bluuebunny/crossref_metadata_2025 huggingface dataset:
Demography
Authors: Timæus Ian M.
Published: July 2005

Demography is the study of human populations with respect to their size and structure and of the components of population change, in particular, fertility, mortality, and migration. This article outlines the more important sources of data, substantive issues, concepts, methods, and models in demography. The discipline's central concern is to measure, explain, and model the dynamics of human populations. Thus, one crucial application of demography is the forecasting of population change by means of cohort‐component projections. Classical demographic measures and techniques of analysis were developed largely for the study of vital statistics with census‐based denominators. They include the calculation of age‐specific rates, standardization, and life‐table analysis. More recently, the growing importance of individual‐level analysis of survey data has led to convergence between demographic methods and other forms of statistical analysis.
Radiation Epidemiology
Authors: Ron Elaine , Lubin Jay H.
Published: July 2005

Radiation epidemiology is a specialized field of epidemiology that seeks to characterize and quantify the health risks associated with exposure to ionizing and nonionizing radiation. One of the principal aims of radiation epidemiology is to provide the human data needed to recommend or set protection standards for workers and the general public. The data also are used to estimate levels of risk from diagnostic radiation procedures, to indicate how radiotherapy protocols can be improved to reduce acute and long‐term side effects, to better understand individual susceptibility, and to learn more about disease mechanisms.
Bias in Case–Control Studies
Authors: Shapiro Samuel , Rosenberg Lynn
Published: July 2005

We discuss two classes of bias that arise in case–control studies, selection bias and information bias. A third source of bias, confounding, is not considered in this article. Selection bias arises either when cases in the study sample are not representative of cases arising from the source population (“study base”) or when controls are not representative of corresponding noncases in the study base. Sources of selection bias include bias in identifying cases or noncases in the study base, nonrepresentative sampling techniques, and selective refusal to participate (nonresponse bias). Use of nonrepresentative controls, such as hospital‐based controls, can lead to bias if the exposure distribution differs from that of controls in the study base. Information bias arises from inaccurate reporting of exposures and other covariates by cases or controls, and can result in serious distortion of estimated odds ratios when the errors in reporting by cases and controls are differential (recall bias).
Birth Defect Registries
Authors: Hanson James W. , Oakley Godfrey P.
Published: July 2005

Birth defects registries can be used to determine the prevalence of birth defects in newborns and can serve as a source of cases for etiologic investigations. We discuss the types of information in population‐based and nonpopulation‐based birth defects registries. We describe some prevention policies that were based on studies of registered cases and population controls.
Case–Control Study
Authors: Wacholder Sholom , Hartge Patricia
Published: July 2005

We review design options for case–control studies and considerations for determining whether a case–control or cohort study is more appropriate for a given purpose. One issue is exposure data quality, which may be poorer in a case–control study than in a cohort study, and subject to differential error (recall bias). This must be weighed against the cost efficiencies and other advantages of the case–control design. We describe case and control selection, including the use of hospital‐based controls (secondary base studies) in which controls are not sampled from the population base that gave rise to cases. Other design options, including matching and the use of two‐phase studies are described, as well as approaches to analysis. It is pointed out that not only odds ratios, but also absolute risks, are estimable from population‐based case–control studies.
Case–Control Study, Prevalent
Authors: Lang Janet M.
Published: July 2005

Case–control studies based on incident cases are well suited to studies of etiologic factors that affect disease onset. A prevalent case–control study includes subjects who have survived to the time of the study and had a previous history of disease onset. Associations with prevalent disease may therefore reflect not only disease onset but also influences on survival following disease onset. In a steady state population, the prevalence odds ratio for an exposure equals the incidence odds ratio times the ratio of mean survival times following disease onset. We discuss the interpretation of prevalent case–control studies, with examples of nosocomial infection and of neural tube defects.
Cohort Study
Authors: Prentice Ross L.
Published: July 2005

A cohort study is based on a sample of individuals who are followed to determine disease events over a defined follow‐up period. Disease rates can be calculated from such a study as well as relative risks associated with measured exposures and other covariates. If the cohort identification precedes the follow‐up period, the study is prospective; otherwise, the cohort study is retrospective. Some advantages of the cohort design, compared to the case–control design, include the ability to study a variety of health outcomes and to obtain high quality exposure information before disease develops, thus avoiding recall bias. We review basic elements, including study design and sample size, cohort selection and follow‐up, covariate history ascertainment, study conduct, data analysis, effects of measurement error, and validation substudies. We discuss the cohort study in relation to case–control designs, nested case–control designs, and case–cohort studies, as well as the role of intervention studies versus observational cohort studies.
Collapsibility
Authors: Greenland Sander
Published: July 2005

