bluuebunny/crossref_metadata_2025_split huggingface dataset:
Sample Surveys in the Health Sciences
Authors: Brock Dwight B. , Beckett Laurel A. , Bienias Julia L. 
Published: September 2014

Abstract
The use of sample surveys in biostatistics arises from the need to answer questions about health issues in the community. The earliest uses of survey methodology in health research in the United States were motivated more by policy issues than by epidemiologic questions, and paralleled the use of surveys by the Census Bureau and other Federal agencies to address social and economic concerns. More recently, it has been recognized that research into the causes and outcomes of disease can benefit from studies in the entire community, rather than just in the formal health care system, particularly in countries like the United States, where access to health care is not uniform. A number of practical concerns about conducting studies in the community then lead to the use of sample surveys, rather than complete enumeration. In this article, we review the history of sample surveys in the health sciences, present an overview of the major elements and features in the design of sample surveys and analysis of data from such studies, and discuss major methodological advances especially in the last decade. Finally, we provide a large set of references that might be of use to the reader wishing to delve more deeply into specific areas.
Snowball Sampling: Introduction
Authors: Johnson Timothy P. 
Published: September 2014

AbstractSnowball sampling is a well‐known, nonprobability method of survey sample selection that is commonly used to locate hidden populations. This method relies on referrals from initially sampled respondents to other persons believed to have the characteristic of interest. Limitations of this approach include nonrandom selection procedures, correlations between network size and selection probabilities, reliance on the subjective judgments of informants, and confidentiality concerns. Advantages include cost and efficiency.
Superpopulation Models in Survey Sampling
Authors: Dorfman Alan H. , Valliant Richard 
Published: September 2014

AbstractIn sampling from a finite population, we often find it reasonable to posit a probability model (“superpopulation model”) that characterizes relations among variables that pertain to the units of the population. Such a model enables us to make inferences about population characteristics based on sample measurements and “auxiliary information”. In effect, we use the model to predict values for those units of the population that have not been sampled. In such prediction‐based (or model‐based) sampling and inference, it is important to guard against problems arising from model failure. Selecting a balanced sample or weighted balanced sample provides bias protection in the important case of estimating means or totals. Robust variance estimators guard against misapprehension of the variance structure.
Bayesian Measures of Goodness of Fit
Authors: Rice Kenneth 
Published: September 2014

AbstractWe consider methods for critical assessment of the appropriateness of fitted Bayesian models. This is done for situations where no particular alternative model is specified, and where the discrepancy between model and data is measurable in a user‐defined way. We review methods for testing goodness of fit in nonhierarchical models before discussing hierarchical models.
Goodness of fit ‐ Examples
Authors: Atkinson A. C. 
Published: September 2014

AbstractPearson's classical chi‐square test compares observed and expected frequencies in various classes. It tests for unspecified departures from the model, is based on aggregate rather than partial data, and uses an asymptotic distribution. Goodness of fit in multiple regression may be explored by including further explanatory variables in the model, or by comparing residual variation against external predictions. Tests based on residuals are described, as are extensions to generalized linear models.
Linear Regression, Simple
Authors: Matthews David E. 
Published: September 2014

AbstractSimple linear regression involves finding the best‐fitting curve of a suitable functional form that relates the value of an explanatory variable,X, and the mean value of a response variable,Y, givenX. The goals of regression modeling are to determine whetherYandXare associated in some systematic way, and to estimate or predict the value ofY, or its mean, corresponding to a known value ofX. We describe estimation, statistical inference, and diagnostic checking of the assumed model and any associated unknown parameters, giving due importance to their statistical and scientific interpretations. An example concerning the relationship between systolic blood pressure and age in men illustrates these concepts concretely.
Residuals
Authors: Atkinson A. C. 
Published: September 2014

AbstractResiduals are the differences between observed responses and those predicted by a model. Any pattern in the residuals is evidence of an inadequate model or of irregularities in the data, such as outliers, and suggests how the model may be improved. Various graphical methods are described, for both the normal regression and the generalized linear models, and are illustrated for the analysis of various data sets.
Marginal Models
Authors: Lindsey J. K. 
Published: September 2014

AbstractRepeated observations on the same subject are likely to be correlated. This situation may arise in longitudinal studies or in other cases where observations are clustered in some way. A multivariate model will refer both to the marginal distributions over the whole data and to the conditional distributions for individual subjects or clusters. A marginal model puts primary emphasis on marginal aspects. Relationships between responses and covariates may differ between marginal and conditional models. The issues are discussed with particular reference to paired binary data.
Misclassification Models
Authors: Albert Paul S. 
Published: September 2014

