bluuebunny/crossref_metadata_2025 huggingface dataset:
Computerized Therapeutic Decision Support
Authors: Pifer Eric , Weiner M. G. , Williams Sankey V.
Published: July 2005

The increasing breadth and depth of clinical information stored electronically has enabled computerized therapeutic decision support systems to provide appropriate and timely advice to providers, which that is tailored specifically to a patient's clinical status. This chapter provides a taxonomy for therapeutic decision support systems in terms of the goals of the advice, the mechanism in which the advice is given, the information needed to generate the advice, and the underlying reasoning used. Examples of applications of therapeutic decision support systems are provided with an assessment of their utility within the complex processes of clinical care.
Admixture Mapping
Authors: Majumder Partha P.
Published: July 2005

Admixture between populations leads to linkage disequilibrium between loci if the allele frequencies are different between populations. One can test whether the linkage disequilibrium is due to linkage or admixture. One can condition the analysis on parental genotype or parental admixture. In the former case, what is scored is whether a haplotype in a parent is transmitted or not to an affected offspring.
Adoption Studies
Authors: Neale M. C.
Published: July 2005

The adoption study is a “natural experiment” but has methodological difficulties, such as confidentiality, sampling (ascertainment), and selective placement. When performed in nuclear families or combined with twin analysis (of special note are monozygotic twins reared apart), adoption studies have the potential to allow estimation of broad sense heritability and genotype environment interaction. A common method of analysis for continuous traits uses path analysis together with maximum likelihood. In the case of binary traits, logistic regression may be used, or in the framework of structural equation modeling, integration of the multivariate normal distribution is necessary.
Assortative Mating
Authors: Wilson Susan R.
Published: July 2005

Assortative mating occurs when the phenotypes of biological parents are more (or less) similar than would occur under random mating. In contrast to inbreeding, mechanisms for assortative mating are poorly defined. The classical model for assortative mating makes strong assumptions, such as independent genetic and environmental contributions to a trait and no interaction between genotype and environment. More complex models have been developed, especially for human behavioral traits. Assortative mating affects the estimations and interpretation of heritability and lowers the power of linkage studies.
Genetic Markers
Authors: Elston Robert C.
Published: July 2005

Genetic markers are genetic polymorphisms, used for the study of population structure, linkage and association analysis, paternity testing, and forensics, that segregate in a simple Mendelian fashion. They include blood cell antigens, restriction fragment length polymorphisms, minisatellites (variable number of tandem repeat), microsatellites (short tandem repeat), and single nucleotide polymorphisms.
Blood Groups
Authors: Reisner E.
Published: July 2005

The term
blood groups
encompasses the products of genes expressed as molecules on the surface of red cells in humans. They were first investigated for their clinical importance in the transfusion of blood products and then became useful as genetic markers for population genetic studies. Included in the blood groups are the ABO, Rhesus (Rh), MNSs, P, Kell, Duffy, Kidd, Lutheran, and Lewis blood.
Case‐Only Gene Mapping
Authors: Weir B. S. , Nielsen D. M.
Published: July 2005

When individuals can be characterized as being affected or unaffected by a disease, marker‐trait association can be addressed by comparing marker frequencies between these two categories. It is also possible to infer linkage or association on the basis of marker data from affected individuals only. When there is linkage disequilibrium a test for Hardy‐Weinberg proportions among marker genotypes in the affected population is a test about marker allele and genotype associations with the disease locus. However, rejection Hardy‐Weinberg at the marker locus in the affected population may simply reflect nonrandom mating in the whole population.
Cladistic Analysis
Authors: Zhu Xiaofeng , Cooper Richard S. , Elston Robert C.
Published: July 2005

Haplotype based association analysis is playing an important role in dissecting the genetic factors underlying complex diseases. Cladistic analysis, which incorporates the evolutionary information among haplotypes, can improve the power to detect genetic factors by limiting the number of hypothesis tests that need to be performed. In this article, we describe the cladistic analysis method and its application to mapping quantitative trait loci.
Commingling Analysis
Authors: Mendell Nancy Role , Finch Stephen J.
Published: July 2005

Commingling distributions have been proposed as a logical extension to the genetic model for genetic traits that are either polygenic or multifactorial. Mixture models can be used to describe unobserved heterogeneity in many situations. For normal component distributions with equal variance, the EM algorithm can be used to find the maximum likelihood estimates of the parameters. The asymptotic distribution of the likelihood ratio test of the null hypothesis of a single normal distribution is unknown but can be approximated by the parametric bootstrap. A Bayesian approach to this problem can also be taken.
Comparative Genomic Hybridization
Authors: Moore Dan H.
Published: July 2005

