bluuebunny/crossref_metadata_2025 huggingface dataset:
Treatment Interruption
Authors: Grund Birgit
Published: September 2014

Interruption of active drug treatment in clinical trials can be classified broadly as therapeutic treatment interruption (TI), in which the potential therapeutic benefit of supervised interruption of treatment is investigated, and analytic TI, in which participants are randomized to stopping versus continuing active treatment; the TI arm serves as control group. Design issues for therapeutic TI trials are discussed in the example of a trial in HIV/AIDS.

Analytic TIs are used in therapeutic HIV vaccine trials, in randomized discontinuation designs, and in other situations. The use of a randomized discontinuation design for a Phase II drug trial in cancer is discussed.
Sample Size Calculation for Comparing Means
Authors: Wang Hansheng , Chow Shein‐Chung
Published: September 2014

In this article, the focus will be on sample size calculation based on a continuous study endpoint for comparing means (i.e., treatment effects) under some study designs. These designs include parallel designs, crossover designs, titration designs, and enrichment designs (2). Among these designs, parallel designs and crossover designs are probably the two mostly commonly used designs.
Monotherapy
Authors: Darbyshire Janet
Published: September 2014

A trial that evaluates a monotherapy would most often test a single drug, but the definition could be extended to include other interventions such as immunotherapy or even a different modality such as radiotherapy that contain a single element. The issues around trial design are essentially the same and, therefore, this section focuses on monotherapy trials that evaluate a drug.
Assessment of Health‐Related Quality of Life
Authors: Wayne Weng C. S.
Published: September 2014

This article is intended to provide an overview of assessment of HRQOL in clinical trials. For more specific details on a particular topic mentioned in this article, the readers should consult the cited references. The development of a new HRQOL questionnaire and its translation into various languages are separate topics and are not covered in this article.
Hierarchical Bayesian Space‐Time Analysis
Authors: Berliner L. Mark
Published: September 2014

This article introduces the hierarchical Bayesian (HB) approach to modeling the spatial‐temporal structure and dependence as well as the model uncertainty. Many problems in the environmental sciences involve inferences for space‐time‐varying physical processes, which can be summarized in three stages: Data model, process model and prior on parameters. The HB approach allows for combining observations with physical models.
Posterior Distribution: Introduction
Authors: Gelman Andrew
Published: September 2014

The posterior distribution summarizes the current state of knowledge about all the uncertain quantities in a Bayesian analysis.
Automatic Differentiation
Authors: Skaug Hans Julius
Published: September 2014

Automatic differentiation (AD) is a technique for numerical differentiation of computer algorithms.
Conditional Simulation
Authors: Shafer John M.
Published: September 2014

Conditional simulation, also referred to as stochastic imaging, is a stochastic simulation process whereby equally probable realizations of a spatial random function are created with each realization honoring discrete data values at specific locations or geometric patterns, i.e. ‘conditioned’ on the data. Conditional simulations of a random function satisfy two exactitude constraints, the local exactitude of honoring data values and the global exactitude of reproduction of a specified spatial correlation structure. The random variable may be categorical such as an indicator of the presence or absence of some feature (e.g. rock type), or spatially continuous such as porosity or ore grade. Conditional simulation is often used to address problems associated with the spatial distribution of physical properties relevant to the mining industry and several fields of earth sciences, especially hydrogeology, contaminant hydrology, meteorology, and gravimetry. Through Monte Carlo analysis, for example, conditional simulation can be used to evaluate the uncertainty in numerical model parameter values and the translated uncertainty in model response.
Genetic Algorithms
Authors: Sheehan N.A.
Published: September 2014

