its phenotype, or outward appearance. If the two alleles at a locus are the same, the genotype is homozygous, otherwise it is heterozygous. If a heterozygote has the same phenotypic distribution as one of the corresponding homozygotes, the allele in that heterozygote is dominant and the other allele is recessive with respect to that phenotype. A multilocus genotype is made up of two haplotypes. In the case of a quantitative trait, dominance corresponds to intralocus interaction; epistasis to interlocus interaction.
Calibration
Authors: Lee J. Jack , Moon Hojin
Published: July 2005

Statistical calibration is often used in biomedicine as a means to estimate the quantity of a substance that is difficult or expensive to measure by another measurement, which is easier or cheaper to obtain. Classical or inverse estimators can be computed from parametric or nonparametric regression models. Multivariate calibration, Bayesian modeling, and optimal designs are reviewed. Selected topics such as interval estimation, measurement error, robustness, heteroscedasticity, instrumental calibration, and survey sampling are discussed as well.
Dynamic Allocation Index
Authors: Gittins J.
Published: July 2005

When a process comprises a succession of projects, with each chosen from a pool of competing projects, there may be advantages to undertaking the projects in one order rather than in others. An example of such a process would be testing different candidate compounds when searching for a new pharmaceutical product. Dynamic Allocation Indices are a way of attributing indices to projects so that at each stage, choosing the project with maximum index optimizes the whole process, with respect to some reward function.
Stimulus–Response Studies
Authors: Morgan Byron J. T.
Published: July 2005

Simple stimulus–response experiments result in estimates of the probability of a hit (getting it right) and probability of a false alarm (getting it wrong), which produce a point on a receiver operating characteristic (ROC) curve. Signal‐detection models convert this information into a single measure of performance. There are several elaborations of the simple experiment. ROC curve methodology has been applied in areas such as ecology, medicine, engineering, and psychology.
Conception, Models for
Authors: Weinberg Clarice R.
Published: July 2005

Time to conception offers a stochastic surrogate for fertility, in that subfertile couples not using contraception tend to take longer to conceive than do fertile couples. Couples can be studied retrospectively, by asking about how long it took them to achieve an index pregnancy, or prospectively, by recruiting couples during or prior to an attempt to conceive. The resulting data play out in discrete time, as measured by the number of menstrual cycles required. Because of heterogeneity among couples in their fecundability (per cycle probability of conception), the data are overdispersed compared to the geometric. This overdispersion can be modeled parametrically (e.g. with a beta‐geometric) or nonparametrically (based on the moments of the dispersed but unknown underlying fecundability distribution). If more detailed data are available, on days with intercourse and time of ovulation, then the models for conception can additionally incorporate the strong effects of timing.
Epidemic Models, Multi‐Strain
Authors: Scalia‐Tomba Gianpaolo
Published: July 2005

Deterministic and stochastic models are briefly described for an infectious process caused by two strains of a pathogenic agent, where infection by one strain confers immunity to the other.
Epidemic Thresholds
Authors: Ball Frank
Published: July 2005

This article gives an overview of the threshold behavior of epidemic models, focusing primarily on stochastic closed population models. A key parameter is the reproduction numberR0of an epidemic. For a broad range of models, branching process theory is used to show that an epidemic initiated by a trace of infection in a large population can take off only ifR0is larger than one. These models assume either a homogeneous population or a stratified population in which all the subpopulations are large. Models for the spread of an epidemic among a population partitioned into a large number of small households, or among a spatially configured population, are also considered. In both of these casesR0no longer provides a good indicator as to whether an epidemic can take off. The article closes with a brief discussion of the threshold and long‐term behaviors of open population models, which incorporate demographic effects.
Hidden
M
arkov Models
Authors: Churchill Gary A.
Published: July 2005

Hidden Markov models are a generalization of the finite mixture model that allow for dependence in a sequence of observations via Markovian dependence of an unobserved (hidden) sequence of states. Inference problems associated with hidden Markov models include parameter estimation and restoration of the hidden state sequence. The recursive algorithms employed to solve these problems are related to the Kalman filter and have spawned a wide variety of applications. Areas of application range from speech recognition and signal processing through analysis of molecular sequence data.
Michaelis–Menten Equation
Authors: Dunn Graham
Published: July 2005