Consider theI × J × Kcontingency table representing the joint distribution of three discrete variables,X,Y, andZ, theI × Jmarginal table representing the joint distribution ofXandY, and the set of conditionalI × Jsubtables (strata) representing the joint distributions ofXandYwithin levels ofZ. A measure of association ofXandYis said to bestrictly collapsibleacross Z if it is constant across the conditional subtablesandthis constant value equals the value obtained from the marginal table. Noncollapsibility (violation of collapsibility) is sometimes referred to as Simpson's paradox after a celebrated article by Simpson, but the same phenomenon had been discussed by earlier authors, including Yule. The termcollapsibility, however, seems to have arisen later in the work of Bishop and colleagues.
Cumulative Incidence Rate
Authors: Gail Mitchell H.
Published: July 2005

The cumulative incidence rate is a cumulative hazard for a specific disease and should be distinguished from crude (or absolute) risk.
Ecologic Fallacy
Authors: Morgenstern Hal
Published: July 2005

The ecologic fallacy is the mistaken assumption that a statistical association observed between two ecologic group‐level variables is equal to the association between the corresponding variables at the individual level in the same population. This mistaken assumption often leads to incorrect inferences about the effects of exposures on disease occurrence.
Experimental Study
Authors: Gail Mitchell H.
Published: July 2005

An experimental study is a study in which conditions are controlled and manipulated by the experimenter. Often, randomized treatment assignment is used to assure that potential confounders have similar distributions in the various treatment groups.
Exposure Effect
Authors: Gail Mitchell H.
Published: July 2005

An exposure effect is a quantitative measure of the impact of an exposure on an outcome measure. Exposure effects, such as relative risk or risk difference, correspond to coefficients of terms in regression models. In the presence of interactions, an exposure effect defends on the levels of other factors, Exposure effects based on regression models can be regarded as summary measures of individual‐level causal exposure effects.
H
awthorne Effect
Authors: Gail Mitchell H.
Published: July 2005

The Hawthorne effect is an effect on study participants, which results from their knowing that they are being studied. It can bias estimates of true exposure effects.
Interviewer Bias
Authors: Gail Mitchell H.
Published: July 2005

Interviewer bias is a type of information bias that arises when an interviewer consciously or unconsciously elicits inaccurate information from study subjects. Methods to reduce the likelihood of interviewer bias are mentioned.
Latent Period
Authors: Tan Wai‐yuan , Chen Chao W.
Published: July 2005

Different definitions of latency used in the biological and statistical literature have been reviewed and illustrated by examples. In particular, a distinction has been made between the biological latent period and the epidemiological latent period. This article also discusses the latency of infectious diseases, such as the incubation period of HIV and the time to tumors in cancers. Some stochastic models of the time period to cancer tumors and its applications have been discussed in some detail.
Overmatching
Authors: Gail Mitchell H.
Published: July 2005

Overmatching refers to the unnecessary or inappropriate use of matching in a cohort or case–control study.
Prevalence
Authors: Gail Mitchell H.
Published: July 2005

Prevalence is the number of persons who have a disease or condition at a given point in time in a defined population.
Propensity Score
Authors: Rosenbaum Paul R.
Published: July 2005

The propensity score is the conditional probability of exposure to treatment rather than control given observed covariates, or more generally, the conditional probability of selection into a group given observed covariates. It is used in an effort to adjust for nonrandom treatment assignment or nonrandom selection. Matching or stratifying on the scalar propensity score tends to balance the many observed covariates used to construct the score. If it suffices to adjust for the observed covariates, then it also suffices to adjust for the propensity score.
Retrospective Study
Authors: Gail Mitchell H.
Published: July 2005

The term retrospective study describes case–control studies and other designs, such as historical cohort studies, in which relevant exposures and/or disease incidences occurred before the time of the study data collection.
Smoothing Methods in Epidemiology
Authors: Greenland Sander
Published: July 2005

Standard statistical methods (such as regression analysis) presume the data are generated by an identifiable random process, and attempt to model that process in a parsimonious fashion. In contrast, observational data in the health sciences are generated by complex, nonidentified, and largely nonrandom mechanisms, and are analyzed to form inferences on latent structures. Despite this gap between the methods and reality, most observational data analysis comprises application of standard methods, followed by narrative discussion of the problems entailed by doing so. Alternative approaches employ latent‐structure models that include components for nonidentified mechanisms. Standard methods can still be useful, however, provided their modeling philosophy is modified to encourage preservation of structure, rather than achieving parsimonious description. With this modification they can be viewed as smoothing or filtering methods for separating noise from signal before the task of latent‐structure modeling begins. A hierarchical‐modeling implementation can be carried out with popular software.
Target Population
Authors: Greenland Sander
Published: July 2005