Forest inventory is an accounting of trees and their related characteristics of interest over a well‐defined land area. It may be compared to census methods for human populations. For example, one of the goals of the periodic decennial census of the US is to enumerate its human population and to retrieve demographic variables such as age, sex and race. This is accomplished by a comprehensive survey of all households in the country. Similarly, forest inventories seek to enumerate the population of trees within a forest and ascertain other information, such as their volume, value, growth and species composition. For all but the smallest tracts of land, complete enumeration of individuals is usually infeasible and survey sampling techniques are required. Unlike human or animal populations, trees are sessile organisms and there is no immigration or emigration to consider. However, tree populations vary widely in their species composition, age, size, site requirements, potential value, longevity and growth–all factors that may influence the design of a forest inventory. In addition, the tree population of interest may exist over a wide variety of topography, making access potentially costly and sometimes even dangerous. Such variety often dictates sampling protocols that may be optimal only for some portion of the population in question. Alternatively, it may call for varying sampling intensity or strategy (the combination of the sampling design and associated estimators) between different regions within the population.
Binary Data and Quantal Response
Authors: Piegorsch Walter W.
Published: September 2014

Environmental data often occur in discrete form, such as the number of individuals living near a waste site, or whether or not a subject develops cancer after exposure to an environmental agent. This latter example is one of the simplest forms of discrete data: a dichotomous indicator of whether or not an event has occurred, i.e. a ‘success’ or a ‘failure’. Such an outcome can be coded simply as either 1 or 0 – corresponding to success or failure – and we refer to this as a case of
binary data
. If the data on each subject or unit in the study are coded in this binary fashion, and if each subject contributes one and only one such binary observation to the experimental data, we call this a case of
ungrouped binary data
. Alternatively, when the subjects have some underlying or coordinating feature that relates them, it is common to group the like subjects and record the proportion of subjects responding; i.e. take the proportion Y/N, where Y is the number of observed successes out of the N observed subjects in the common group. This is
grouped binary data
.
Bivariate Distributions
Authors: Christman Mary C.
Published: September 2014

Bivariate distributions play a special role in environmental science since they are the underpinnings of analyses of relationships between two random variables. These relationships include such analyses as biserial correlation between continuous and discrete random variables; measures of association in an
r
×
c
contingency table; Pearson's product–moment correlation; Kendall's tau; Spearman's rank correlation; and many others. In addition to studies of the dependency between two variables, interest may center on other analyses; for example, multivariate general (or generalized) linear modeling when two or more response variables are involved. Inferences involving two random variables rely on knowledge of their bivariate distribution. Probably the best known example is estimation and testing of the correlation coefficient in the bivariate normal distribution for two continuous random variables. There are many other distributions of importance as well, especially those relating two discrete random variables or a discrete to a continuous variable. This article describes a few of the more common distributions in environmental practice and, where appropriate, mentions the multivariate distribution of which the bivariate is a special case.
Bivariate Extreme Value Distribution
Authors: Teugels Jozef L.
Published: September 2014

In many situations within environmetrics, investigators deal with bivariate measurements. While each of the components might have its own extreme characteristics, frequently there is a need for insight into the simultaneous happening of two or more extreme events. First a few theoretical aspects are dealt with on how to model the dependence and the location of more information in the literature is indicated. Some specific applications of bivariate extremes within an environmental context are then described.
Inverted Wishart Distribution, Generalized
Authors: Brown Philip J.
Published: September 2014

The generalized inverted Wishart (GIW)
distribution
is a flexible extension of the inverted Wishart (IW) distribution which overcomes the major deficiency of that distribution whilst retaining much of the ease of computation inherent in the natural conjugate roots of the inverted Wishart distribution in Bayesian analysis for normal sampling. In offering a more flexible prior distribution for the covariance matrix of a multivariate normal distribution it has general applicability. It also offers a conjugate Bayesian analysis for problems of missing data where the missing data has a monotone structure. It has been especially useful in simultaneous modeling of the spatial distribution of ozone where monitoring stations come on‐stream in sequence, using multivariate regression analysis for interpolation and prediction.
Mixing Distribution
Authors: Leroux Brian
Published: September 2014

A random variableYis said to have a mixture distribution if its probability density (or mass) function can be written as an average over a parametric family of distributions. An example is the Poisson‐gamma distribution, in which conditional on a gamma‐distributed variableM, the variableYhas a Poisson distribution with meanM. The probability distribution assigned to the conditioning parameter (e.g., gamma) is called the mixing distribution. Mixture distributions are particularly useful in environmental and other sciences for modeling overdispersion in discrete data. An extension called the hidden Markov model is available to also account for autocorrelation in discrete data.
Normal and Multinormal Distribution
Authors: Hallin Marc
Published: September 2014