AbstractClassification errors in categorical data may distort the results of statistical analyses. Misclassification models have been developed in various areas of biostatistical application to account for this distortion. This article reviews selected methods that have been proposed for (i) modeling the natural history of a disease or growth process, (ii) evaluating diagnostic tests, and (iii) identifying epidemiological risk factors. We consider methods that incorporate known estimates of misclassification rates, methods that estimate misclassification rates from a subsample in which the presumably “true” classification is known, and methods in which both the true process and the misclassification rates are simultaneously modeled from misclassified data. The various methodological approaches are discussed along with their limitations, and we note an important issue for additional research.
Ante‐dependence models
Authors: Kenward M. G. 
Published: September 2014

Abstract

Ante‐dependence models are flexible nonstationary covariance structures for repeated measurements that generalize stationary autoregressive models. The structures can only be used for data in which the times of measurement are common across units. They can be defined in the Gaussian setting by conditional independence relationships: an
r
th order structure holds if and only if two repeated measurements are conditionally independent given
r
intermediate measurements. Equivalently, an
r
th order ante‐dependence covariance matrix has a inverse of band form of order r + 1, with no other constraints on the matrix, other than that it is positive definite. It provides a compromise between the unrealistic stationary structures, such as the autoregressive, and the potentially inefficient unstructured form. In certain repeated measurements settings, it allows test statistics to be constructed with known small sample distributions, that can be regarded as generalizations of Wilks' lambda statistic.
Nonlinear Mixed Effects Models for Longitudinal Data
Authors: Bates Douglas M. 
Published: September 2014

Abstract
The analysis of longitudinal data may require a mixed‐effects model, incorporating parameters for fixed effects associated with the whole population and also parameters describing distributions of random effects associated with individual subjects. These may enter the model nonlinearly, as in compartment models used in pharmacokinetics. Maximum likelihood estimation is carried out by numerical optimization.
Random Coefficient Repeated Measures Model
Authors: Goldstein Harvey 
Published: September 2014

Abstract
Biostatistical data often have a hierarchical structure. Typically, these structures are naturally occurring ones: animal populations are characterized by individuals nested within parents, themselves often nested within groups or herds that may also be nested within spatial entities. In other cases, the structure may result from research designs, as in multicenter clinical trials. Other examples are repeated measure designs, where measurements are “nested” within individual subjects and multivariate response data, where measurements are “nested” within individuals. In addition to nesting relationships among data units, we may also have cross‐classifications. For example, an individual cow may be nested within a herd of cattle, but also be the offspring of parent stock where any parent may contribute to several herds: individual cows are thus cross‐classified by parents as well as nested within their herds. A further complexity is also often present whereby individual units at one level of a data hierarchy may be nested within more than one higher‐level unit as in spatial data.
The article describes models for all these kinds of data structures, increasing in complexity as they move from simple hierarchies with continuously distributed responses, to cross‐classifications and multivariate data and to discrete responses. Various extensions and special cases will also be considered. The emphasis is on model specification with a brief section on estimation.
Ancillary Statistics
Authors: Reid N. 
Published: September 2014

AbstractAn ancillary statistic is a function of the data whose distribution is free of the parameters in the model. Ancillary statistics are complementary in a certain sense to sufficient statistics. In the theory of statistics, it is often argued that inference should be conditional on ancillary statistics, when this is possible. Fisher showed that in a location model, the conditional distribution of the maximum likelihood estimator could be obtained by renormalizing the likelihood function, or, in other words, treating the likelihood function as a posterior distribution for the location parameter. This result has been generalized to provide an approximate conditional distribution to the maximum likelihood estimator, given an approximately ancillary statistic, a result known as thep* approximation.
BANEstimates
Authors: Bemis Kerry G. 
Published: September 2014

AbstractBAN (Best Asymptotically Normal) estimates and their corresponding chi‐squared test statistics form the core of classical categorical data analysis. Historically, these estimates were developed for the multinomial distribution. This article describes the optimal properties of these classical estimators and the form of their chi‐squared test statistics. It is also shown that these are special cases of BAN estimators and chi‐squared test statistics from a more general family of discrete multivariate distributions (Sum Symmetric Power Series Distributions), which include multinomial, negative multinomial, and multivariate Poisson as special cases. These results are in turn generalized to the multivariate exponential family. BAN estimators and their test statistics take on familiar forms and properties as the classes of distributions are generalized. Estimation and hypothesis testing are described from the point of view of constraint equations and the more familiar freedom equations.
Bonferroni Inequlities and Intervals: Practical Aspects
Authors: Costigan T. 
Published: September 2014

AbstractThe first‐order Bonferroni inequality relates the probability that at least one of a series of events occurs to the sum of the probabilities of the individual events. In statistical applications, it provides an upper bound to the probability of falsely rejecting at least one of a series of true null hypotheses, and therefore, a possible correction to a significance level to account for multiplicity of hypotheses tested. Further developments include sequential rejection procedures and the use of higher‐order Bonferroni inequalities.
Cauchy Distribution
Authors: Glynn Robert J. 
Published: September 2014