The concept of a
target population
is an informal one, sometimes defined as “the population about which information is wanted” or the “totality of elements which are under discussion and about which information is desired”. Often, the word “population” refers to this concept; see, for example, Kendall & Stuart or Freedman et al. The word “target” emphasizes, however, that this population is not necessarily the same as the one that we end up sampling. The latter population is sometimes called the
sampled population
or (in epidemiology) the
source population
.
Confidentiality in Epidemiology
Authors: Leufkens Hubert G.
Published: July 2005

This entry describes the need for confidentiality in conducting clinical and epidemiologic research, particularly with respect to informational privacy of individuals. Ethical principles (including beneficence, nonmalfeasance, autonomy, and justice) are reviewed, and mention is made of the legal framework and guidelines to prevent the violation of confidentiality.
Drug Utilization Patterns
Authors: Abrahamowicz Michal , Tamblyn Robyn
Published: July 2005

We review methodological challenges in the observational studies of the patterns and outcomes of drug utilization. First, we address issues related to design and data collection in different studies that rely on administrative databases, discuss their limitations in accounting for clinical indication bias, and outline new opportunities created by the emergence of the integrated electronic patient records. Then, we focus on the different analytical issues related to such complexities as prescriber effects, assessing the impact of policy changes on drug utilization, description and classification of longitudinal patterns of medication use, alternative methods of measuring time‐dependent exposure status and medication dose, use of nonparametric modeling to represent time‐varying, lagged and/or nonlinear effects of exposure.
False Negative Rate
Authors: Walter Stephen D.
Published: July 2005

The false negative rate of a diagnostic or screening test is defined as the complement of sensitivity. Its appropriate denominator is specified.
Gold Standard Test
Authors: Walter Stephen D.
Published: July 2005

This entry describes the concept of an error‐free diagnostic test, and the practical difficulties of attainting this ideal. The consequences of assuming a test to be error‐free when in fact it is not are also mentioned.
Diagnostic Tests, Likelihood Ratio
Authors: Roberts Robin S.
Published: July 2005

This article concerns the use of diagnostic test information in medical diagnosis. Traditionally, the association between a diagnostic test and the true state of disease has been quantified in terms of sensitivity and specificity. The application of Bayes Theorem allows the formal incorporation of the diagnostic test information as a post‐test probability of disease. The positive and negative likelihood ratios (LRs) are alternative expressions of the informational properties of the diagnostic test, which are computed from sensitivity and specificity. LRs offer several advantages including (a) simplifying the calculation of post‐test probability (via odds), (b) providing a more direct indication of the diagnostic value of the test, and (c) avoiding the need to dichotomize a quantitative test. Given enough data, one could estimate a continuous LR curve and thus compute post‐test probability for any test value.
Meta‐Analysis of Diagnostic Tests
Authors: Macaskill Petra , Glasziou Paul , Irwig Les
Published: July 2005

Meta‐analysis can summarize the performance of a diagnostic test based on all available high quality studies, investigate reasons for variation in test performance, and compare the performance of two or more tests. Strategies are outlined for finding all relevant primary studies, and assessing the quality of studies. Study quality, study design factors, and patient characteristics should be assessed and explored as possible sources of heterogeneity in diagnostic performance. Summary ROC analysis (SROC) is the most common meta‐analytic method for diagnostic studies. In addition, linear regression is used to model test accuracy as a function of implicit test threshold and other study level covariates. The SROC approach shows the trade‐off in sensitivity and specificity as the threshold for a positive test result varies. The more complex, hierarchical SROC model, takes account of both within and between study variability, and can be used to explore variation in both accuracy and threshold.
Number Needed to Treat (NNT)
Authors: Bender Ralf
Published: July 2005

The number needed to treat (NNT) has gained much attention in the past years as a useful way of reporting the results of randomized clinical trials. Defined as the reciprocal of the absolute risk reduction (ARR), NNT is the average number of patients needed to be treated to prevent an adverse outcome in one additional patient. This measure has been applied to a number of other research areas involving the development of more sophisticated techniques to calculate and interpret NNTs in medical research. The most important application areas are screening studies, public health research, epidemiology (case–control and cohort studies), crossover studies, studies measuring continuous and survival time data, risk–benefit analyses, and systematic reviews. An overview of the recent developments regarding NNT is given as well as a discussion of the advantages, drawbacks, and usefulness of the NNT statistic as a reporting tool.
Predictive Values
Authors: Walter Stephen D.
Published: July 2005

This entry considers predictive values for a diagnostic test in terms of the disease prevalence, and test sensitivity and specificity. Clinical implications of high or low predictive values are discussed.
Prevalence of Disease, Estimation from Screening Data
Authors: Pickles Andrew , Dunn Graham
Published: July 2005