We briefly summarize the definitions of univariate and multivariate normal distributions, along with some of their main properties.
Pattern Recognition
Authors: Stein Alfred
Published: September 2014

Pattern recognition is defined as the automatic identification of figures, characters, shapes, forms and patterns without active human participation in the decision process. These can be structures in one dimension, for example an array of characters, a time series or any other signal, or a structure in two dimensions, such as an image. Higher dimensional patterns are rarely if ever encountered. Pattern recognition can be further divided into recognizing existing features that have a well‐known effect on an image, or the search for coherent subpatterns that may have a common cause. A pattern therefore consists either of features that are known to exist, but are somehow difficult to identify, or of features that may get a specific meaning afterwards (i.e. after they are detected).
Dispersion Parameter
Authors: Piegorsch Walter W.
Published: September 2014

To describe the stochastic nature of an outcome variable, environmetricians use probability distributions. A crucial feature of many simple probability models is that structural relationships may be required between the population mean and other components of the model. Many environmental sampling and experimental settings occur, however, where such a mean/variance structure is too restrictive: the data often exhibit variation larger than or, in some instances, smaller than that required under these simpler models. Such occurrences are known collectively as overdispersion or underdispersion, respectively. We quantify the extent of the over/underdispersion by dedicating a model parameter to it in the variance term. The resultingdispersion parametercan be used to identify, study, test, or otherwise account for the excess variation. This entry reviews statistical aspects of modeling and estimation for such dispersion parameters.
Empirical Bayes Methods
Authors: Louis Thomas A.
Published: September 2014

Statistical design, analysis, and reporting are fundamental to environmental research and assessment; to environmetrics. The variety and complexity of applications rapidly grows with a commensurate growth in statistical design and analysis. Environmental applications include all aspects of design, the analysis of spatially structured information (exposure, health outcomes, and demographics), nonlinear dose–response assays, interspecies extrapolation, placement of air or water monitoring stations, remote sensing, and gene–environment interactions. Analytic challenges include stabilizing estimates via statistical modeling and otherwise ‘borrowing information’, integrating information that is misaligned in space and time, dealing with missing data, accounting for measurement error in input information (e.g. exposures), missing data, causal modeling, addressing nonstandard goals and ensuring that statistical evaluations account for the dominant stochastic and modeling uncertainties. In addressing these and other challenges and goals, Bayes and empirical Bayes (EB) designs and analyses have proven valid, efficient, and informative. The beauty of the Bayesian approach is its ability to structure complicated assessments, guide development of appropriate statistical models and inferences, and produce summaries that properly account for uncertainties. Properly structured, these methods can produce objectively valid analyses, commonly more effective than traditional methods. When available, prior information can be integrated into the design and analysis. Computing innovations enable implementation of complex, relevant models and applications burgeon. This article outlines the Bayesian approach, traces the history of the EB approximation, gives a small sampling of environmetric applications and speculates on future developments.
Equivariant Estimation: Theory
Authors: Hallin Marc , JureČková Jana
Published: September 2014

The concepts of invariance and equivariance of estimators with respect to various groups of transformations of the sample space are defined. The structure and properties of equivariant and minimum risk equivariant estimators are characterized. Emphasis is put on equivariance with respect to shift, scale, and affine transformations.
Exact Randomization Technique
Authors: Moir Rob
Published: September 2014

The exact randomization technique is a distribution‐free, computationally‐intensive statistical method of dealing with small samples and uncertain distributions. The technique was first proposed by Fisher in 1935 as a method of dealing with small biological samples. Because of the computational demands, only the recent development of powerful desktop computers permits researchers to regularly use this technique. Suppose two sets of observations are recorded and labeled according to whether they come from a treatment or a control group. The concept of randomization is based on the observation that a conventional test statistic (e.g. a
t
statistic) can be interpreted as a typical draw from the distribution of test statistics that would be generated from randomly shuffling the treatment and control labels among the observed data. In fact, the exact randomization test is essentially a controlled example of bootstrapping.
Multinomial Distribution, Inferences for
Authors: Hallin Marc
Published: September 2014