AbstractThe Cauchy distribution, discovered by S.D. Poisson in 1824, arises as the ratio of two independent standard normal variables. It does not have finite moments. The sample mean has the same distribution as a single observation, and so is not a consistent estimator of the median. It is a useful model for situations where error distributions have very long tails.
Consistent Estimator
Authors: Liang Kung‐Yee , Rathouz P. J. 
Published: September 2014

AbstractAn estimator of a statistical parameter is consistent if it converges in probability to the parameter as the sample size increases. Two methods of obtaining consistent estimators are described by minimizing a specific function of the data and the parameter (e.g. maximum likelihood,M‐estimation, weighted least squares), or by solving an equation involving an estimating function (e.g. quasi‐likelihood).
Cramer‐Rao Inequality
Authors: Bhapkar V. P. 
Published: September 2014

AbstractThis inequality provides a lower bound for the variance of any unbiased estimator of a one‐dimensional parameter or more generally of a function of the parameter. It involves the Fisher information (the expectation of the squared derivative of the log likelihood). If equality is attained, the statistic is a minimum variance unbiased estimator, and the density function belongs to a one‐dimensional exponential family. The inequality can be generalized for a multidimensional parameter.
Decision Theory: Biostatistical Aspects
Authors: Lewis Roger J. , Berry Donald A. 
Published: September 2014

AbstractStatistical decision theory is a set of techniques for making optimal decisions in the setting of uncertainty. Both frequentist and Bayesian approaches have been developed. The definition of a Bayesian decision problem requires the specification of an unknown parameter and its prior probability density function (pdf), observed data (if any), a likelihood function, a set of possible decisions or actions, and a loss or utility function whose expectation is to be optimized. The expected loss can be defined in a number of ways, yielding a frequentist risk, the conditional Bayes risk, and the Bayes risk. The goal is generally to select a decision rule that maps the possible observed data to a set of actions so that the Bayes risk is minimized. Alternatively, a frequentist may seek to minimize the maximum frequentist risk that might be experienced over all possible fixed values of the unknown parameter, yielding the optimal “minimax” decision rule. Examples in the chapter include a problem of selecting drug therapy when the patient diagnosis is unclear and the decision to order a test to determine the disease present, choosing a sample size when the goal is to estimate an unknown mean of a normally distributed variable, sequential stopping rules determined through back induction, and sequential allocation or assignment (bandits).
Efficiency and Efficient Estimators
Authors: Rotnitzky Andrea 
Published: September 2014

Abstract
The efficiency of a point estimator of a parameter reflects its tendency to be distributed closely around the parameter value. Asymptotic efficiency refers to the limiting distribution in large samples, which is often asymptotically normal, the minimum variance being given by the Cramér–Rao lower bound in terms of the information matrix. Concepts discussed here include asymptotic relative efficiency, semiparametric efficiency, partial likelihood, and quasi‐likelihood.
Experimentwise Error Rate in Practice
Authors: Iglewicz Boris 
Published: September 2014

Abstract

Multiple comparisons are frequently performed in medical experiments. These occur when dealing with multiple treatments, multiple endpoints, multiple subgroups, or multiple looks. Use of the nominal significance level for each comparison results in an inflated overall type I error rate, called the
experiment‐wise error rate
. Approaches for controlling this error rate are discussed and a number of references are provided.
Exponential Family: Overview
Authors: Pierce Donald A. 
Published: September 2014

AbstractThe overview focuses on aspects of exponential families important in biostatistics, particularly by emphasizing not identically distributed observations involving covariables. This is closely related to generalized linear models. The distinction is made between regular and curved exponential families. In the former, the maximum likelihood estimator is sufficient, the expected and observed information are the same, and there are exact frequency methods for some inferences. In the latter, there is information not contained in the maximum likelihood estimator, much of which is carried by the ratio of observed to expected information, and asymptotic methods must always be used. Of these, likelihood ratio and score methods are preferable to the Wald method. Modern higher‐order asymptotic methods, including the modified profile likelihood, are mentioned. The tractability of Bayesian inference in exponential families is indicated.
F

Distributions
Authors: Selvin S. 
Published: September 2014

Abstract

The
F
‐distribution is fundamental to much of statistical analysis, particularly the analysis of variance. The article entitled “
F
‐Distribution” is a brief but complete description of this probability distribution. Its properties are first discussed, followed by a description of the relationship between the
F
‐distribution and other common statistical distributions (e.g. beta, t‐, chi‐square, and binomial distributions). The article concludes with a typical application of this distribution to a small set of sampled observations.
Lehmann Alternatives with Emphasis on Biostatistics
Authors: Razzaghi Mehdi 
Published: September 2014

