bluuebunny/crossref_metadata_2025 huggingface dataset:
Financial Reinsurance
Authors: Halliwell Leigh J.
Published: September 2014

The article presents ‘financial reinsurance’ as a continuum between finance and reinsurance. It discusses features of finance and reinsurance, illustrates simple combinations of the two, and describes basic financial‐reinsurance contracts. It concludes with the benefits and dangers of financial reinsurance, its accounting treatment, and the need to define risk transfer.
Largest Claims and
ECOMOR
Reinsurance
Authors: Beirlant Jan
Published: September 2014

There exist a few intuitive and theoretically interesting reinsurance contracts that are akin to excess‐of‐loss treaties, but refer to the larger claims in a portfolio. An unlimited excess‐of‐loss contract cuts off each claim at a fixed, nonrandom retention. A variant of this principle is ECOMOR reinsurance where the priority is put at the (
r
 + 1)th largest claim so that the reinsurer pays that part of the
r
largest claims that exceed the (
r
 + 1)th largest claim. Compared to unlimited excess‐of‐loss reinsurance, ECOMOR reinsurance has an advantage that gives the reinsurer protection against unexpected claims inflation if the claim amounts increase, then the priority will also increase. A related and slightly simpler reinsurance form is largest claims reinsurance that covers the
r
largest claims but without a priority.

The article highlights some of the theoretical results that can be obtained for the case where the total volume in the portfolio is large. In spite of their conceptual appeal, largest claims type reinsurance are rarely applied in practice. The discussion hints at some of the possible reasons for this lack of popularity.
P
areto Rating
Authors: Mata Ana J.
Published: September 2014

The Pareto family of distributions is widely used in insurance and reinsurance practice to model the individual claim cost in an insurance portfolio. One of the practical advantages of the Pareto‐type distributions is that it extrapolates better beyond the observed data, and therefore it is more appropriate when rating high excess layer.
Stop‐Loss Reinsurance
Authors: Rytgaard Mette M.
Published: September 2014

Stop loss is a nonproportional type of reinsurance protecting the annual result of the ceding company. Stop loss is, under certain conditions, the optimal form of reinsurance for the ceding company but not optimal to the reinsurer. Considerations to be made by the reinsurer before accepting stop‐loss covers are listed. An overview of various classes of methods to price reinsurance is given.
Surplus Treaty
Authors: Mata Ana J.
Published: September 2014

Surplus treaty is a type of proportional reinsurance in which the percentage ceded to the reinsurer varies by original policy limit in order to keep the maximum loss amount retained by the ceding company fixed. The surplus treaty provides the ceding company greater capacity to write higher limits and to reduce fluctuations in its financial results.
B
liss,
C
hester
I
ttner
Authors: Holford Theodore R. , White C.
Published: September 2014

Born in 1899 in Springfield, OH; died in 1979. Bliss is best known for work on probit (probability integral transformation) analysis, much of it in collaboration with R.A. Fisher, and also for playing a major role in founding the International Biometric Society.
B
radley,
R
alph
A
Authors: Billard Lynne
Published: September 2014

Ralph Bradley's contributions to the world of statistics fall under two headings: his statistical research (especially the Bradley–Terry test used extensively in taste‐testing experiments) and his professional leadership role in statistical science, as evidenced by his development of statistical programs, by his presidency (1981) of the American Statistical Association, and by his editorial efforts.
C
halmers,
T
homas
C
lark
Authors: Wright E.
Published: September 2014

Born in 1917 in Forest Hills, NY; died in 1995 in Hanover, NH. Chalmers was a leader in the design, conduct, and evaluation of clinical trials, favoring randomized controlled trials in all areas of medicine, with independent policy advisory committees. He helped found the Society for Clinical Trials.
Galton,Francis
Authors: F. Edwards A. W.
Published: September 2014

Born 1822; died 1911. Galton was the founder of biometry, and the origins of many statistical methods can be seen in his pioneering efforts, for example branching processes, the normal probability distribution, and regression. He was particularly interested in heredity, and wrote also on eugenics.
G
reenwood,
M
ajor
Authors: Wilkinson Lise
Published: September 2014