This article describes various approaches to the analysis of quantitative responses assumed to follow a hyperbolic dose–response relationship (the Michaelis–Menten equation) characterized by the values of two parameters: the Michaelis constant (the dose at half‐maximal response) and the asymptotic maximum response. Methods include diagnostic graphical representations, including the double reciprocal or Lineweaver–Burk plot, the Hanes plot and the Eadie–Hofstee plot. Curve‐fitting and parameter estimation is described using either least squares or maximum likelihood. The latter includes using a generalized linear model incorporating a reciprocal link function and the possibility of nonnormally distributed errors. Robust and distribution‐free estimation procedures, such Theil's method (known as the direct linear plot in biochemistry) are also covered.
Ornstein–Uhlenbeck Process
Authors: Blackwell Paul G.
Published: July 2005

The Ornstein–Uhlenbeck process (OUP) is a unique Gaussian, stationary diffusion process. Originating as a model for the Brownian motion of a particle, it has a wide range of applications in biology and elsewhere. These include the modeling of membrane potentials of nerve cells, modeling the location or velocity of anything from whole organisms to individual cells and the use of the OUP as a limiting approximation to population models in epidemiology and genetics. Another area of application is the large‐sample behavior of likelihood ratios for multiple genetic markers. As well as including discussion of these (and other) applications, this article describes likelihood‐based inference and mathematical properties such as first passage times.
Queuing Processes
Authors: Chiang Chin Long , Ball Frank
Published: July 2005

This article is primarily concerned with two queuing models,M/M/sandM/G/1, both of which assume Poisson (M) arrivals. In theM/M/squeue, there aresservers and the service time is exponentially (M) distributed. In theM/G/1 queue, there is a single server and the service time follows an arbitrary but specified distribution (G). For theM/M/smodel, the equilibrium distribution of the number of customers in the system is derived, as are other equilibrium properties of the system, such as the mean waiting time of a typical customer and the probability that a given server is busy. Two approaches to analyzingM/G/1 queues are outlined,embeddingand themethod of stages. Formulae are given for the equilibrium mean number of customers in the system and the equilibrium mean total time spent in the system by a typical customer, and properties of a typical busy period of the server are outlined. TheM/M/∞ model, in which there are infinitely many servers, is described briefly.
Serial‐Sacrifice Experiments
Authors: Dewanji A.
Published: July 2005

Simple survival experiments provide little information to study the progress of different disease(s) and possible interaction between them. In serial sacrifice experiments, individual animals are randomly selected and killed (sacrificed) at fixed or adaptively selected time points, allowing the examination of presence or absence of the different diseases. Therefore, a serial sacrifice experiment, with interim observation on some individuals before natural death occurs, allows one to probe into the disease processes and the complex interrelationships between different diseases. Data from the sacrificed animals provides an estimate for prevalencep𝒜(t), the probability being that an alive animal has a particular disease combination 𝒜 at timet. On the other hand, death data provides an estimate of probability of death with the particular disease combination 𝒜, given by μ𝒜(t)p𝒜(t), where μ𝒜(t) denotes the mortality rate from disease combination 𝒜. In animal carcinogenicity experiments with serial sacrifice, in particular, the tumor occurrence time distribution is estimable. Design issues regarding the optimal sacrifice schedule are of some interest, but not much work has been done on this. There are few examples of serial sacrifice experiments, the ED01 study with 2‐acetylamino‐fluorene (2‐AAF) conducted by the US national center for toxicological research (NCTR) being probably the largest.
Shape Analysis
Authors: Dryden Ian L.
Published: July 2005

Shape is defined to be all the geometrical information that is invariant under a set of registration transformations. For example, the registration transformations might be translation, rotation, and scaling. We discuss Kendall's shape space for two‐dimensional sets of landmarks, which is the complex projective space. Probability distributions for planar shapes are reviewed and some approximate distributional results for higher‐dimensional cases are given. Practical shape inference using Procrustes analysis is discussed, and particular emphasis on multivariate analysis in tangent spaces is given. We discuss principal component shape analysis and hypothesis tests, and provide some examples from biology and medicine. Finally, we discuss some applications of shape analysis in image analysis.
Tumor Incidence Experiments
Authors: Dinse Gregg E.
Published: July 2005

This article describes a variety of methods for analyzing data from animal tumorigenesis experiments. The primary endpoint of interest is the tumor incidence rate. Both the estimation of tumor incidence rates and the comparison of these rates across treatment groups are discussed. Analyses are complicated by the fact that all onset times are censored when tumors are occult, censoring is informative unless tumors are completely nonlethal, and biases arise if proper adjustment is not made for survival differences across groups. Existing methods address such concerns by assuming a particular level of tumor lethality, assigning individual causes of death, requiring some animals to be sacrificed, specifying parametric models, or imposing functional restrictions. This article describes each of these approaches and summarizes the associated advantages and disadvantages.
Two‐Mutation Carcinogenesis Model
Authors: Moolgavkar Suresh H.
Published: July 2005