This article briefly summarizes, for the purpose of easy reference, the definition and main properties of multinomial distributions.
Order Restricted Inference
Authors: Dykstra Richard , Kuo Hsun‐chih
Published: September 2014

A wide variety of statistical techniques have proven useful in biological and environmental studies. Frequently, these techniques can be improved upon and/or made more powerful if the prior knowledge that certain parameters satisfy an order restriction can be incorporated into the analysis. Moreover, since the existence and implications of orderings can be easily grasped and interpreted by even casual readers and observers, the ability to identify such structure can be especially important. Such structure may exist in many ways. Two possibilities that have been widely discussed are the presence of ordered parameters and the identification of ordered distributions.
PValue and Bayesian Statistics
Authors: Delampady Mohan
Published: September 2014

ThePvalue is one of the tools from classical statistics that is used very widely in applied sciences. It is also one of the concepts that is highly misunderstood and misused. The basic idea behind Fisher's original (1925) definition ofPvalue did have a great deal of appeal: it is the probability under a (simple) null hypothesis of obtaining a value of a test statistic that is at least as extreme as that observed in the sample data.
Quantiles
Authors: Allen O. Brian
Published: September 2014

Quantiles are defined for a sample ofnobservations and for the probability distribution of a population of observations. In many cases, the sample quantile may be viewed as an estimate of the corresponding quantile for a population. Some of the most commonly used quantiles have special names. The first, second and third quartiles divide a probability distribution into four equal parts. Thus, 25% of observations are less than the first quartile and 25% of observations are greater than the third quartile. The second quartile is better known as the median. Other quantiles with special names include the quintiles, which divide a distribution into five equal parts, and percentiles, which divide a distribution into 100 equal parts. Quantiles play an important role in environmental science in a number of ways, examples of which are given in this article.
Robust Estimation of Location and Scale
Authors: Croux Christophe , Dehon Catherine
Published: September 2014

Sample mean and standard deviation are the classical estimators of the location and scale parameters of a statistical distribution. They are, however, unreliable in the presence of outliers. Robust alternatives have been proposed, of which the median and the median absolute deviation are best known. Several robust estimators of location and scale are reviewed and their properties discussed. The multivariate case is also discussed.
Spectral Methods
Authors: Fuentes Montserrat
Published: September 2014

Spectral methods are a powerful tool for characterizing and modeling spatial dependence, while offering significant computational advantages. Using the spectral representation of a spatial process, we can easily construct valid (positive definite) covariance functions and introduce new models to characterize complex dependence structures of spatial processes. Likelihood approaches for very large spatial datasets are often very difficult, if not infeasible, to implement owing to computational limitations. Even when we can assume normality, exact calculations of the likelihood for a Gaussian spatial process observed at
n
locations requires O(
n
3
) operations. The spectral version of the Gaussian log‐likelihood for gridded data requires O(
n
log2
n
) operations and does not involve calculating determinants.
Competing Risk Analysis
Authors: Gupta Ramesh C.
Published: September 2014

In studies of risk assessment due to environmental exposures, we are interested in the mortality due to a particular disease when several other diseases are acting on a person's life. The method of analyzing survival data in such a population is called “competing risk analysis.” We also have a fundamental assumption that each death takes place due to a single cause. When an individual is put on test, only his time of death and cause of death are recorded. This competing risk data provides insufficient information to determine the joint distribution of the survival times giving rise to an identifiability problem. In this article, the cause‐specific hazard functions are introduced and their estimation and testing, for modeling, both independent and dependent lifetimes are discussed. The identifiability problem is also addressed and some ways to deal with the competing risk data in the presence of association between the latent survival times are suggested.
Compositional Data
Authors: Billheimer Dean
Published: September 2014