Major Greenwood is known principally for the important role he played in the development of biostatistics during the first half of the twentieth century, both as an epidemiologist and as a pioneer medical statistician. Having qualified in medicine in 1904, he turned to medical research rather than practice, influenced by the work of the physiologist (Sir) Leonard Hill and by Karl Pearson's teaching of biological statistics at University College London. From then on, he developed the methodology of medical statistics to make it ultimately acceptable to an initially reluctant medical profession, adding good clinical judgment to Pearson's rigorous mathematics. A few weeks before his sudden death in London during a meeting on cancer research, he argued the case for the Voluntary Euthanasia Society in a debate broadcast by the BBC.
Kolmogorov, Andrey Nikolayevich
Authors: Suhov Yurii
Published: September 2014

Kolmogorov (1903–1987), who worked in the Moscow State University, was one of the greatest mathematicians of the twentieth century. In probability theory, which was merely one of his fields of study, he introduced axioms and clarified various basic concepts. In statistics, he introduced the Kolmogorov–Smirnov statistic for testing goodness of fit, and worked on problems in estimation theory. His work in population genetics involved stochastic processes.
L
ancaster,
H
enry
O
liver
Authors: Armitage Peter
Published: September 2014

Oliver Lancaster (1913–2001) was a distinguished Australian medical statistician. He was unique in having held university chairs in both medical and mathematical statistics, in making important contributions to the history of quantitative medicine, and in his pioneering work in the bibliography of statistics.
M
ahalanobis,
P
rasanta
C
handra
Authors: Ghosh J. K. , Majumder Partha P.
Published: September 2014

Mahalanobis (1893–1972) became involved with the analysis of anthropologic data in the 1920s and developed his measure of generalized distance in 1930. In the Indian Statistical Institute, he made important theoretical and practical contributions to sample surveys and became Chairman of the United Nations Sub‐Commission on Statistical Sampling.
M
oran,
P
atrick
A
lfred
P
ierce
Authors: Wilson Susan R.
Published: September 2014

Pat Moran was an Australian statistical scientist with an enormous breadth and depth to his research interests. During his prolific career, Moran made substantial contributions to population genetics, medical statistics (particularly psychiatry), geometric probability, mathematical statistics, time series, and applied probability. He received numerous scientific honors, and now is commemorated by two Australian awards for young research statisticians.
Pearson,Karl: His Life and Contribution to Statistics
Authors: Magnello M. E.
Published: September 2014

Karl Pearson (1857–1936) was the founder of biometrics andBiometrikaand a principal architect of the mathematical theory of statistics. He was a polymath, with a wide interest in intellectual and social pursuits, and first taught applied mathematics at University College London. He started to teach statistics and to develop new methods during the 1890s. He developed measures of correlation and discovered the chi‐ square distribution and used it for tests of goodness of fit and association in contingency tables. He established and ran four laboratories and established the first degree course in mathematical statistics in Britain. He worked closely with Galton and Weldon, and eugenics and heredity remained central interests throughout his life.
Bayesian Methods for Contingency Tables
Authors: Albert James H.
Published: September 2014

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.
Binary Data
Authors: Collett D.
Published: September 2014

When a response variable can take one of two possible forms, such as alive or dead, the resulting data are said to be binary. The focus of this article is on models for binary response variables, and the use of logistic regression models is emphasized. The models can be fitted using most statistical software packages. Alternative models can be compared using the deviance, and for grouped binary data, this statistic may be used as a measure of goodness offit. Techniques for assessing model adequacy are outlined and the use of these methods is illustrated with an example.
Capture–Recapture
Authors: Chao Anne
Published: September 2014

Capture–recapture methods are used to estimate population sizes and related parameters such as survival rates, birth rates, and migration rates. A typical capture–recapture experiment places traps in the study area and samples the population several times. At each trapping sample, one records and attaches a unique tag to every unmarked animal, records the capture of any animal that has been previously tagged, and returns all animals to the population. This article describes the history of the method, discusses applications to epidemiology, discusses potential models, and discusses the challenges inherent in estimating the population size well.
Contagious Distributions
Authors: Kemp Adrienne W. , Kemp C. D.
Published: September 2014