Comparative genomic hybridization is a method for directly identifying regions of gains and losses of genomic material in chromosomes. The results are measured as a series of test‐to‐reference signals from fluorescent dyes for a large number of distinct chromosomal regions and statistical methods are used to identify regions where the signal ratios are significantly different from 1.0. It is applied to microarrays to define abnormality in tumours.
Complex Diseases
Authors: Palmer Lyle J.
Published: July 2005

The principal distinction between “simple” monogenic diseases and “complex” diseases is that the latter do not exhibit classic patterns of Mendelian inheritance. Complex diseases tend to involve greater difficulties in phenotype definition and present challenges for genetic epidemiology. There is, typically, incomplete penetrance and genetic heterogeneity and they are often closely associated with “intermediate” phenotypes that are themselves highly heritable. The use of isolated populations, inbred animal models, and linkage and association analysis with haplotypes are often used in the study of complex diseases.
Family‐based Association for Quantitative Traits
Authors: Horvath Steve , Laird Nan M.
Published: July 2005

Tests of allelic association are designed to demonstrate relationships between genetic and phenotypic information. The class of tests using transmission information from parents to offspring (TDT and its generalizations) are very popular with dichotomous phenotypes because of their lack of sensitivity to population heterogeneity. Here we discuss the generalization of this approach to quantitative phenotypes.
Gene
Authors: Elston Robert C.
Published: July 2005

A commonly accepted definition of a gene is a combination of segments of DNA that together code for a functional unit; but the word is used with other meanings, better differentiated as “locus” and “allele”, depending on the nationality, age, and specific genetic discipline of the writer.
Genetic Heterogeneity
Authors: Olson Jane M.
Published: July 2005

The term genetic heterogeneity refers to the underlying diversity in genetic architecture of different individuals in the population with a common phenotype. Two types of genetic heterogeneity are commonly distinguished: locus heterogeneity in which variants at different loci can predispose to the same phenotype, and allelic heterogeneity in which different variants at the same loci can predispose to the same phenotype. Although allelic heterogeneity is certainly of interest, once a susceptibility locus is identified, the presence of locus heterogeneity so dramatically reduces the power of gene mapping for complex traits that it remains a major statistical challenge. In this article, we primarily discuss models of linkage analysis that allow for locus heterogeneity, including more recent models that allow for heterogeneity‐related covariates.
Linkage Disequilibrium
Authors: Chakravarti Aravinda
Published: July 2005

The nonrandom association between alleles at different loci is termed linkage disequilibrium. This note discusses the origin of this concept, its theoretical genetic basis, its estimation and tests of significance, and applications. Linkage disequilibrium studies are critical in human disease gene mapping and is now a major area of research with the availability of variation of the human genome sequence.
Linkage Information Content
Authors: Guo Xiuqing
Published: July 2005

The probability of knowing IBD sharing status of relative pairs at polymorphic genetic markers is an important factor for a model‐free linkage study. Here, Linkage Information Content (LIC) value is introduced, which measures the informativeness of a marker for identity‐by‐descent (IBD) sharing status of relative pairs. LIC value is independent of the mode of inheritance of the disease, but is specific to the type of relative pairs used.
Mendel's Laws
Authors: Wijsman Ellen M.
Published: July 2005

Gregor Mendel's experiments with peas lead to the development of two laws that describe, in quantitative terms, trait distributions in the offspring of a mating. The first, which still forms the fundamental basis behind much of genetics, is the law of segregation. In modern terms, this law states that each individual, as a parent, transmits to an offspring, exactly one randomly chosen allele of the two present at each locus in the individual. The second law, or law of independence, describes the joint behavior of more than one gene. This law states that alleles at one locus segregate independently of alleles at other loci. This proposition is now known to be false for genes on the same chromosome, but still, usually adequately describes the inheritance patterns of multiple genes, other than those on the same chromosome.
Linkage Analysis, Multipoint
Authors: Speed Terry P.
Published: July 2005

Multipoint linkage analysis is the analysis of linkage data involving three or more linked loci. Such analyses are carried out to order or map a set of loci, to position a new locus in relation to a mapped set of loci, or to exclude a locus from a region containing two or more loci. Multipoint linkage analysis can be viewed as an attempt to make more efficient use of recombination data in furthering the aims of linkage analysis. It is more complicated than two‐point linkage analysis in several ways: the order of loci needs to be specified; a joint distribution for all recombination patterns needs to be specified; and the calculations can become prohibitive rather quickly. Likelihood methods are used in multipoint linkage analysis; there are two principal approaches to calculating likelihoods in the literature: the Elston–Stewart algorithm, which works on a relatively few loci and many individuals in a pedigree, and the Lander–Green algorithm, which is effective for many loci and relatively few individuals in human pedigrees.
Linkage Analysis, Multivariate
Authors: de Andrade Mariza , Amos Christopher I.
Published: July 2005