The two‐mutation carcinogenesis model, better known as the two‐stage clonal expansion (TSCE) model, is a type of multistage carcinogenesis model that explicitly considers stochastic growth of intermediate cells on the pathway to malignancy. Because of this fact, this model can be used not only for analysis of time‐to‐tumor data, which requires the hazard function, but also for analysis of intermediate lesions, such as colon polyps, which requires expressions for the number and the size distribution of such lesions. The model has been extensively used for analyses of both types of data. Extensions of the model to incorporate more than two mutations have also been proposed.
Chronomedicine
Authors: CornÉlissen Germaine , Halberg Franz
Published: July 2005

Chronobiology (fromchronos, time;bios, life; andlogos, science) investigates the mechanisms underlying variability in the otherwise unassessed physiological range, including rhythms found in us, resonating with cycles around us. Broad time structures (chronomes) consisting of deterministic chaos and trends organized by rhythms are found in organisms and in their environments. They are mapped by chronomics as the reference values for both an applied chronomedicine and a basic chronobiology. Chronomics quantify health, identifying new disease risks, diagnosing predisease and overt illness, enabling timely and timed treatment (Rx), and validating the short‐ and long‐term efficacy of a givenRxon an inferential statistical individualized (as well as population) basis.
Community Medicine
Authors: Johnson Anthony L.
Published: July 2005

Community medicine is a broad medical specialty developed during the twentieth century to cover various aspects of medicine and care in relation to populations (communities) rather than individuals.
Otorhinolaryngology
Authors: Zielhuis Gerhard A. , Straatman Huub , Schilder Anne G. M.
Published: July 2005

Biostatisticians entering the field of ORL are confronted with large numbers of patients and a diversity of diseases and treatment options. Most of the statistical procedures used are similar to those used in other branches of medicine. Special features are the potential of each patient having two ears, the fluctuating course of many of the common ORL diseases, and the diversity of management options.
Critical Care
Authors: Corwin Howard L.
Published: July 2005

The randomized controlled trial (RCT) has become the “gold” standard for clinical research. However, the complex nature of critical illness has made the design and conduct of RCTs difficult. Research in critically ill patients presents unique challenges. The disease processes are often not well defined. There are also multiple therapeutic interventions being administered and the disease processes themselves often have a variable clinical course. Finally, outcome selection is a challenge, mortality (short or long) versus nonmortality outcomes. The last few years have seen the publication of the results of five RCTs that have had a major impact on the practice of critical care.
Akaike's Criteria
Authors: Stone M.
Published: July 2005

This entry covers Akaike's Final Prediction Error and information criteria for model selection, their links with Mallows'Cpand cross‐validation, and user's expectations of such criteria.
Bayesian Measures of Goodness of Fit
Authors: Rice Kenneth
Published: July 2005

We consider methods for critical assessment of the appropriateness of fitted Bayesian models. This is done for situations where no particular alternative model is specified, and where the discrepancy between model and data is measurable in a user‐defined way. We review methods for testing goodness of fit in nonhierarchical models before discussing hierarchical models.
Bayesian Methods for Model Comparison
Authors: Rice Kenneth
Published: July 2005

We consider Bayesian methods for comparing competing models. The Bayes factor is the simplest and best‐known tool for this purpose, but other criterion‐based methods are also considered, together with model averaging.
Model Checking
Authors: Chandler R. E.
Published: July 2005

Most statistical analyses are, implicitly or explicitly, based upon an underlying model for the data at hand. The conclusions from any analysis can therefore be justified only if the model is adequate. This article gives an overview of general principles for checking the adequacy of a statistical model. The focus is primarily upon models for relationships between variables. Specific techniques are summarized; for the reader who requires more detail, pointers to the relevant literature are given.
Random Effects
Authors: Farewell Vern T.
Published: July 2005

The concept of random effects in a regression model is explained and contrasted with that of fixed effects. Statistical methods that make use of the concept are identified.
Separate Families of Hypotheses
Authors: De Braganca Pereira Basilio
Published: July 2005

In the last forty years since statistical procedures were first developed to test separate (nonnested) families of hypotheses, a huge amount of literature has developed for testing a null model against one or more separate alternatives. In the first two decades, mainly statisticians were interested in this problem. During the eighties the econometricians took a great interest and in the nineties, Bayesian statisticians developed some new results on the subject. The purpose of this paper is to given an introductory overview of the subject and an updated bibliography.
Transformations
Authors: Farewell Vern T.
Published: July 2005