Polya proposed a model for the spread of an infection, whereby the probability of catching a disease depended on the existing number of cases. This leads to a distribution that has a limiting negative binomial form. Neyman proposed an alternative approach that arises from a Poisson distribution of clumps, with the number of cells for each clump being Poisson. This article surveys probability distributions and corresponding generating functions that result from such constructions.
Correlated Binary Data
Authors: Pendergast Jane F. , Gange Stephen J. , Lindstrom Mary J.
Published: September 2014

Correlated binary data may arise in longitudinal or spatial studies or through some other form of clustering of sampling units. The simplest setting, with clusters of size two and no covariates, leads to familiar methods of analysis. Models with covariates include response feature models, conditionally specified models, transitional models, marginal models, and cluster‐specific models. These may lead to different interpretations of the regression parameters.
Hypergeometric Distribution: Introduction
Authors: Shuster Jonathan J.
Published: September 2014

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.
Polytomous Data
Authors: Tutz Gerhard
Published: September 2014

The article describes regression models for categorical responses, distinguishing between nominal, ordinal, and nested response categories. Basic concepts of estimation, testing, and goodness‐of‐fit statistics are given.
Spatial Models for Categorical Data
Authors: Waller Lance A.
Published: September 2014

After reviewing characteristics of spatially correlated counts, rates, and proportions that compromise traditional methods of inference, we briefly survey general approaches for the analysis of such spatially referenced categorical data. The survey focuses on auto‐models, generalized linear models, and generalized linear mixed models, emphasizing structural and conceptual aspects rather than computational details.
Beta‐Binomial Distribution
Authors: Rosner Bernard
Published: September 2014

The beta‐binomial distribution results from a beta distribution mixture of binomials. It is useful for clustered binary data, for which the ordinary binomial distribution is usually inappropriate because different observations are correlated rather than independent. Models using this distribution permit the mean to depend on explanatory variables. An implicit assumption of the distribution is that subunits are exchangeable within a cluster. Generalizations of it allow for data structures with multiple levels of nesting.
Multivariate Methods for Binary Longitudinal Data
Authors: Glynn Robert J. , Rosner Bernard
Published: September 2014

Longitudinal data in which the repeatedly measured response variable is binary often occur in medical investigations, particularly clinical trials. This article describes a number of suitable approaches to modeling such data including marginal models, mixed effects models, and transition models.
Chi‐Square Distribution Properties
Authors: Klotz Jerome
Published: September 2014

This article complements the introductory article on the chi‐square distribution, with details of its derivation as the distribution of the sum of squares of standard normal deviates, the density being a gamma function, and the relationship between its distribution function and that of the Poisson distribution. When the component normal distributions have nonzero mean, the sum of squares has a noncentral chi‐square distribution, depending on a noncentrality parameter, the sum of squares of the normal means. This plays a role in determining the power of a chi‐square test.
Normal Values of Biological Characteristics
Authors: Harris Eugene K.
Published: September 2014

This entry focuses on clinical biochemistry and hematology measurements, this being the area where most progress has been made in the estimation of normal values. Other examples are noted in passing. Parametric and nonparametric methods to estimate normal ranges are described, together with the identification and treatment of outlying observations. Calculation of normal ranges for population subgroups is discussed. There is a brief review of the establishment of time‐dependent normal values, and estimation of multivariate normal indexes or regions for correlated clinical variables.
Time Trade‐Off Technique
Authors: Gafni Amiram
Published: September 2014

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.
Cost–Benefit Analysis, Willingness to Pay
Authors: O'Brien Bernie
Published: September 2014

Cost–Benefit Analysis (CBA) is a technique of economic evaluation, where the benefits of programs are valued in monetary terms to permit direct comparison with program costs. There are a number of measurement and statistical challenges that arise while attempting to assign money values to health program benefits such as reduction in the risks of morbidity and mortality. The basic measurement goal is to quantify the trade‐offs that consumers are willing to make between reduced health risk and money. Specifically, to identify the maximum willingness to pay (WTP) for health benefits. In this chapter, we review several approaches to both market‐based “revealed preference” and survey‐based “stated preference” WTP estimation. A prevalent method developed in environmental economics is to ask respondents to accept/reject questions for increasingly higher monetary amounts (“bids”) and then to use survival‐type methods to estimate a bid curve, with covariates, that can be used to solve mean or median WTP.
Blinding or Masking
Authors: Day Simon J.
Published: September 2014