This article provides an overview of the methodology currently available for multivariate linkage analysis. We presented and discussed model‐free multivariate methods that have been developed and used in linkage analysis.
Mutation
Authors: Elston Robert C.
Published: July 2005

Mutations arise from mistakes in copying DNA. They may be nonsense mutations (resulting in the formation of an incomplete protein) or missense mutations (resulting in the change of an amino acid in a protein).
Parental Effects
Authors: Fallin Dani , Palmer Lyle J.
Published: July 2005

An individual's risk for a genetic disease or phenotype, conditional on their own genotype, may depend on parental effects such as imprinting, or the genotype or phenotype of a particular parent. For example, under imprinting, a risk‐conferring allele may only be expressed in an individual if it is inherited from a particular parent. Alternatively, a mother's genotype, even if not transmitted to her offspring, may influence
in utero
conditions and increase risk and/or interact with genetic predisposition for particular diseases among those offspring. The existence of such parental effects may lead to incorrect interpretations of the (marginal) effects of particular genes when performing human genetic studies at the individual level, unless such effects are accounted for in the analysis. We discuss potential scenarios of such parental effects, and present an overview of current methods for accommodating these effects when performing segregation analysis, linkage analysis, or genetic association studies.
Polymorphism
Authors: Elston Robert C.
Published: July 2005

Polymorphism refers to the different forms an organism can have. In genetics, it refers to the different genotypes possible. The term is used by some authors merely to mean a common allele.
Polymorphism Information Content
Authors: Elston Robert C.
Published: July 2005

The polymorphism information content of a marker is the probability that the marker genotype of the offspring of a heterozygous parent affected with a dominant disease allows one to deduce which marker allele the offspring inherited from the parent. It is a measure of a marker's usefulness for linkage analysis.
Relationship Testing
Authors: Epstein Michael P. , Boehnke Michael
Published: July 2005

Linkage analyses of genetic diseases are accomplished using data from related individuals in families. These analyses assume that one correctly specifies the relationships among all pairs of relatives within these different families. Relationship misclassification may lead to inappropriately reduced or increased evidence for linkage. Sometimes, one can identify misspecified relationships by detecting Mendelian inconsistencies. However, for smaller family subsets such as sibling pairs, it may not be possible to identify misspecified relationships with certainty. Still, with an adequate amount of marker data, one may be able to identify misspecified relationships probabilistically. This section describes a variety of different statistical methods that one can apply to identify misspecified relationships of relative pairs. Generally, these methods are accurate and computationally fast.
Bioassay
Authors: Armitage Peter
Published: July 2005

This term is effectively synonymous with “biological assay”, the strict form of which involves the estimation of relative potency. It is sometimes used in a wider sense, to include any experiment in which agents are applied to animals or other biological systems and their effect is measured.
Bioavailability and Bioequivalence
Authors: Chow Shein‐Chung , Liu Jen‐Pei
Published: July 2005

A brief history of regulatory development using bioavailability and bioequivalence studies for approving generic drug products is provided. Concepts of drug exchangeability and switchability are illustrated and their relationship with average bioequivalence, population bioequivalence, and individual bioequivalence is elucidated. The commonly used crossover designs for bioavailability and bioequivalence studies are presented. They include the standard two‐sequence two‐period crossover design, some higher‐order crossover designs for comparing two treatments, and Williams design. Statistical methods for evaluation of average bioequivalence, including the confidence interval and two one‐sided tests approaches, are illustrated with reference to sample size determination. Current issues and future challenges for bioavailability and bioequivalence studies are also given.
Biological Standardization
Authors: Gaines Das Rose E.
Published: July 2005

The potency of a biological product usually needs to be assessed in terms of its biological activity rather than in terms of its chemical or physical properties. Biological variability means that this assessment depends on statistical techniques, such as bioassay and on the availability of biological standards, which have known properties. Standards can be local, as might be used within a company for the assessment of a new assay or international standards, which are required for the primary calibration of biological products.
Chemometrics
Authors: Fearn Tom
Published: July 2005

Chemometrics may be defined as the application of quantitative methods, and particularly multivariate methods, in chemistry. The methods include familiar ones such as principal components analysis and discriminant analysis, as well as less familiar ones such as partial least squares regression (PLS). Typical applications involve regression or discrimination problems with very large numbers of predictor variables.
Dilution Method for Bacterial Density Estimation
Authors: Gaines Das Rose E.
Published: July 2005

There are many methods for the measurement of bacterial mass and concentration. Different measures reflect different characteristics of the bacterial mass, and not all measures reflect the number of viable bacteria. If direct counting and characterization of individual bacterial cells is not possible or feasible, indirect methods must be used. Determination of the “most probable number” and serial dilution assays are indirect methods intended to reflect the number of viable bacteria.
Dose–Response Models in Risk Analysis
Authors: Gaylor David W.
Published: July 2005