Transformation of variables and/or parameters to facilitate the use of standard statistical methodology is described. Particular reference to regression models is made.
Two‐stage Least Squares Regression
Authors: Sprent P.
Published: July 2005

In systems of simultaneous equations, if some explanatory variables are correlated with errors, ordinary least squares regression gives inconsistent estimators. Two‐stage least squares overcomes this difficulty. The approach is closely related to procedures that use instrumental variables in models that allow for errors in explanatory variables.
Variance Components
Authors: Solomon P. J.
Published: July 2005

Random variation may have a complex structure, with several identifiable sources and corresponding components of variance. In a hierarchical or multilevel model, parameters may change, for example, between individuals, their variation being measured by variance components. This article reviews the history of the study of variance components and describes methods of estimation. Topics include synthesis of variance, empirical Bayes methods, nonnormal models, and model assessment and prediction.
Binary Data
Authors: Collett D.
Published: July 2005

When a response variable can take one of two possible forms, such as alive or dead, the resulting data are said to be binary. The focus of this article is on models for binary response variables, and the use of logistic regression models is emphasized. The models can be fitted using most statistical software packages. Alternative models can be compared using the deviance, and for grouped binary data, this statistic may be used as a measure of goodness offit. Techniques for assessing model adequacy are outlined and the use of these methods is illustrated with an example.
Binomial Distribution
Authors: Wypij David
Published: July 2005

The binomial distribution refers to the number of successes in
n
independent trials with a common success probability
p
in each. With large
n
, the distribution is approximated by the normal, and with large
n
and small
p
, it is approximated by the Poisson. This article reviews its properties and discusses point estimation, confidence interval estimation, and hypothesis testing for the parameter
p
. Extensions are also briefly considered.
Bradley–Terry Model
Authors: Imrey Peter B.
Published: July 2005

Bradley–Terry models parsimoniously summarize preferences expressed in paired comparisons of objects through a set of latent “merit” or “preference” parameters linked to the individual objects rather than to the pairs. When comparisons of all pairs ofkobjects are observed, the resultingk(k‐ 1)/2 linearly independent proportions are reduced tok‐ 1 latent parameters, or potentially fewer if these are further modeled using characteristics of the objects. This entry introduces the basic model, discusses its relationship with the probit, logit, and loglinear models developed in other contexts, and describes some extensions that allow for data with ties, varying degrees of preference, or simultaneous expressions of preferences along multiple dimensions of assessment.
Correlated Binary Data
Authors: Pendergast Jane F. , Gange Stephen J. , Lindstrom Mary J.
Published: July 2005

Correlated binary data may arise in longitudinal or spatial studies or through some other form of clustering of sampling units. The simplest setting, with clusters of size two and no covariates, leads to familiar methods of analysis. Models with covariates include response feature models, conditionally specified models, transitional models, marginal models, and cluster‐specific models. These may lead to different interpretations of the regression parameters.
Exact Inference for Categorical Data
Authors: Corcoran Christopher D. , Senchaudhuri Pralay , Mehta Cyrus R. , Patel Nitin R.
Published: July 2005

Commonly used methods for analyzing categorical data rely on asymptotic theory and may be misleading for small data sets. ExactPvalues and confidence limits are available based on the permutation distributions of appropriate test statistics. Details are given here for a wide range of settings with contingency tables, which may be stratified or involve clustering, including also logistic regression. Various software packages are available.
Fisher's Exact Test
Authors: Routledge Rick
Published: July 2005

Fisher's exact test can be used to assess the significance of a difference between the proportions in the two groups. In particular, it provides a widely applicable way to assess the results of simple, completely randomized experiments leading to two‐by‐two contingency tables with small frequency counts, However, it has low power, especially when the standardP‐value is used. The power can be increased considerably through either using the mid‐Pvalue, or carefully constructing a test based, at least in part, on a binomial model.
Generalized Linear Mixed Models
Authors: McCulloch Charles E. , Neuhaus John M.
Published: July 2005

Generalized linear mixed models (GLMMs) are an extension of the class of generalized linear models in which random effects are added to the linear predictor. This allows the modeling of correlated, possibly nonnormally distributed data with flexible accommodation of covariates. We describe this class of models and the inferences possible and contrast them with marginal modeling techniques such as generalized estimating equations.
Interaction Model
Authors: Kreiner Svend
Published: July 2005