The need for blinding in clinical trials and epidemiological studies is reviewed and its importance stressed. Various reasons for blinding include the potential for patient bias, bias in patient management and evaluation, bias in data management and study management. Blinding and unblinding interim analyses need special attention, and procedures for emergency unblinding need to be available.

Four levels of blinding are described from the slightly ambiguous term “single‐blind” through to quadruple‐blinding. Methods to maintain the blind at various stages such as use of placebos, “double‐dummy” designs, and sham procedures are discussed.

Finally, some of the difficulties of blinding are highlighted. Often, it may be ineffective and reporting of the achieved quality of blinding is recommended. There are special issues with regard to equivalence studies, and regulatory guidance exists discussing many issues included in this article.
Clinical Significance versus Statistical Significance
Authors: Friedman Lawrence M.
Published: September 2014

Clinical significance (medical importance) and statistical significance (whether or not the value of a statistical test exceeds some prespecified level) are contrasted. Factors that affect the interpretation of these, such as sample size, outcome measure, and level of risk, are discussed, as are situations where one, but not the other, may exist.
Data and Safety Monitoring
Authors: O'Brien Peter C.
Published: September 2014

We consider the role of a Data and Safety Monitoring Board (DSMB) in overseeing the conduct of a randomized clinical trial. This includes insuring both the scientific integrity of the study and patient safety, monitoring the occurrence of adverse events and assessing efficacy. Formal stopping rules are particularly useful in clinical trials for monitoring efficacy, with a view towards terminating the trial early if the evidence for or against efficacy becomes overwhelming prior to the scheduled completion of the trial. The most commonly used approaches in formal stopping rules are discussed in some detail. These include the Pocock and O'Brien–Fleming boundaries and the spending function approach developed by Lan and DeMets. Discussion of stochastic curtailment, point and interval estimation associated with early termination, multiple endpoints, and a brief overview of decision theoretic methods (including Bayesian methods) is provided.
Data Monitoring Committees
Authors: Demets David L.
Published: September 2014

Randomized clinical trials are the standard by which new interventions are evaluated for benefit or harm. Federal guidelines in the United States now recommend that all trials have a monitoring plan for early evidence of harm. For trials that have serious irreversible outcomes such as death, heart attack, stroke, or cancer recurrence, an external independent committee called a Data Monitoring Committee (DMCs) is recommended to evaluate the accumulating interim data. Trials for which interim data are convincing for benefit or harm may be terminated early. DMCs began in the early 1970s by trials sponsored by the National Institutes of Health and more recently by the pharmaceutical industry. DMCs review not only the primary outcome data and the serious adverse events but also the recruitment progress, patient compliance to the intervention, other secondary outcome variables, and high risk subgroups of patients if such exist. Because of the complexity of such monitoring, DMCs have a composition with biological, clinical, and biostatistical expertise.
Guidelines On Statistical Methods in Clinical Trials
Authors: Facey Karen M. , Lewis John A.
Published: September 2014

This article provides an overview of the International Conference on Harmonization (ICH) and its work in producing regulatory guidelines that are of interest to medical statisticians. The scope and key issues of the ICH E9 Guideline on Statistical Principles in Clinical Trials are outlined. This includes topics related to minimizing the bias in trial design, analysis and reporting, and includes specific issues such as multicenter trials, interim analysis, analysis sets, and subgroups. Other regulatory guidelines that include statistical issues are mentioned and the manner in which guidelines should be used is debated.
Medical Devices
Authors: Campbell Gregory , Irony Telba Z. , Lao Chang S. , Li Heng , Pennello Gene , Vishnuvajjala R. Lakshmi , Yue Lilly Q.
Published: September 2014