Various biological insults, such as exposure to hazardous chemicals, pose a risk to human health. For various purposes, including attempting to set safe limits of exposure, it is useful to quantify the risk. Direct evidence from human exposure is seldom available and most substances are assessed through bioassays on animals. The form of the dose–response relation obtained from these studies is important, as extrapolation to doses lower than those used in the experiments is necessary to try to estimate risks at the doses encountered in human exposure. Various dose–response models are presented, including multistage and multimutation carcinogenesis models. Models for continuous data are also mentioned. Models for litters are discussed as these are important in reproduction and developmental studies.
Extrapolation, Low Dose
Authors: Gaylor David W.
Published: July 2005

While many substances are toxic to humans at high doses, naturally there is concern about the safety of long‐term exposure to much lower doses of certain materials. Such effects are difficult to observe directly and the usual approach is to expose animals to high doses of the substance, establish a dose–response relation, and use this to extrapolate much lower doses. The use of maximum likelihood to estimate extreme quantiles of the tolerance distribution is explained. Methods for measuring carcinogenic potency, such as the dose causing a tumor in 50% of animals, TD50, and the maximum tolerable dose (MTD) are introduced. For noncancer outcomes, the concepts of acceptable daily intake (ADI) and no observed adverse effect level (NOAEL) are also mentioned.
Immunotoxicology
Authors: Portier Christopher J. , Germolec Dori
Published: July 2005

Immunotoxicology is the study of the response of the immune system to toxicological insults, which are usually induced by xenobiotics. Experiments are carried out
in vitro
or
in vivo
. These can be
host resistance assays
, which concern the ability of the immune system to protect the host from infectious agents and so on or they can be
immune function assays
, which measure the response of the immune system to a stimulus. The former are largely analyzed using methods for categorical data, whereas the latter usually involve very large counts and these are generally analyzed using methods for continuous data. There is current interest in using immunotoxicity data in risk assessment.
Infectivity Titration
Authors: Armitage Peter
Published: July 2005

The virulence of a suspension of particles, typically viruses or bacteria, can be assayed by administering several dilutions of the suspension into host organisms and observing the number of hosts that become infected at each dilution. The usual analysis uses likelihood methods to estimate a parameter that depends on both the density of particles in the suspension and on the chance that each particle will cause an infection. In the simplest model, each particle acts independently of the others and each gives rise to an infection with the same probabilityp. In these circumstances, the probability that a host becomes infected can be found using the Poisson distribution. More elaborate models allowpto vary from host to host according to some distribution. Methods for detecting suchhost variabilityare available. Some discussion is given to the effects of failure of the assumption of independence.
Quality Control in Laboratory Medicine
Authors: Strike P. W.
Published: July 2005

An overview of the principles and practices of Quality Control (QC) in laboratory medicine, encompassing the origins of bias and variability in laboratory measurement, the regulation of same through internal (within‐lab) and external (between‐lab) QC programs, and concluding with an account of the strategies proposed for defining meaningful analytical goals in respect of the “quality” component of QC.
Mutagenicity Study
Authors: Piegorsch Walter W.
Published: July 2005

Biometric methods are discussed for analyzing data from bioassays of mutagenic response. Emphasis is placed on the classic microbial system in environmental mutagenesis: the Ames/Salmonellamicrosome assay. The assay produces count data to quantify the mutational response; statistical issues of interest when analyzing such data include testing for extra‐Poisson variability, trend testing for a dose response, and trend testing under a nonmonotone dose response.
Parallel‐Line Assay
Authors: Redmond Carol K.
Published: July 2005

Parallel‐line assays are the most common form of indirect analytical assays. The aim is to estimate the potency of substance under test relative to the potency of a standard. The test and standard preparations are administered at several dose levels. The key assumption is that the expected response for a given dose of the test preparation is the same as that which would be obtained from the standard preparation administered at a dose that is ρ times the given dose: ρ is known as the relative potency. It is further assumed that the expected response is linearly related to the logarithm of the dose. If this obtains, the graphs of expected response against log dose for the test and standard preparations will give parallel lines. The response can be continuous, in which case estimation is through a linear model, or quantal, in which case analysis usually assumes a logistic model. The estimator of ρ is defined in terms of ratios of regression coefficients and interval estimates are often obtained by use of Fieller's theorem.
Radioimmunoassay
Authors: Redmond Carol K.
Published: July 2005

Radioimmunoassays (RIA) use radioactive tracers to model biochemical reactions in which specific antigens bind to antibodies in the immune system. The radiation counts of bound labeled to free‐ligand labeled antigen (or antibody) at various fixed dose levels of antigen are utilized to estimate indirectly the unknown concentration of unlabeled antigen (or antibody) in the system. Statistical methods, analogous to those employed in standard quantal bioassay designs, are available to estimate the parameters of the models and the absolute or relative potency of the concentration of antigen (antibody) in the system and its associated confidence intervals.
Serial Dilution Assay
Authors: Ridout Martin
Published: July 2005