Compositional data are vectors of proportions describing the relative contributions of each ofDcategories to the whole. This structure is an essential feature of data in many disciplines: in geology as oxide composition of rocks, in ecology as the relative abundance of plants or animals, in air pollution monitoring as the relative concentrations of different chemical species (among others). Statistical approaches for modeling compositional data exhibiting temporal or spatial correlation structure are described in this article. Because methods for compositions are not widely included in statistics education, a brief introduction is given to data characteristics and analysis techniques for independent observations. The focus is observations with three or more categories (D ≥ 3). With only two categories, compositional data are (essentially) univariate, and can be addressed by means of standard statistical techniques (e.g. logit transform). Since the compositional structure is present in a wide variety of problems, many of the methods summarized in this article have been developed outside the environmental context. The approach is to present methods in a general form, and note when there is special development for an environmental application.
Random Fields, Nonparametric Methods
Authors: Tjøstheim Dag
Published: September 2014

An overview is given of nonparametric methods in random fields including estimation of the density, the autocovariance, the specrum, and nonlinear additive models. The difference between expanding domain asymptotics and infill asymptotics is highlighted. Throughout the article similarities and differences relative to time series modeling are pinpointed.
Ranks
Authors: Hallin Marc
Published: September 2014

Rank tests were introduced as a reaction against the traditional assumption of Gaussian observations. The most attractive feature of ranks and rank statistics is that they are distribution‐free, and thus, in principle, allow for exact critical values, irrespective of the underlying distribution of the observation. Their domain of application is, mainly but not exclusively, the class of semiparametric models obtained from the traditional parametric ones (location, scale, regression, autoregression, etc.) by treating the density of the underlying error or noise as an unspecified nuisance. Their popularity is explained by their success in a variety of practical situations, and their robustness against deviations from standard distributional assumptions.
Lasso, the
Authors: Knight Keith
Published: September 2014

The LASSO (least absolute shrinkage and selection operator) is a method of estimation in linear regression (and related) models that combines shrinkage estimation achieved in ridge regression with model selection where some (or all) parameter estimates are set to zero. The LASSO is capable of producing a “sparse” estimate of the parameter and can be used effectively even when the number of parameters exceeds the number of observations. LASSO estimates can be computed very efficiently using a number of methods, including coordinate descent methods. A number of generalizations of the LASSO have been proposed, including the fused LASSO, the group LASSO, and the adaptive LASSO.
Multivariate Adaptive Regression Splines
Authors: Kooperberg Charles
Published: September 2014

The multivariate adaptive regression splines (MARS) algorithm was developed by Friedman as a nonparametric method for multiple regression. The MARS algorithm uses adaptively selected spline functions. Because of its adaptivity MARS is often able to model functions that express high variation in one region of the predictor space and are smoother in other parts.
Line‐Transect Sampling, New Approaches
Authors: Melville Gavin , Cowling Ann
Published: September 2014

The widespread use of line‐transect surveys to estimate the abundance of ecological populations has seen a number of new developments in methodology. For example, nonparametric approaches have been introduced to estimate detection probabilities for objects in the target population. Also line‐transect data have been increasingly used to study a range of spatial models that may be of interest to ecologists. The treatment of measurement errors and recent sampling innovations such as sequential and adaptive sampling have increased the flexibility of the line‐transect approach and provided more robust estimates of abundance. Debate over an appropriate frame of inference, specifically design‐based versus model‐based, is a motivation for alternative estimation techniques such as mark–recapture and the use of Bayesian statistics. This article summarizes some of the recent developments in line‐transect sampling.
Multistage Design
Authors: Christman Mary C.
Published: September 2014

Multistage sampling designs are probability based sampling strategies for obtaining more information about a population with less cost than would be possible under a single stage design. Examples of such approaches include ranked set sampling, double sampling for stratification, and multistage cluster sampling. In all cases a first stage sample is selected, e.g. a set of randomly selected transects through a habitat, and subsequently a subset of observations from this initial sample, e.g. observations at randomly selected locations along the transects, are selected for data collection.
Size‐Biased Sampling
Authors: Zimmerman Dale L.
Published: September 2014

Size biased sampling refers to a type of nonrandom sampling in which the likelihood of an object's inclusion in the sample is proportional to the size (or length) of the object.
Age‐Growth Modeling
Authors: Nokoe K. Sagary
Published: September 2014