Loglinear models that describe association patterns among categorical variables are sometimes calledinteraction models. Graphical interaction models are useful for portraying conditional independence and indicating when an association remains the same after collapsing over a variable. This article discusses a “Separation theorem” that describes how conditional independence patterns are maintained by conditioning on a certain subset of variables as indicated by an interaction graph. Collapsibility issues are also discussed.
Mantel–Haenszel Methods
Authors: Landis J. Richard , Sharp Tonya J. , Kuritz Stephen J. , Koch Gary G.
Published: July 2005

This 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

Matched 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

Many 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

Count 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

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

Power 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

The 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

This 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.
Structural and Sampling Zeros
Authors: Ten Have Thomas R.
Published: July 2005

Structural and sampling zeros are addressed in the context of fitting loglinear (and by definition logistic) models to cross‐classified tables. The specific issues of parameter identifiability, degrees of freedom, exact inference, and software limitations are considered.
J
‐Shaped Distribution
Authors: Ghosh Pankaj
Published: July 2005

This is a probability distribution or frequency distribution shaped roughly like a letter J or its mirror image, with highest frequency at one end of the range. Formal characterizations are given, relating to the characteristic function.
Quartimax Rotation
Authors: Jackson J. Edward
Published: July 2005

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

The 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

Great 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.
Bootstrapping in Survival Analysis
Authors: Veraverbeke Noël
Published: July 2005

We survey the main developments in bootstrapping survival data since the paper of Efron [17] on resampling procedures for censored data. We consider bootstrap versions of the product‐limit estimator and also deal with resampling in semi‐ and nonparametric regression models.
Copula
Authors: Oakes David
Published: July 2005

Bivariate distribution (or survivor) functions can conveniently be specified by their marginal distributions and their associated dependence structure, the latter summarized by a copula. The special class of archimedean copulas is important in survival analysis because of its connection to proportional hazards frailty models.
Counting Process Methods in Survival Analysis
Authors: Chang I‐Shou , Hsiung Chao Agnes
Published: July 2005

A 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.
Cure Models
Authors: Farewell Vern T.
Published: July 2005

Cure models are used for time to event data when a subset of subjects who will not experience the event of interest may exist. A formulation of such models is presented and special cases in the literature are highlighted. Estimation of such models is discussed. The issues of identifiability of parameters and nonstandard hypothesis testing are highlighted.
Event History Analysis
Authors: Andersen Per Kragh , Keiding Niels
Published: July 2005

An introduction to event history analysis via multistate models is given. Examples include the two‐state model for survival analysis, the competing risks and illness–death models, and models for bone marrow transplantation. Statistical model specification via transition intensities and likelihood inference is introduced. Consequences of observational patterns are discussed.
Hazard Models Based on First‐Passage Time Distributions
Authors: Aalen Odd O.
Published: July 2005

When 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

Survival 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

Length 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

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

In 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

Survival 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

Product 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

In 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.
Repeated Events
Authors: Lawless J. F.
Published: July 2005

Subjects in longitudinal studies often experience repeated events. Data on the timing of such events allow us to study patterns of event occurrence, to characterize within‐ and between‐subject variability, and to relate event occurrence to other processes. This article describes statistical models for recurrent events and associated methods of analysis.
Structural Nested Failure Time Models
Authors: Robins James M.
Published: July 2005

Structural 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

Statistical 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.
Tied Survival Times
Authors: Zhang Mei‐Jie
Published: July 2005

Tied survival times occur in survival studies frequently. We discuss adjustment for ties for some common statistical procedures.
Time‐Dependent Covariate
Authors: Andersen Per Kragh
Published: July 2005

Models 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

Truncation 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

The 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.
Type‐Specific Covariates in Survival Analysis
Authors: Andersen Per Kragh
Published: July 2005

In regression analysis of event history data using multistate models it is sometimes useful to consider models where some covariates have the same effect on several transition intensities. It is demonstrated how this may be achieved using type‐specific covariates.
W
eibull Distribution
Authors: Klein John P. , Andersen Per Kragh , Keiding Niels
Published: July 2005

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.
Bayesian Approaches to Cure Rate Models
Authors: Ibrahim Joseph G. , Chen Ming‐Hui , Sinha Debajyoti
Published: July 2005

Bayesian approaches to cure rate modeling have gained great popularity in the analysis of survival data. In this chapter, we review several Bayesian approaches, discussing various alternative formulations of the cure rate model, their interpretations, and their properties.
Autocorrelation Function
Authors: Rabe‐Hesketh Sophia
Published: July 2005

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.