Serial dilution assays are used to estimate concentrations of bacteria in samples of food, water, soil, and so on. Key assumptions are that the bacteria are distributed randomly throughout the medium, and that the presence or absence of bacteria in subsamples can be ascertained reliably. The concentration of bacteria can then be estimated based on the presence or absence of bacteria in subsamples of different volumes. Essentially, the same method can be used to estimate the proportion of individuals in a population that have some characteristic, for example, in immunology, the proportion of cells that are immunocompetent. The term limiting dilution assay is often used for this type of application. This article considers point and interval estimation of concentration, including bias correction, tests of the underlying assumptions, and issues of experimental design for dilution assays.
Slope–Ratio Assay
Authors: Redmond Carol K.
Published: July 2005

Slope‐ratio assays are similar to parallel‐line assays insofar as both are indirect analytical assays, which aim to estimate the potency of a test preparation relative to that of a standard. Slope‐ratio assays are most often encountered in microbiologic applications. As with a parallel‐line assay, the key assumption is that the expected response to a given dose of the test preparation is the same as that which would be obtained from the standard preparation administered at a dose that is ρ times the given dose. As in parallel‐line assays, the parameter ρ is known as the relative potency. Unlike the parallel‐line assay, the expected response, which is almost always continuous, is linear in the dose, not its logarithm. The graphs of the response against dose for test and standard preparation will be straight lines of different slopes and common intercept, as the assumptions of the assay demand the same outcome for standard and test preparations when the dose is zero. The analysis can be accomplished by a multiple regression, with the estimator of ρ being the ratio of the slope estimators. Interval estimates are often obtained using Fieller's theorem.
Stereology
Authors: Marriott F. H. C.
Published: July 2005

Sampling methods used in stereology are briefly discussed. The fundamental formulae give estimates of volume ratios for the volume of a particular phase, the area of two‐dimensional structures, the length of linear features, and the number of particles. Some inference is also possible about curvature of surfaces. Estimation of the size distribution of spherical particles is described, and the extension to ellipsoidal particles, possible only in restricted cases, is discussed. The properties of tesselations, particularly the cell model and the Johnson–Mehl model for crystal growth, are described. Mathematical morphology, developed by Matheron and Serra as a system of transformations of digitized images, is a valuable technique for revealing relevant features, and stereological indices based on the modified images may be compared.
Up‐and‐Down Method
Authors: Gross Alan J. , McLean David C.
Published: July 2005

The Up‐and‐Down method is employed in dose–response studies where the aim is to model the probability of a binary outcome in terms of covariates, one of which is the dose being administered. The method allows for sequential choice of doses, dependent on the outcome of the previous dose. It is used in toxicology experiments in which the outcome is death: following a death, the next unit receives a lower dose, whereas a survival leads to the dose being increased.
Accident Proneness
Authors: Kemp Adrienne W. , Kemp C. D.
Published: July 2005

The entry reviews five competing models for the occurrence of accidents: (1) pure chance, (2) true contagion, (3) apparent contagion, (4) spells, and (5) liability. The distributions for accident count data that they yield (e.g. Poisson, negative binomial, Neyman type A, short, and generalized Waring) can, however, arise from more than one model. Model identification, in order to modify behavior and hence reduce the number of accidents, has proved largely ineffective. Since 1985, research has moved from model detection to risk evaluation and analysis.
Aging Models
Authors: Müller Hans‐Georg
Published: July 2005

Models for aging have come under intensive scrutiny in recent years due to increasing interest in aging, not least due to the ever‐increasing human lifespan. The methods used to model aging are largely similar to those in survival analysis, with unique features such as the use of lifetables and less prominence of incomplete data. An increasingly prominent role is played by event history analysis. Nonparametric, frailty, event history, and extreme value approaches are increasingly prominent due to the uncertainties regarding the shape of population hazard functions, which display remarkable plasticity across sexes, species, and environmental conditions. These newer approaches complement classical likelihood methods associated with the Gompertz and Gompertz–Makeham parametric models and are therefore the methods of choice in the emerging field of biodemography. Recent problems where aging models are relevant concern the influence of genetic variants and signaling pathways on mortality, the modeling of plateaus in the right tail of hazard functions, and the complex interplay between reproduction, diet, and mortality.
Back‐Calculation
Authors: Bacchetti Peter
Published: July 2005