This section is on growth of nonhuman individuals. Growth of an individual or a group of organisms is generally defined as the change in dimensions over time. Growth rates vary between and within plant and animal species. They are generally influenced by both genetic and phenotypic factors, and may be negative or positive. Positive growth relates to increases in dimensions (weight, height, and number of component parts) over time, whereas decay or negative growth refers to the decline over time. Human interference, either intentionally or accidentally, environmental influences, and management practices can substantially influence the growth forms and patterns of individuals and population. Age‐growth functions constitute important analytical tools in the management of natural resources. These models are explicit expressions of both theory and empirical knowledge, and are useful for growth and yield prediction and evaluation of alternative management strategies, among others. The approach to age‐growth modeling may be based on either primary (single) unit or stand (aggregate of units). Irrespective of modeling philosophy, the goal is identification of the most parsimonious and biologically reasonable model that best describes the relationship between the response variable (which is a measure of growth) and time (age).
CorrelatedMultinomialData
Authors: Zhu Yiliang
Published: September 2014

Correlated multinomial data, including correlated binomial, arise from clustered sampling schemes such as grouped sampling or repeated measurements. Correlation induced by clustering can be of interest in its own right, but must be accounted for in statistical analyses to avoid inaccurate or inefficient inference. This article discusses common approaches to the treatment of correlated multinomial data and illustrates dose‐response modeling via generalized estimating equations using an example from developmental toxicity experiment.
Databases, Health Assessment
Authors: Darnell Ross
Published: September 2014

Environmental issues regarding possible environmental pollution links to human and ecological health are becoming more numerous and controversial. The ideal approach to assessing potential health risks from environmental exposure is to conduct well‐designed, prospective, environmental, epidemiological studies. However, prospective epidemiological studies are difficult and expensive to undertake, and even retrospective studies can be prohibitively complex. Reliable environmental data are not easy to find and often they may not have been collected in a manner that makes them easy to use. The availability of data increases the risk of identifying single units using increasingly powerful search engines by ill‐intentioned users. The increasing public availability of health and environmental data raises the risk of identifying individuals, forcing data owners to develop techniques to reduce this risk.
Dose‐Response Model
Authors: Gaylor David
Published: September 2014

A measurement,
Y
, of an effect can be represented by
Y
 = E(
Y
) + error. E(
Y
) is the expected (true) value of an effect and error is the deviation of the measurement from its true value due to inherent measurement error and/or experimental variation. A dose–response model is a mathematical function
f
that relates the expected value, E(
Y
), of some measurable effect,
Y
, to a dose,
d
, of a substance E(
Y
) = 
f
(
d
).
Epidemic Models
Authors: Isham Valerie
Published: September 2014

Mathematical modeling of infectious diseases has a long and distinguished history and is one of the most successsful areas of mathematical biology. Understanding the dynamics of the spread of an infection brings possibilities for its control. Human infections such as influenza, malaria, and HIV are still major worldwide causes of morbidity and mortality. In 2003, a new infection, SARS, spread rapidly around the world, with considerable transmission taking place before the infection was even recognized. In such situations, a large‐scale epidemic can only be avoided if strict control strategies are imposed quickly. A clear understanding of the basic theory of epidemic models is a prerequisite for this and, equally, for informing the development of the successful vaccination policies against a wide range of infections in routine use around the world. This article provides a brief introduction to that theory and to some natural extensions of the simple models and the practical concerns that they are designed to address.
Gene‐Environment Interaction: Introduction
Authors: Ryan Louise
Published: September 2014

Gene‐environment interaction refers to the fact that response to an environmental exposure may differ according to an individual's genotype. It represents a major component of genetic epidemiology, the discipline focused on investigating the role of genetic factors, as well as their interaction with environmental factors, in the occurrence of human disease.
Healthy Worker Effect
Authors: Eisen Ellen A. , Picciotto Sally , Robins James M.
Published: September 2014