A medical device is any item that treats or diagnoses a health condition but whose action is primarily not chemical or biological. The main focus concerns the evaluation of clinical studies to establish the safety and effectiveness of different kinds of medical devices. The design and analysis of medical device studies pose unique statistical challenges. Both nondiagnostic and diagnostic devices are considered. Nondiagnostic devices include therapeutic ones and implants, among others. Statistical issues for these kinds of devices include the placebo effect, sham controls, inability to perform blinded studies, noninferiority, survival analysis, repeated measures, and historical controls. Diagnostic devices pose a very diverse set of challenges, with markedly different design and analysis considerations. Special attention is devoted here to microarrays in particular. Bayesian approaches to medical device studies are discussed.
Missing Data in Clinical Trials
Authors: Murray Gordon D.
Published: September 2014

Missing data is an almost universal problem in clinical trials, and substantial bias can arise if the statistical analysis does not take proper account of the issue. The article reviews the different mechanisms that can lead to missing data, and describes appropriate approaches to the statistical analysis. As in so many aspects of clinical trials, the correct approach depends crucially on what question is being asked, and, in particular, whether the trial design is explanatory or pragmatic.
Multicenter Trials: Rationale and Examples
Authors: Bryant John , Cronin Walter , Wieand Sam
Published: September 2014

The chapter deals with multicenter clinical trials, which are defined as studies involving two or more field sites conducted according to a common protocol that uses a single data coordinating center to receive, process, and analyze study data. Several examples are provided. Organizational, structural, and analytic aspects of trials, and guidelines for the conduct of such studies are discussed.
Quality of Life
Authors: Fairclough Diane L. , Ganz Patricia A.
Published: September 2014

In the health sciences, assessment of quality of life and other patient‐reported outcomes are now an integral component of patient‐focused research. Health‐related quality of life (HRQoL) is a multidimensional construct that assesses the extent to which one's usual or expected physical, emotional, and social well‐being are impacted by a medical condition or its treatment. HRQoL may be assessed using generic or disease‐specific instruments. These instruments consist of a set of questions, method of administration, instructions for administration, method of scoring and analysis, and interpretation. Validation of these instruments includes assessment of content validity, internal consistency, test–retest reliability, and discriminant and predictive validity. Some of the statistical issues that arise in the analysis of studies with HRQoL assessments are multiple endpoints, missing data (informative dropout), and interpretation (statistical versus clinical significance).
Sample Size Determination in Clinical Trails Including Adjustments for Noncompliance, Loss to Follow‐Up and Groups Sequential Analysis
Authors: Lakatos E.
Published: September 2014

Conceptual issues in sample size calculation for clinical trials are discussed. Each parameter and related issues are highlighted: type I and II errors and the balance between them, one versus two‐sided testing, the smallest clinically meaningful difference versus the anticipated treatment effect, endpoint selection, multiple comparisons, missing data, unequal allocation, repeated measures, equivalence, and group sequential trials. For survival trials, conceptual issues are discussed in further detail, including the binomial versus log rank statistic, exponential versus proportional and nonproportional hazards, and adjustment for treatment lag, staggered entry, noncompliance, drop‐in, loss‐to‐follow‐up and competing risks, and duration of treatment effect.
Time‐Varying Treatment Effect
Authors: Lavori Philip W. , Dawson Ree
Published: September 2014

This entry is concerned with assessing the effect of treatments that vary in time on the outcomes for individual patients. For example, levels of compliance with therapy may vary over time among participants in a clinical trial. Assessment of treatment effects in this situation is complicated by the fact that the relevant comparison may not be between randomized groups of patients. The so‐called “ignorability of treatment” condition is discussed, relating to the requirement that treatment actually received should be independent of potential patient responses to treatment. Other issues relating to the observational comparisons in medicine and adjustment for confounders are reviewed, together with a brief mention of recent developments in structural equation modeling of treatment effects in this context.
Vaccine Studies
Authors: Halloran M. Elizabeth
Published: September 2014

This entry begins with a brief overview of the biological background for vaccine action, and then describes the various phases of vaccine development, including early phases of identification of candidate vaccines, establishment of safety and immunogenicity in animals, safety and immunogenicity in humans, field efficacy trials, and post licensure studies. Measures of vaccine efficacy are described, and certain potential study biases are identified.
Interim Analysis of Censored Data
Authors: Tsiatis A. A.
Published: September 2014

Many clinical trials of chronic diseases are monitored periodically and interim analyses are performed, both for reasons of “safety”, that is, to monitor possible side effects, and to avoid continuing a trial from which no more convincing evidence can be expected. The adequate handling of this monitoring requires close collaboration between the Data and Safety Monitoring Committee and statistical expertise.