Back‐calculation estimates past infection rates of an epidemic disease by working backward from observed incidence. This requires: external knowledge about the distribution of incubation times between infection and disease, possibly including how it is changing over time; incidence data that have been adjusted for reporting delay, underreporting, and possibly seasonal effects; and a parametric model or smoothness assumption that imposes some structure on past infection rates. In the case of human immunodeficiency virus, sensitivity analyses have found that uncertainty in back‐calculation is mainly due to uncertainty in these inputs. Projected incidence is obtained by applying the assumed incubation distribution to the estimated (and extrapolated) infection rates, but direct extrapolation of observed incidence may do as well or better in some circumstances.
Bacterial Growth, Division, and Mutation
Authors: Gusev Y. , Armitage Peter
Published: July 2005

Models of cell growth and division in bacteria were considered more than 60 years ago. The evolution of models of bacterial growth was closely followed by the development of models of the cell cycle in budding and fission yeast, cell cultures, and mammalian cells. In some of these theoretical models, new mechanisms have been hypothesized, which later have been confirmed in experiments on spontaneous and induced mutations, signal transduction pathways, cell cycle regulation, and programmed cell death. Thus, for many years, modeling of the bacterial cell cycle has been a “proving ground” for refinement of theoretical models in cell biology. The major questions addressed in bacterial growth models have included: stochastic and deterministic models of cell population dynamics; different models of the cell cycle in individual cells, such as growth control, random transition, and mitotic clocks; generational dependence models; unequal cell‐division models; spontaneous mutation models and fluctuation tests.
Branching Processes
Authors: Jagers Peter
Published: July 2005

Branching processes are stochastic population models based on explicit descriptions of individual life and reproduction. The basic assumption is that individuals live and multiply independently. This can, however, be relaxed. Individuals may be of various types and have varying life spans. In the simple branching processes, there is only one type of individual and life span is determistic (one year or season) or exponentially distributed, yielding Markov processes, and as simple special cases, birth‐and‐death processes. But more general branching processes allow complex reproduction patterns as well as arbitrary life distributions.

The main results are that no finite population can persist forever. It either dies out or it grows, usually at the exponential rate postulated by Euler and Malthus. However, recent results show that if population size can influence individual reproduction, other growth modes, like linear, can also occur. In exponential growth, the age‐distribution, and population composition generally, stabilize.
Brownian Motion and Diffusion Processes
Authors: Chiang Chin Long
Published: July 2005

A brief review of the one‐dimensional Brownian motion in terms of three perspectives. (1) As the limiting case of a random walk, the total displacement has a normal distribution. (2) The mathematical model leads to a partial differential equation, which is known as Fokker–Planck diffusion equation. And (3) as a stochastic process, both the time element and the displacement are continuous variables. The solution of the partial differential equation for the transition density function also has the normal distribution. Wiener–Levy process is a special case.

The Ornstein–Uhlenbeck process, which describes the velocity of the movement of a particle in a Brownian motion is also mentioned.
Cell Cycle Models
Authors: Obeyesekere Mandri N.
Published: July 2005

The models for cell cycle regulation and cell cycle analysis are discussed as microscopic or macroscopic models.
Chain Binomial Model
Authors: Longini Ira M.
Published: July 2005

The chain binomial model arises from chains of binomial probability mass functions, where each function is conditioned on previous function. Products of these probability mass functions give the probabilities of particular sequences of binomial realizations. This chain structure allows for detailed analysis of physical phenomena that can be represented by chain binomials. The simple chain structure allows for statistical inference based on likelihood theory.

The chain binomial model forms the statistical underpinnings of the life table. In addition, the chain binomial model has been important in the analysis of infectious disease spread in small groups such as households. For example, the Reed–Frost model is a chain binomial model where the number of new infectives at some time
t
depends on the number of infectives and susceptibles at time
t
 − 1. This model has been used to estimate epidemiological parameters for the spread of such diseases as measles, smallpox, and influenza.
Chronic Disease Models
Authors: Manton Kenneth G.
Published: July 2005

We discuss the need for multidimensional stochastic models of physiological processes to describe the evolving risk of chronic disease over a lifetime. Modifications of that type of model needed to describe different types of risk factor and health effects collected in different longitudinal studies are described. How health processes are “captured” in different longitudinal study designs is discussed, as is the description of the intra‐individual dynamics of degenerative processes. The concept of hormesis is introduced as are more standard types of hazard models (Weibull and Gompertz) drawn from reliability theory. Measurements that may be made in molecular epidemiological studies are discussed and issues that they raise for statistical modeling of disease processes reviewed. Methods for analyzing the genetic contributions to chronic disease risks are presented and discussed.
Clinical Signals
Authors: Campbell Michael J.
Published: July 2005

Clinical signals are obtained when human activity is monitored, usually electronically. Typical examples are brain activity via the EEG, and heart activity from the ECG. Other signals include blood pressure and measures of lung function. The signals can be sampled at short time intervals, such as 0.1 s for measuring autonomic function, or a longer periods such as every 2 hrs for measuring circadian activity. Techniques of analysis include spectral analysis, and time‐varying spectral analysis. Examples are given for heart rate and blood pressure variability, the EEG, and human luteinizing hormone levels.
Epidemic Curve
Authors: Rosenberg Philip S.
Published: July 2005