Epidemiologic studies of occupationally exposed cohorts are useful in identifying and quantifying environmental risks because workers are generally exposed to higher levels of toxic materials than the general population. Although higher exposures make it easier to detect and characterize modest elevations in risk, such studies are plagued by a particularly pervasive form of selection bias, referred to as the healthy worker effect (HWE). The HWE is reflected in better health status of exposed workers relative to the general population. This bias arises from two sources: (i) workers were initially healthy enough to be hired, whereas the general population includes persons unfit for work, and (ii) workers who stay healthy (survivors) remain exposed, whereas less healthy coworkers reduce exposure via time off work, job transfer, or early termination. Unlike standard methods, G‐estimation has been shown to reduce healthy worker survivor bias.
Litter Effect
Authors: Kupper Lawrence L.
Published: September 2014

It has long been recognized that humans exposed to certain drugs, chemicals, and other environmental hazards may be at increased risk of various health problems. Exposure‐related, adverse, heritable, human health outcomes currently receiving increased attention by public health professionals are fertility and pregnancy complications, birth defects, and developmental abnormalities. Well‐conducted environmental epidemiology studies on human populations would provide the most relevant data for quantifying relationships between exposure levels and adverse pregnancy‐ related outcomes. However, useful information from observational data on humans is often limited in both quantity and quality. So, despite the obvious species‐to‐species extrapolation problem, controlled laboratory experiments on rodents are commonly conducted to provide developmental toxicology data. This article focuses specifically on developmental toxicology studies, where pregnant rodents are exposed to a suspected harmful agent during the period of major fetal organogenesis and structural development. It is well known that an inherent characteristic of data from such rodent teratology studies is the so‐calledlitter effect, i.e. the tendency for littermates all to respond in the same way to stimuli, unlike animals from different litters. Litter effects seem to be present in almost all developmental toxicology studies, and data analyses that do not appropriately account for these litter effects can lead to erroneous statistical inferences.
Longitudinal Studies
Authors: Dean C. B. , Hu X. J.
Published: September 2014

A longitudinal study observes its subjects repeatedly over time. The subjects can be individuals or pre existing groups of interest, such as species and regions, and the time refers to the metameter for the occasions of observation. Longitudinal data allow one to separate cohort and time effects. This article summarizes the special features of longitudinal studies, and overviews statistical study design and data analysis in longitudinal settings.
Mixed Outcomes
Authors: Molenberghs Geert , Geys Helena
Published: September 2014

Measurements of both continuous and discrete outcomes are encountered in many statistical problems. A common example is a developmental toxicity study, which typically involves exposing timepregnant animals (rats, mice) to an environmental agent during major organogenesis. The dams are sacrificed prior to normal delivery, at which time the uterus is removed and thoroughly examined. Among viable fetuses, the incidence of any malformation (binary data) and reductions in fetal weight (continuous data) are typically of primary concern, since both have been found to be sensitive indicators of a toxic effect. This motivates the formulation of a joint distribution with mixed continuous and discrete outcomes.
Population Health Surveillance
Authors: Lawson Andrew B.
Published: September 2014

This article described the basic issues and principles underlying Population health surveillance. First, temporal and then spatial and spatio‐temporal aspects of the problem are considered. The emphasis is on change‐point methods and jump detection methods in time and clustering in space. The intersection of space and time leads to the concept of persistence of features.
Spatial Scan Statistics
Authors: Zhang Tonglin
Published: September 2014

This article reviews the spatial scan statistic, including its definition, adjustment for overdispersion, bootstrap methods for
p
‐value computation, and selected software for implementation.
Aquatic Toxicology
Authors: Bailer A. John , Oris James T.
Published: September 2014

Water is the key to life, and aquatic toxicology evaluates the potential adverse outcomes associated with exposure to contaminated waters. These adverse outcomes can be observed at all trophic levels and can be framed at differing levels of ecosystem function. Statistical analysis of concentration‐response relationships provides one foundation for evaluating the impact of toxicants on aquatic systems and for setting exposure limits to such toxicants. This entry describes stressors on aquatic systems, considers ecosystem impact of stressors, reviews statistical methods that have been used for evaluating these impacts and considers current and future challenges for evaluating aquatic toxicants.
Capture‐Recapture Methodology
Authors: Gould William R. , Kendall William L.
Published: September 2014