Simple estimation of prevalence from sample survey data may be biased because of imperfections in the measurement instrument. An alternative approach is to use two‐phase sampling in which a subsample of screened individuals is investigated more intensively with a gold standard measure to reveal their true disease status. A variant design is to use a calibration or validation sample of individuals who are assessed using both the screen and gold standard methods. The analysis of two‐phase samples is described, including the use of simple conditional probabilities, inverse probability weights, and a more general framework in which the EM algorithm is used. Bayesian approaches are also mentioned briefly. Statistical software for the analysis of multiphase data is mentioned, together with an outline of certain design considerations.
Receiver Operating Characteristic (ROC) Curves
Authors: Hanley J. A.
Published: July 2005

The receiver operating characteristic(ROC) curve describes the relationship between the false positive fraction and true negative fraction associated with a diagnostic test as the test threshold defining the boundary between individuals classified as cases or noncases is varied. The ROC curve avoids certain arbitrariness involved in the choice of a single overall index of accuracy. This entry describes how the ROC curve is derived from data, and reviews summary indices that may represent its performance. The comparison of ROC curves for competing tests is discussed, and appropriate software is identified.
Secondary Attack Rate
Authors: Halloran M. Elizabeth
Published: July 2005

The secondary attack rate is defined as the probability that infection occurs among susceptible persons within a reasonable incubation period following known contact with an infectious person or an infectious source. It is a key epidemiologic parameter in infectious diseases that are transmitted by contact. It can be estimated using a variety of epidemiologic study designs, models, and methods of estimation. Inference needs to take into account the correlation of susceptibles exposed to the same infectious source.
Screening, Sojourn Time
Authors: Duffy Stephen W.
Published: July 2005

Sojourn time is the duration of a disease before clinical symptoms become apparent but during which it is detectable by a screening test. Its clinical relevance is that it represents the duration of the temporal window of opportunity for early detection. Its statistical interest lies in the estimation of the mean sojourn time of a screened population, taking into account the sensitivity of the screening test. Common models for its distribution include the exponential and Weibull distributions. Methods of estimation include maximum likelihood, generalized estimating equations, and Markov Chain Monte Carlo.
Standard Gamble Technique
Authors: Gafni Amiram
Published: July 2005

In recent years, the concept of utility has been introduced to both clinical decision‐making and program evaluation. The standard gamble (SG) technique is a classic method of measuring an individual utility (i.e. preferences) under uncertainty. Its most prominent use is in generating the preference weights to be used in the quality adjusted life year (QALY) calculation. In this section, we briefly describe the technique and its underlying assumptions.
Time Trade‐Off Technique
Authors: Gafni Amiram
Published: July 2005

Decisions about medical treatments and the setting of health programs involve both technical and value judgments. An important one is evaluating potential tradeoffs between quality of life and length of life or between different domains of quality of life resulting from different treatment options. The time trade‐off TTO) technique is one of the methods used for that purpose. Its most prominent use is in generating the preference weights to be used in the QALY (quality adjusted life years) calculation. In this section, we briefly describe the technique and its underlying assumptions.
Admixture in Human Populations
Authors: Majumder Partha P.
Published: July 2005

When parental populations give rise to a hybrid population, it is possible to estimate the proportions of admixture from each parental population on the basis of known marker allele frequencies if there has been no genetic drift. Methods include generalized least squares and maximum likelihood. It is also possible to use a measure of genetic similarity. All these methods assume that the admixture is a static, one‐time phenomenon, whereas in reality there is usually a continued, long‐term exchange of genes among populations.
Familial Correlations
Authors: Keen K. J.
Published: July 2005

Methods of statistical inference for correlations among members of families and pedigrees are summarized.
Family History Validation
Authors: Petersen Gloria M.
Published: July 2005

Analysis of family data relies on accurate reports of family history. Sensitivity and specificity of family history of disease or exposures can be measured, and have been found to vary, depending upon different factors. These include: who provides the history (self versus proxy), the circumstances of the condition being studied, and demographic characteristics of the informant.
Multilocus (Gene × Gene Interaction)
Authors: Cordell Heather J.
Published: July 2005

An important topic in molecular and quantitative genetics is epistasis, or the interaction between genes. There has been much confusion in the literature owing to differing definitions and interpretations of gene–gene interaction. This article reviews some of the most popular definitions used in the literature and notes that the correspondence between statistical and biological interaction effects may be more limited than is sometimes assumed.
Paternity Testing
Authors: Baur Max P.
Published: July 2005