An epidemic curve is a plot of time trends in the occurrence of a disease or other health‐related event for a defined population and time period. The event rate that is plotted may measure the number of cases per unit time, or it may express the numbers of events relative to the number in the study population (incidence rates). In infectious disease epidemiology, the epidemic curve is used to document the scope and duration of an epidemic, to help determine the source of the infection and the modes of transmission or exposure, and to glean information about the incubation period of the disease. In other settings, including behavioral and chronic disease epidemiology, epidemic curves are used to document the scope of public health problems.
Epidemic Models, Control
Authors: Clancy Damian
Published: July 2005

Two approaches are considered in relation to classic deterministic and stochastic epidemic models: to reduce the basic reproduction ratio below unity; or to define costs of intervention and infection and choose the optimal intervention policy.
Epidemic Models, Deterministic
Authors: Heesterbeek J. A. P. , Roberts M. G.
Published: July 2005

In this article, we briefly review some of the approaches to deterministic modeling of epidemic phenomena. We have chosen to structure the approaches by specific biological examples that exemplify a certain approach and that were, in addition, historically important in shaping the development of the deterministic theory. These examples are measles, malaria, helminth infections, and HIV. For types of models, we briefly discuss ODE models and PDE age‐structured models of compartmental SIR‐type (both for microparasitic agents), ODE models for helminth parasites, formulated in terms of average parasite load, and the more general microparasite models in terms of integro‐differential equations. In the latter, there is flexibility in defining the infectivity of individuals as a function of infection‐age, which does not exist in the compartmental models. We also discuss the way to calculate the basic reproduction ratioR0for each class of models.
Epidemic Models, Inference
Authors: Britton Tom
Published: July 2005

This article reviews inference procedures for the general epidemic model assuming a homogeneous community, and for a model for a community partitioned into households. The data may be complete, with the epidemic observed continuously, or may record only the final epidemic size. Methods for estimation of the contact rate, recovery rate, and reproduction number are described, using maximum likelihood, Martingale theory, and Markov chain Monte Carlo.
Epidemic Models, Recurrent
Authors: Nåsell Ingemar
Published: July 2005

Deterministic and Stochastic epidemic models are described and various aspects of long‐term behavior are contrasted. The threshold predicted by the deterministic model is a poor approximation to the stochastic analogue. Damped oscillations given by the deterministic model are seen when stochastic models are averaged over realizations, but not for individual realizations. Extinction is seen only in stochastic models, with a probability dependent on population size.
Epidemic Models, Spatial
Authors: Renshaw Eric
Published: July 2005

For a proper understanding of the dispersal and control of infectious diseases, it is often necessary to consider spatial models in which individuals do not mix homogeneously. A birth, death, and migration/infection process for separate colonies, with migration/infection to nearest neighboring colonies, is considered from both deterministic and stochastic viewpoint. Topics covered include Monte Carlo simulation and threshold levels, with particular reference to the transmission of HIV/AIDS and rabies.
Epidemic Models, Stochastic
Authors: Gani J.
Published: July 2005

This article describes the most commonly used stochastic epidemic models. For discrete time, the Greenwood and Reed–Frost chain binomials are outlined, with examples. In continuous time, the simple SI, the general SIR and the carrier‐borne CSR models are discussed, and Whittle's Threshold Theorem stated. The article concludes with some references to recent literature.
Epidemic Models, Structured Population
Authors: O'Neill P. D.
Published: July 2005

Real‐life epidemics invariably occur within populations composed of individuals who do not mix with each other entirely at random. Instead, there is frequently a nonhomogeneous mixing structure, so that individuals are more likely to spend time with those they live or work with, or who are geographically close, for example. Here we review a number of stochastic epidemic models, which attempt to incorporate population structure, providing descriptions of the models and highlighting associated results of interest. Aspects of related statistical inference are also considered. Such models offer a more realistic alternative to those that assume homogeneous mixing of either the entire population, or large subpopulations.
Image Analysis and Tomography
Authors: Glasbey C. A. , Berman M. , Hudson H. M.
Published: July 2005

Image analysis is the use of computers to extract quantitative information from images, such as those that arise from microscopes, medical scanners, electrophoresis gels, and illuminated objects. We give examples of such images, an overview of the different types of digital image, and the eclectic collection of methodologies that have been proposed to analyse them. We then consider the tomographic reconstruction of images from projections, and the three major components of image analysis: enhancement, segmentation, and taking measurements. We illustrate the methods using the examples.
Infectious Disease Models
Authors: Becker Niels G.
Published: July 2005

Infectious disease models are used to gain insights into strategies for the control of infectious diseases. Stochastic versions are also used in the analysis of infectious disease data, where they help to focus the analysis on epidemiologically meaningful parameters, take care of dependence in the data, and compensate for the fact that only part of the infection process is observable. Different characteristics of disease transmission and progression have promoted a variety of models, including transmission chain models that keep track of infected individuals in “generations” and models that monitor the transmission dynamics continuously over time. Models formulated to describe outbreaks in households are particularly useful, because households are a convenient unit for empirical studies.
Ion Channel Modeling
Authors: Hawkes Alan G.
Published: July 2005

Electrical activity in the nervous system is regulated by the passage of minute electrical currents due to charged ions passing though ion channels in cell membranes. Studying them increases our understanding of normal physiology and the effect of drugs and toxins.