Statistical methods have been developed for respecting basic rules of hypothesis testing when multiple views are involved. Usually some form ofgrouped sequentialapproach fits best to the practical situation. A complication is that often the entry of study subjects isstaggeredover time, so that time on trial does not correspond to calendar time.
Sample Size Determination: Overview
Authors: Lachin John M.
Published: September 2014

This concerns the evaluation of sample size required for a study before data are collected. This may be done by specifying either the required precision of an estimate, or the power of a test to detect an effect regarded as important. It may be necessary to consider the effects of missing data and of measurement unreliability. Many examples are considered in detail.
Medical Ethics and Statistics
Authors: Hutton J. L.
Published: September 2014

Ethical choice and behavior in health care practice and research require an understanding of uncertainty and the contribution that can be made by statistical methods. Various criteria for judging what is “best” are discussed in relation to routine medical practice, the perception of “normality”, screening for disease, epidemiologic research, and the communication of uncertainty. Attention is given to the ethics of medical research in developing countries, informed and uninformed consent, and cluster randomized trials. Guidelines provided by various national and international organizations are described.
Medical Research Council Streptomycin Trial
Authors: Sutherland I.
Published: September 2014

This is an outstanding early example of a rigorously planned clinical trial with concurrent controls. Only a limited supply of the drug was available. Patients with acute bilateral pulmonary tuberculosis were allocated by a random process to treatment either with bed rest alone or to streptomycin plus bed rest, and precautions were taken to avoid bias in their management and assessment. The streptomycin patients showed early radiologic improvement compared with the controls, but resistant strains of the bacilli emerged rapidly and there was much vestibular toxicity.

The trial provided an explicit model for subsequent tuberculosis research and, more importantly, served as a catalyst for the scientific investigation of other treatments and interventions throughout clinical and preventive medicine. The introduction in this trial of an allocation scheme based on random sequences represents the most important single advance in the evolution of the clinical trial in the twentieth century.
Pharmaceutical Industry, Statistics in: Including Two Examples
Authors: Senn Stephen
Published: September 2014

The role of the statistician is traced from early, basic research through the various stages of drug development leading to phase III clinical trials and phase IV postmarketing surveillance. Specific areas of activity, and statistical topics of particular interest, are listed. Examples are taken from the development of drug for treating asthma, and work on project prioritization. Future trends will be affected by financial constraints, by a need to specialize that may lead to work being done by contract research organizations, by the need for speed, and by the need for marketing to be more “evidence‐based”.
Algorithm ‐ Some Theory
Authors: Maindonald John H.
Published: September 2014

The term algorithm is generally used to describe a series of logical steps that, when implemented within a computer program, will perform a desired computational task. The task must be defined precisely. Issues that are generally important in finding or choosing such an algorithm include: computational cost, computer memory or storage requirements, accuracy and precision, simplicity of description, and the tuning of the algorithm to computer architecture and organization.
Computer Algebra
Authors: Kendall Wilfrid S.
Published: September 2014

This article begins by presenting basic common features, and by listing and giving references for current commercial computer algebra packages. There follow two simple introductory examples of the use of computer algebra in statistical contexts, and then a discussion of some typical constraints and features of computer algebra systems: it is important to be aware of these, since in this area, unrealistic expectations lead all too rapidly to frustration and disappointment. Finally, we list a few representative examples of research uses of computer algebra in statistical science, and conclude with suggestions for further reading.
Computer Architecture and Organization
Authors: Nielsen Ole M.
Published: September 2014

Computer technology has made amazing progress since the first general‐purpose electronic computer was created half way through the last century. This rapid rate of improvement is mainly driven by advances in the technology used to build computers but is also (and increasingly so) due to innovations in computer design needed to harness the tremendous capabilities of integrated circuits. Examples are memory hierarchies, pipelining, and parallelism.