The use of genetic marker systems for the analysis of questionable paternity situations has been introduced in 1920 to prove in a deterministic way, situations of nonpaternity. Statistical evaluation of positive results (nonexclusion) was first performed by Essen–Möller in 1938. The general idea, which holds for any question of possible relationship, is the formulation of two alternative hypotheses regarding the postulated relationships of the persons involved. Subsequently, the likelihoods of the marker‐typing results conditional on these hypotheses are calculated using population frequencies estimated from large population samples and Mendelian proportions for transmission from parents to children. The complete genetic information is contained in the likelihood ratio of these two conditional likelihoods and serves as the basis for the decision between the two alternative hypotheses. Introduction of prior probabilities for the two hypotheses allows the calculation of Bayesian posterior probabilities using these conditional likelihoods.
Penetrance
Authors: Wijsman Ellen M.
Published: July 2005

Penetrance is a probability model that relates, for an individual, the observed phenotype to the underlying genotype. Penetrance functions may be continuous or discrete, may include measured covariates, and may involve more than one locus. All variables not explicitly in the model are assumed to be randomly distributed among individuals, leading to variance in estimates of penetrance, in part because of variability in unmeasured covariates and genetic background among populations.
Bioinformatics in Functional Genomics
Authors: Kohane Isaac S. , Butte Atul
Published: July 2005

Databases of DNA sequences, physical maps, genetic maps, gene polymorphisms, protein structures, and gene expression have produced a need for systematic quantitative analysis that goes by the name of bioinformatics. To manage these large datasets in the domain of functional genomics requires algorithmic implementation on computers. Functional genomics will continue to be hypothesis‐driven and hypothesis‐generating biological research. Because the datasets are of high dimensionality, involving relatively small numbers of cases, a large number of solutions can explain the data; the computational techniques to unravel these involve both supervised and unsupervised learning.
Animal Screening Systems
Authors: Haseman Joseph K.
Published: July 2005

Animal screening systems are experimental protocols designed primarily to screen substances in laboratory animals for possible adverse effects in humans. These experiments include long‐term rodent toxicity/carcinogenicity bioassays and shorter duration studies that focus on reproductive and developmental toxicology endpoints. These experiments are the first step of a broader risk assessment process to determine the magnitude of human risk associated with exposure to a test substance. Statistical issues that arise in these studies include (i) selection of the number, magnitude, and spacing of doses; (ii) use of statistical methodology that adjusts for potentially confounding factors such as survival, body weight, and litter effects; (iii) multiple comparison adjustments for the large number of variables evaluated; (iv) use of historical control data; and (v) development of appropriate statistical methodology to permit extrapolation of experimental results from high to low doses and from species to species.
Biological Assay, Overview
Authors: Sen Pranab K.
Published: July 2005

Biological essay (or “bioassay”), in its classical form, is concerned with the measurement of the concentration of an active ingredient in a test preparation, by estimation of its potency relative to that of a standard preparation. Assays, usually by animal experimentation, form an essential tool of biological standardization. Standard designs and methods of analysis are described here, including stochastic approximation, radioimmunoassays, semiparametric and nonparametric methods, and bioequivalence studies. In a broader sense, Bioassay refers to experiments, with biological units, to detect possible dose–response (or toxicity‐adverse effect) relationships. Underlying toxicodynamics (and/or pharmacodynamics) and toxicokinetics (and/or pharmacokinetics), possibly in conjunction with toxicogenomics (and/or pharmacogenomics) may render such studies statistically quite different from conventional biometric studies. Some relevant approaches are considered here.
Median Effective Dose
Authors: Liu Jen‐pei , Chow Shein‐chung
Published: July 2005

The median effective dose (MED) is the median of the tolerance distribution of the dose levels for a stimulus that generates, on average, predefined responses in 50% of experimental units. The median effective dose is usually denoted as ED50. An overview of the design and analysis for inference about ED50is provided. First, two commonly employed tolerance distributions—normal and logistic distributions—are introduced to characterize the relationship between the dose and response. Under a location/scale model for the tolerance distribution, estimation procedures for ED50are reviewed. Interval estimation methods include delta method, the Fieller's theorem, likelihood approach, and Bayesian procedures. The difficulties associated with interval estimation by the Fieller's theorem and likelihood method are addressed. Inference procedures for ED50are also summarized for the situations where (a) the underlying population consists of a mixture of homogeneous subpopulation, (b) the responses of individual experimental units are dependent, and (c) responses are observed at some prespecified time points. Nonparametric methods such as Spearman–Kärber estimators as well as other robust procedures are reviewed. An account of different nonsequential designs for MED under various optimality conditions is given. Finally, a brief summary of sequential procedures and designs is provided.
Stochastic Approximation
Authors: Gross Alan J. , McLean David C.
Published: July 2005

Stochastic approximation is a method for approximating the root of the equationM(θ) = m0, when the functionM(.) is not directly observable but can be cast as the expectation of a suitably defined regression function. The method was introduced by Robbins and Munro in 1951 and has since been extensively refined and extended. It has found application in many areas of biostatistics and in the application of neural networks.
Compartment Models
Authors: Matis James H. , Wehrly Thomas E. , Kiffe Thomas R.
Published: July 2005