Stochastic modeling of ion channel mechanisms is needed to infer the nature of the mechanism from observation of ionic currents, and to estimate the parameters involved. The models are Markov or semi‐Markov processes where, typically, states are aggregated into groups with the same conductance level because we can see what level it is at, not what state it is in.

Many distributions can be obtained, such as open times or shut times, and the likelihood can be calculated for a record of sojourns at the various levels that are first extracted from observational noise. Hidden Markov methods have also been applied.
Migration Processes
Authors: Chiang Chin Long , Ball Frank
Published: July 2005

A migration process describes the temporal evolution of a population of individuals who reside in colonies. There is both immigration and emigration, and also migration between colonies. However, there is no reproduction in the population. In the models described in this article, individuals behave independently according to continuous time Markov processes. A single colony model is treated in some detail and the distribution of population size at any given time is derived. Extension to a population comprising
m
 > 1 colonies is described. The single colony model is used to motivate a survival model for an individual who is continuously exposed to a low level of toxic material.
Multistage Carcinogenesis Models
Authors: Sherman Claire D. , Portier Christopher J.
Published: July 2005

Biologically‐based mathematical models of carcinogenesis have been used for quantifying cancer risks for approximately fifty years. These models are developed to understand the mechanisms of carcinogenesis as well as to determine reasonable margins of safety for exposure to carcinogens. It is important to capture the biological aspects of carcinogenesis within the framework of the mathematical model to help provide a better understanding of the carcinogenesis process. In addition, it is important to have an accurate model when extrapolating to exposures (doses) observed in the human population since predictions from these models may vary dramatically.
Partner Study
Authors: Shiboski S. C.
Published: July 2005

Partner studies are epidemiologic investigations of transmission of infectious diseases in susceptible partners of known infected individuals. Widely used for studying transmission of sexually transmitted diseases (STD) such as Human Immunodeficiency Virus (HIV), these studies are applicable in situations where “partnerships” which link known susceptible and infectious individuals can be identified. Eligibility typically requires that exposure to infection in susceptible individuals is limited to a previously infected partner. This allows potential bias associated with uncertainty about the source of infection to be reduced or eliminated. Partner studies focus primarily on the influence of measured covariates on the probability of transmission, but can also be used to gain knowledge of key parameters such as the infectivity (transmission risk per unit of exposure). Statistical analyses of data from these studies provide a number of unique challenges, most of which arise from the incomplete nature of data describing exposure and infection.
Poisson Processes
Authors: Kingman J.F.C.
Published: July 2005

Poisson processes are a class of models for random sets of points in one or more dimensions. They are characterized by a Poisson distribution for the number of points in any set, and by independence of the counts in nonoverlapping sets.
Renewal Processes
Authors: Chiang Chin Long , Ball Frank
Published: July 2005

Renewal theory is concerned with a sequence of events in which the waiting times between successive events (known as renewal times) are independent and identically distributed. This article provides a brief introduction to the properties of renewal processes, such as the time until thenth renewal and the number of renewals by timet, treating the cases of discrete and continuous renewal time distributions separately. In the latter case, the limiting distributions asof the backward and forward recurrence times at timet(i.e. the time since the previous renewal and the time until the next renewal) are considered. Delayed, equilibrium and alternating renewal processes are also described briefly, as are renewal reward processes. The theory is illustrated by a few examples.
Epidemic Models, Sensitivity Analysis
Authors: Cairns Andrew J. G.
Published: July 2005

In this article, we consider how one can analyze the sensitivity of epidemic models to changes in the various inputs. We start by discussing the different reasons for conducting a sensitivity analysis. The article then proceeds by discussing the different methods of sensitivity analysis that can be employed.

One of our main concerns is to assess which parameters have a significant impact on epidemic dynamics and which do not. However, when we consider relatively complex models, we find that the impact of changes in one parameter can be almost cancelled out by a corresponding change one or more other parameters (e.g. by keeping the reproduction number,R0, fixed). This concept introduces the concept of primary component analysis. The aim here is to identify the small number of components of a model (such asR0) that are the key determinants of epidemic dynamics with the remaining parameters having a relatively small impact.