AbstractIn a nonparametric comparison of two groups, the test statistic may not be distribution‐free under alternatives to the null hypothesis. Lehmann proposed a family of alternatives under which the distribution function of the response variable in one group is a specified function of that in the other. A power relationship is usually considered. The distribution of the rank vector under the alternative then depends only on the specified function and rank statistics are distribution‐free. An extension covers the situation where a proportion of the population is unaffected by treatment.
Likelihood Principle
Authors: Lindsey J. K. 
Published: September 2014

AbstractThe likelihood function is central to all approaches to statistical inference. Principles have been proposed to justify the equivalence of inferences based on data with likelihood functions identical apart from a proportionality factor independent of parameters. The weak principle refers to replications with the same design; the more contentious strong principle refers to results from different designs. The latter, implied by Bayesian theory, needs to be supported by strong confidence in the validity of the model.
Location–Scale Family
Authors: Datta Gauri Sankar 
Published: September 2014

Abstract
A set of random variables has a location‐scale family distribution if their joint distribution function can be expressed as a function of the standardized observations (xi ‐μ)/s, where μ and s are, respectively, the location and scale parameters. Important examples are the uniform, normal, and Cauchy distributions. Least squares estimation and minimum risk equivariant estimation are described.
Combining P‐values
Authors: Westfall Peter H. 
Published: September 2014

Abstract

When a null hypothesis is tested on different sets of data, the individual
P
values may usefully be combined to provide a more powerful test than any individual one. If the null hypothesis is true, and the statistical model is correct, each
P
value follows a uniform distribution. Various methods of combination have been suggested for situations where the data sets are independent, and some comparisons of power against alternative hypotheses are presented for a particular case. Most of these methods are invalid for dependent data.
Graeco–Latin Square Designs
Authors: Martin Richard J. , Nadarajah Saraleesan 
Published: September 2014

AbstractA Graeco‐Latin square is a pair of orthogonal Latin squares (each letter combination occurs exactly once). Such squares exist for all positive integers except for 1, 2, and 6. They, and the extension to sets of mutually orthogonal Latin squares, are useful for constructing experimental designs in several situations in which there are four or more blocking or treatment structures. However, they are limited because essentially the numbers of treatments, blocks, or factor levels must all be the same.
Statistics, an Overview
Authors: Cox D. R. 
Published: September 2014

AbstractThe current topic may be called “statistical science”, encompassing statistical theory and its applications in science and technology. One pillar is probability theory, underpinning statistical inference and forming the basis for special models. Various types of models are distinguished. A second pillar is the design, analysis and interpretation of investigations. The discussion here touches on measurement issues, methods of analysis, detailed techniques, causation, and decision analysis. Formal theories of inference are discussed. Issues arising in the provision and use of official statistics are briefly discussed.
Moment Generating Function
Authors: Koehler Kenneth 
Published: September 2014

Abstract
Moment generating functions are used to derive moments of distributions, establish the distribution of sums and differences of independent random variables, and derive limiting distributions of sequences of random variables. It is an integral transform of the density function and the terms of its Taylor expansion about the origin give moments about zero. Central moments are easily obtained. Properties discussed briefly include the derivation of the MGF for a sum as the product of the separate MGFs, the multivariate case and the derivation of the factorial moment generating function.
Moments
Authors: Koehler Kenneth 
Published: September 2014

Abstract

The
r
th moment of a random variable
X
is the expectation of the
r
th power of
X
. Moments may also be taken about a constant
c
by taking powers of
X
−
c
, and central moments take
c
as the mean of the distribution. Related concepts are absolute moments, factorial moments, and cumulants. The method of moments is a method of estimation by equating estimated moments to theoretical values expressed in terms of parameters.
Noncentral

t

Distribution: Introduction
Authors: Rust Philip F. 
Published: September 2014

Abstract

This is the distribution of the ratio of a normally distributed variable with unit variance to the square root of a ratio of a chi‐square variable to its degrees of freedom. When the noncentrality parameter (the mean of the normal distribution) is zero, the distribution is Student's
t
distribution. The noncentral distribution provides the power function for a
t
test, and other applications concern tolerance intervals and confidence intervals. Details are given here.
Pairwise Independence
Authors: Wermuth Nanny 
Published: September 2014

AbstractIf two explanatory variables are independent, with additive effects on a third, response, variable, then the overall effect of one explanatory variable is qualitatively the same as the effect conditional on the other explanatory variable. If the explanatory variables are dependent, reversal can occur. In multivariate analysis, pairwise independence of all variables does not imply mutual independence.