Compartment modeling is used to describe system kinetics in various branches of biomedical science, and is especially important in pharmacokinetics. The standard model defines constant flow rates into and out of each of several compartments, with linear dependence on compartment contents. More complex models permit time‐varying flow rates, lags in flow, and birth and nonlinear features. Stochastic models provide further insight.
Fan Plot
Authors: Atkinson A. C. , Riani Marco
Published: July 2005

This is a graphical procedure for determining the effect of one or more observations on the transformation parameter in the Box–Cox family of power transformations of the response variable in regression. It is based on a “Forward Search” through the data to fit subsets of increasing numbers of observations, with outliers being included toward the end of the search.
G
alton–
W
atson Process
Authors: Seneta E.
Published: July 2005

The simple branching process is a probability model describing the evolution through successive generations of the descendants of a single ancestor. If the mean number of offspring per individual is less than or equal to one, extinction occurs with probability one; otherwise there is a positive probability of survival.
Mathematical Biology, Overview
Authors: Matthysse Steven
Published: July 2005

Mathematical biology has become a flourishing field in which real mathematics combines with real biology. The most distinctive contribution of mathematics to biology lies, not in simulation, but in proving theorems about models that, although simplified, are biologically adequate. Five examples are selected as examples; illustrating diverse ways that mathematical reasoning can enhance our understanding of biological systems.
Point Processes
Authors: Milne Robin K.
Published: July 2005

This article is a review of the theory of point processes that aims to introduce the reader to the wider literature. It provides a relatively nontechnical summary of foundational ideas, an introduction to the rich variety of point process, and stochastic process models that can be built from more basic point processes such as Poisson and renewal processes, and discusses some aspects of statistical inference for point process data. An annotated bibliography offers guidance to the literature.
Reproduction Number
Authors: Dietz K.
Published: July 2005

The basic reproduction number (or ratio) is the expected number of secondary cases of an infection, which one typical case could generate during its infectious period in a completely susceptible population. It is the most important theoretical concept in communicable disease epidemiology.
Semi‐
M
arkov Processes
Authors: Mode Charles J.
Published: July 2005

Semi‐Markov processes are useful generalizations of a class of stochastic processes commonly referred to as Markov jump processes in continuous time. In most of the applications of this class of processes in biostatistics and biology, the state space is chosen as a discrete set with finite or countable elements that have biological meaning. One of the properties of Markov processes is that it follows from the Markov property in continuous time that the sojourn time (holding time) in any state has an exponential distribution with a parameter depending on that state. Semi‐Markov processes are a generalization of Markov jump processes in that the distribution of the sojourn time in any state can, in principle, be arbitrary. Furthermore, in semi‐Markov processes the finite dimensional distributions of the sample paths of the process are modeled directly in terms of arbitrary distributions of sojourn times for each state and conditional distributions of a jump to another future state, given the present state. In many applications, this property makes it possible to set down a formula for the likelihood function of the data with relative ease. Briefly, the paper contains substantive examples and a description of the mathematical tools needed to work with semi‐Markov processes.
Tumor Modeling
Authors: Byrne H. M. , King J. R.
Published: July 2005

The number and variety of deterministic and stochastic models of solid tumor growth are increasing rapidly and are indicative of the complexity of the mechanisms involved. We outline below some of the theoretical approaches that are being used to model tumor growth and associated processes such as carcinogenesis and tumor angiogenesis.
Y
ule Process
Authors: Chiang Chin Long
Published: July 2005

The Yule process is a birth process with a constant birth rate. The number of births in time interval (0,
t
),
Y
(
t
), has a negative binomial distribution, which is the same as the distribution of the number of new species of a genus produced during (0,
t
) in Yule's study of evolution.

The numbers of species produced in a sequence of time intervals,
Y
(1), …,
Y
(
r
), have a chain of negative binomial distributions.
Communicable Diseases
Authors: Farrington C. P.
Published: July 2005

Many of the statistical methods used in communicable diseases are similar to those used in other areas of epidemiology. Clinical trials, risk‐based epidemiological studies, and survival analysis for example account for much of the infectious disease statistician's toolkit. In addition, however, some more specialized techniques are required. This article aims to give a flavor of the range of statistical methods used in the field of infectious disease epidemiology. Only the simpler versions of the techniques are covered, with references to more complex methods. For common childhood infections, survival models are reinterpreted in the context of epidemic transmission models to estimate hazards of infection, and to derive epidemiological parameters such as the basic reproduction number. Basic back‐calculation methods are described for estimating the incidence of infections with long incubation periods such as AIDS. Simple stochastic models such as branching processes and chain binomial models for use with outbreak data are outlined. Methods are described for estimating latency and infectious periods. Cluster detection methods are also reviewed in the context of identifying infectiousness and detecting outbreaks. Statistical methods for evaluating vaccine efficacy and safety are discussed. Finally, some statistical topics relating to diagnostic testing for infectious diseases using laboratory techniques are touched upon.
Epilepsy
Authors: Johnson Anthony L.
Published: July 2005