This article gives an overview of modern computer architectures and outlines programming practices that will lead to efficient use of the hardware we are likely to encounter in biostatistics. The article concludes with qualified guesses as to the nature of computing in the future.
Computer Languages and Programs
Authors: Lawrence Catherine , Maindonald John H.
Published: September 2014

Computer languages are artificial languages that enable humans to give instructions to computer systems. Texts written in these languages are called
computer programs
or
code
. Influences that explain differences between languages include differences of historical development, of conceptual framework, and of intended use. The use of computer languages for writing large and complex programs raises major issues of program design. The use of computer languages for statistical analysis raises further issues that have been the subject of extensive discussion and research.
Machine Learning
Authors: Wilson Susan R.
Published: September 2014

A brief overview is given of machine learning and its relationship with various commonly used statistical techniques.
Matrix Computations
Authors: Maindonald John H. , Smyth Gordon K.
Published: September 2014

This article gives an overview of modern matrix algorithms, and of widely used high quality matrix routines, with especial reference to statistical computations. The article begins with an account of linear least squares calculations, which are fundamental to many other statistical computations, and from there moves on to discuss other matrix computations.
Optimization and Nonlinear Equations
Authors: Smyth Gordon K.
Published: September 2014

Optimization means finding that argument which minimizes or maximizes a given function such as a likelihood function or a sum of squares. Many optimization algorithms are derived from algorithms that solve the nonlinear equations defined by setting the derivative of the objective function equal to zero. This article discusses a number of methods for unconstrained optimization, including bisection and golden search in the univariate case and Newton's method and quasi‐Newton algorithms in the multivariate case. Applications to maximum likelihood estimation, Fisher's method of scoring, nonlinear regression, and generalized linear models are described. Restricted step modifications are discussed for preventing divergence of Newton‐type algorithms. A number of derivative‐free methods are discussed, including the Nelder–Mead simplex method, methods with numeric derivatives, conjugate methods, and the EM algorithm.
Polynomial Approximation
Authors: Smyth Gordon K.
Published: September 2014

Polynomials are very simple mathematical functions, which have the flexibility to represent very general nonlinear relationships. Approximation of more complicated functions by polynomials is a basic building block for many numerical techniques. This article considers two distinct but related applications. The first is polynomial regression in which polynomials are used to model a nonlinear relationship between a response variable and an explanatory variable. The advantages of using orthogonal polynomials as predictor variables are illustrated using a data set on the height and age of preadult girls. The second problem is that of approximating a difficult to evaluate function, such as a density or a distribution function, with the aim of fast evaluation on a computer. The use of Chebyshev polynomials is illustrated for the purpose of obtaining a uniformly accurate approximation to a function over a finite interval.
R
Authors: Venables W. N. , Maindonald John H.
Published: September 2014

The R system is an independent, open source, freely available implementation of a computer language that is well adapted to the development of scientific calculations, data analysis, and graphics. It has gained particular importance for developing and promulgating new statistical, data analytical, or graphical techniques. Versions of R are available for Microsoft Windows, Unix, Linux, and MacOS 8 or later.
Software, Biostatistical
Authors: Goldstein Richard
Published: September 2014

This article is a brief overview of statistical software available for biostatisticians. Included are historical notes, contact information for some of the more major packages, and some guidelines on how to assess such software.
Software for Sample Survey Data, Misuse of Standard Packages
Authors: Brogan Donna
Published: September 2014

Many health science researchers conduct primary or secondary analyses with data from complex sample surveys but do not realize that specialized statistical software needs to be used. This article compares analyses of survey data conducted with survey software and with standard statistical software. The numerical example illustrates that the inappropriate use of standard statistical software for sample survey data can result in: (a) biased point estimates of population parameters, (b) underestimation of standard errors, (c) confidence intervals that are too wide, and (d) misleading tests of statistical significance. Weighted analyses with standard statistical software, with regular or normed weights, can yield correct point estimates of population parameters but still yield incorrect results for estimated standard errors and statistical tests. Data analysts are advised to use appropriate software for the analysis of survey data.
Magic Square Designs
Authors: Martin Richard J.
Published: September 2014