Epilepsy is a common neurological disorder that affects about one in a hundred people. It is one of the oldest documented diseases that has multiple causes and onset at any age. This article provides a brief overview of epilepsy and its treatment, together with a summary of the types of investigation that have been employed to improve greater understanding of this disease. A few landmark studies in epilepsy are identified.
Oncology
Authors: Duffy Stephen W.
Published: July 2005

Historically, the most influential development in Biostatistics for cancer research is the Mantel–Haenszel estimate. This has contributed massively not only to relative risk estimation in cancer epidemiology, but also to survival analysis in clinical trials of cancer therapies. It has to some extent been superseded by generalized linear models, notably logistic and Poisson regression, in epidemiology, and with Cox regression in survival analysis in recent years. The likely biostatistical developments for the future are likely to be aimed at evaluation of interventions for prevention, early detection, and genetic oncology. Methods for rapid evaluation and modeling of the disease process will be of some relevance. Bayesian estimation techniques such as Markov Chain Monte Carlo are likely to play a major part.
Ophthalmology
Authors: Marsh Marta J. , Gange Stephen J.
Published: July 2005

The field of ophthalmology and vision research provides a rich source for both the application and the development of statistical theory and methodology, particularly with correlated data, due to the paired nature of much ocular data. This article begins with a brief history of ophthalmology, followed by a section describing the variety of types of data available in the field of ophthalmology and optometry. Finally, a section describing the multitude of common statistical issues that anyone analyzing ophthalmologic data must consider concludes this article, with emphasis on methods for the appropriate analysis of paired (correlated) data.
Correlation
Authors: Armitage Peter
Published: July 2005

In a loose sense, two variables are correlated if changes in one tend to be accompanied by changes in the other. More specifically, correlation implies a linear relationship with superimposed random variation. The product–moment correlation coefficient was introduced by Galton and greatly exploited by Karl Pearson. Its square is the proportion of the variance of one variable “explained” by linear regression on a second variable. Standard tests are described in the article. An important extension is to intraclass correlation for measurements on individuals falling into groups, which measures the association between individuals in the same group.
Diagnostics
Authors: Atkinson A. C.
Published: July 2005

Diagnostics are methods for identifying discrepancies between the data and a fitted model. Concepts described here include outliers, decision residuals, leverage, influence, Cook's distance, multiple deletion, and very robust regression methods as illustrated from a study of the relationship between mandible length and gestational age.
General Linear Model
Authors: Farewell Vern T.
Published: July 2005

The components of the general linear model are described. Standard methods of analysis that are based on the model are identified.
Measurement Scale
Authors: Hand David J.
Published: July 2005

The measured variables analyzed in statistics are reflections of aspects of the system being studied. As such, the relationships between values of the variables must reflect properties of the attributes being studied. Different types of measurement scale, amongst which the most familiar are nominal, ordinal, interval, and ratio, reflect different properties of the attributes. Incorrect conclusions can be drawn if a statistical analysis fails to take appropriate account of this relationship between the objects of study and their numerical representations.
Model, Choice of
Authors: Matthews John N. S.
Published: July 2005

The choice of which statistical model to use in a given application is a complex matter, which draws not only on the technical expertise of the statistician but also on the nature of the application and the purpose of the analysis. Different purposes may require quite different models to be applied to the same dataset. The role of modeling in clinical trials, epidemiology, and general biostatistics is discussed. The relative contribution of expertise both in the area of application and in the relevant statistical issues is explored. The use of sensitivity analyses to ensure that substantive conclusions are not heavily dependent on model assumptions is stressed. A strong theme throughout the article is that the judgment of the biostatistician plays an inescapable role in an activity, which nonstatisticians too often see as wholly objective.
Nonparametric Regression
Authors: Hazelton Martin L.
Published: July 2005

Nonparametric methods of regression seek to describe the relationship between an explanatory and response variable while making only the most general type of assumptions about the functional form of this relationship. Techniques for computing nonparametric regression functions include kernel estimation, local polynomial regression, and spline smoothing. In each case, there is a balance to be reached between the smoothness of the regression function and its goodness of fit to the data. Simple nonparametric regression models (with one explanatory variable) can be extended to deal with multiple covariates by employing so‐called generalized additive models.
Prediction
Authors: Farewell Vern T.
Published: July 2005

Statistical usage of the term prediction is discussed. The sources of error in prediction are identified.
Residuals
Authors: Atkinson A. C.
Published: July 2005

Residuals are the differences between observed responses and those predicted by a model. Any pattern in the residuals is evidence of an inadequate model or of irregularities in the data, such as outliers, and suggests how the model may be improved. Various graphical methods are described, for both the normal regression and the generalized linear models, and are illustrated for the analysis of various data sets.
Standardized Coefficients
Authors: Farewell Vern T.
Published: July 2005

The use of standardized regression coefficients to facilitate the comparison of coefficients is described.
Bayesian Methods for Contingency Tables
Authors: Albert James H.
Published: July 2005

Bayesian alternatives to frequentist methods for fundamental problems in categorical data analysis, such as testing independence in two‐way contingency tables and estimating probabilities of categories containing no observations, have been considered for at least four decades. Since the 1980s, Bayesian methods of model selection have also seen extensive and continuing development. These attempt to address the tendencies of frequentist approaches to arrive at overly complex models, and to disregard the effects of variability in model selection on model‐based estimated effects and predictions. This entry briefly reviews several Bayes and empirical Bayes approaches to estimating probabilities of categories, testing equiprobability in a one‐way table, testing independence in a two‐way contingency table, and selecting among generalized linear models, with particular attention to loglinear models, for tables of higher dimension.
Biserial Correlation
Authors: Bedrick Edward J.
Published: July 2005

This article discusses several methods that have been proposed for estimating a bivariate correlation coefficient when one of the observed variables is binary. An example is used to illustrate the different approaches.
Categorizing Continuous Variables
Authors: Altman Douglas G.
Published: July 2005

Continuous variables are often converted to categorical variables by grouping values. For descriptive purposes, this can be useful but problems can arise when this is done as part of a data analysis. This article discusses relevant issues with categorization of explanatory variables in regression. Effects of categorization are discussed, such as loss of information, power, and efficiency. This is considered first for categorizing into two groups and then for categorizing into several groups. Rather than group according to observed values with several variables, one might group according to a weighted sum of the variables–a prognostic index.
Contingency Table
Authors: Altham P. M. E.
Published: July 2005

Contingency tables give counts for cross classifications of categorical variables. This article illustrates two‐dimensional tables (two variables). It then discusses the hypothesis of independence and presents chi‐squared tests. An example of quasi‐independence is presented, and small‐sample tests are mentioned. Extensions to multiway contingency tables and the relevant hypotheses for such tables are also discussed. Loglinear models describe the hypotheses, and there are corresponding logistic regression models when one of the variables is a binary response variable.
Hypergeometric Distribution
Authors: Shuster Jonathan J.
Published: July 2005

For a finite population of subjects of two types, suppose we select a random sample without replacement. The probability distribution of the number in the sample of one of the two types is the hypergeometric distribution. This article presents the hypergeometric distribution, summarizes its properties, discusses binomial and normal approximations, and presents a multivariate generalization.
Latent Class Analysis
Authors: Conaway Mark R.
Published: July 2005

Latent class analysis is a discrete variable analog of factor analysis. It attempts to explain associations by underlying categorical traits that are not directly observable. This article presents the latent class model, discusses its connection with loglinear models, and discusses model fitting and testing.
Logistic Regression, Conditional
Authors: Hosmer David W. , Lemeshow Stanley
Published: July 2005

This section describes the conditional logistic regression model. This model is appropriate when one wishes to model a binary outcome variable with matched or highly stratified data and when one is not interested in matched sets or stratum effects. The resulting fitted model may be used to estimate odds ratios in the same manner as is done with the usual logistic regression model. Examples of estimation and interpretation are given.
Loglinear Model
Authors: Carriquiry Alicia L. , Fienberg Stephen E.
Published: July 2005

The general structure of loglinear models emerged in the 1960s as a response to the need for methods to assess departures from independence (and conditional independence) for multiple categorical variables. This entry describes both frequentist and Bayesian statistical methods for the analysis of multiway contingency tables using loglinear models. Special attention is given to the subclass of graphical models, defined in terms of the simultaneous occurrence of one or more conditional independence relationships. The entry also includes a brief guide to computer programs for categorical data analysis.
Marginal Models
Authors: Lindsey J. K.
Published: July 2005

Repeated observations on the same subject are likely to be correlated. This situation may arise in longitudinal studies or in other cases where observations are clustered in some way. A multivariate model will refer both to the marginal distributions over the whole data and to the conditional distributions for individual subjects or clusters. A marginal model puts primary emphasis on marginal aspects. Relationships between responses and covariates may differ between marginal and conditional models. The issues are discussed with particular reference to paired binary data.