An
n
by
n
magic square with entries 1 to n
2
has all row and column sums equal. If
n
has
k
factors, then a factorial design with n
2
runs and up to 2
k
factors can be obtained from this for which the main effects and at least some of the two‐factor interactions are linear‐trend‐free (their estimates are unaffected if there is a straight line trend over time). An unconnected experimental design called a
magic Latin square
is a Latin square with additional blocking obtained from structured rows and columns.
Branching Processes
Authors: Jagers Peter
Published: September 2014

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: September 2014

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: September 2014

The models for cell cycle regulation and cell cycle analysis are discussed as microscopic or macroscopic models.
Clinical Signals
Authors: Campbell Michael J.
Published: September 2014

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.
Image Analysis and Tomography
Authors: Glasbey C. A. , Berman M. , Hudson H. M.
Published: September 2014

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.
Ion Channel Modeling
Authors: Hawkes Alan G.
Published: September 2014

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.
Multistage Carcinogenesis Models
Authors: Sherman Claire D. , Portier Christopher J.
Published: September 2014

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.
Point Processes
Authors: Milne Robin K.
Published: September 2014

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.
Serial‐Sacrifice Experiments
Authors: Dewanji A.
Published: September 2014

Simple survival experiments provide little information to study the progress of different disease(s) and possible interaction between them. In serial sacrifice experiments, individual animals are randomly selected and killed (sacrificed) at fixed or adaptively selected time points, allowing the examination of presence or absence of the different diseases. Therefore, a serial sacrifice experiment, with interim observation on some individuals before natural death occurs, allows one to probe into the disease processes and the complex interrelationships between different diseases. Data from the sacrificed animals provides an estimate for prevalencep𝒜(t), the probability being that an alive animal has a particular disease combination 𝒜 at timet. On the other hand, death data provides an estimate of probability of death with the particular disease combination 𝒜, given by μ𝒜(t)p𝒜(t), where μ𝒜(t) denotes the mortality rate from disease combination 𝒜. In animal carcinogenicity experiments with serial sacrifice, in particular, the tumor occurrence time distribution is estimable. Design issues regarding the optimal sacrifice schedule are of some interest, but not much work has been done on this. There are few examples of serial sacrifice experiments, the ED01 study with 2‐acetylamino‐fluorene (2‐AAF) conducted by the US national center for toxicological research (NCTR) being probably the largest.
Stochastic processes including birth, death, Yule, Polya and divergent processes
Authors: Chiang Chin Long
Published: September 2014

Several articles in the Encyclopedia of Biostatistics describe various topics in stochastic process, while the present paper covers the main elements of the field, such as random walk, gambler's ruin, Markov chains, a general birth process, an equality in stochastic processes, death process and survival distribution, staging process, birth–death processes, and finite Markov processes. These topics together constitute an adequate representation of the field.

The main feature of this article is the explicit solution for every process presented, especially the K‐M epidemic model, the higher order transition probabilities in Markov chains, and the explicit solution for the Kolmogorov differential equations.

These solutions make it easy for the application of stochastic processes in research in biostatistics, epidemiology, health care, and medical sciences.
Tumor Growth
Authors: White R. Allen
Published: September 2014

The measurement of tumor growth rates has applications in such areas as tumor detection, prognosis, and control. The proliferation of tumors can be measured at different levels including gross measures of size, population progression through the cell cycle, and at the molecular level with biomarkers. Each of these methods has specific requirements and problems, particularly, including the heterogeneity both within and between tumors. Since tumors typically consist of a very heterogeneous mixture of normal and tumor cells, problems of interpretation of results must be made with care. Moreover, since tumors typically are measured only at detection with variable unknown histories and, after detection, at only a single or, at most, a few time points, problems in analysis require special methods.
Tumor Modeling
Authors: Byrne H. M. , King J. R.
Published: September 2014

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.