Capture‐recapture methods were initially developed to estimate human population abundance, but since that time have seen widespread use for fish and wildlife populations to estimate and model various parameters of population, metapopulation, and disease dynamics. Repeated sampling of marked animals provides information for estimating abundance and tracking the fate of individuals in the face of imperfect detection. Mark types have evolved from clipping or tagging to use of noninvasive methods such as photography of natural markings and DNA collection from feces. Survival estimation has been emphasized more recently as have transition probabilities between life history states and/or geographical locations, even where some states are unobservable or uncertain. Sophisticated software has been developed to handle highly parameterized models, including environmental and individual covariates, to conduct model selection, and to employ various estimation approaches such as maximum likelihood and Bayesian approaches. With these user‐friendly tools, complex statistical models for studying population dynamics have been made available to ecologists. The future will include a continuing trend toward integrating data types, both for tagged and untagged individuals, to produce more precise and robust population models.
Change, Detecting
Authors: Esterby Sylvia R.
Published: September 2014

Fundamental to the assessment of the effect of human activities on the environment is the detection of changes in environmental systems. It may be of interest to detect changes occurring over time, over space, or over both time and space. Although closely linked to the determination of status and the estimation of the size and components of change, detection is the primary consideration here. Methods for detecting change include: (i) graphical methods, exploratory, and more formal; (ii) tests of hypotheses, where the hypothesis characterizes the original status; and (iii) diagnostic tests that detect departures from a specified model. Most methods considered in this article are for changes over a single dimension and will often have been developed for data collected over time. However, such methods will usually be applicable to data collected in one dimension over space. Datasets for which more than one dimension needs to be taken into account generally require more modeling and thus are less often investigated from the detection point of view.
Detection Limits
Authors: Walshaw David
Published: September 2014

In analytical chemistry, the
detection limit
is the lowest level of an analyte that can reliably be detected by a well‐defined operating procedure. It is often confused with the
decision limit
, which is a threshold of measurement used to determine whether or not the analyte is present in a particular study. We discuss the history and confusion relating to the definition in a univariate context. We consider the detection limit as a function of the sources of variation within an operating procedure. Estimation of the detection limit assuming constant variance in one‐level designs and calibration designs is described, as well as a brief treatment of the assumption of non‐constant variance. We outline modifications for multiple future detection decisions. Finally we consider approaches to multivariate detection, when decisions are based on more than one quantitative signal.
Echelon Analysis
Authors: Patil G. P.
Published: September 2014

Quantitative spatial data are important inputs for fueling the engines of many environmental models that determine future implications of current resource use, policies, and interventions. End products of applying such models are often mappings of indexes for level of potential environmental impact, which then become guides to allocation of economic and technical resources for amelioration. Errors in quantitative spatial data will propagate through environmental models and find expression in the resulting impact indexes. However, the consequences of such errors for decision making may well depend upon where the errors occur. There may be relatively little confusion introduced by moderate errors occurring in a vicinity that otherwise has consistently high values of a variable. In contrast, errors compound confusion in areas that are highly variable. Errors can also substantially distort the apparent state of areas that otherwise have consistently low values of a variable. It is therefore desirable to have a systematic means of determining spatial organization in mappings of quantitative variables, both for input variables to environmental models and for indexes of potential impact generated by the models. Modern computer capabilities for visualization of surfaces are helpful in this regard, but their interpretation is subjective.
Echelons
are a method for objectively determining quantitative spatial structure for direct mapping, either with or without computer‐assisted visualization. Thus, they can facilitate analysis of errors associated with environmental models that take quantitative layers as input, or produce quantitative output layers, or both.
Ecological Study Design
Authors: Sheppard Lianne
Published: September 2014

The purposes of ecological studies range from descriptive (e.g. hypothesis‐generating) to inferential. The target of inference may be the group (calledecological inference) or the individual (calledbiological inference). Ecological studies are most appropriate for assessing the effects of interventions on populations, although the inference can be limited relative to an individual‐level study. Their applicability to etiological hypotheses about individuals is much more controversial, due to the risk of committing theecological fallacy. This fallacy is present when characteristics of individuals are wrongly inferred from grouped data. Although these reservations have a sound basis, most ecological study literature does not distinguish between issues inherent to the analysis of opportunistic observational data, and those pertinent to valid biological inference from group‐level analyses.
E
nvironmental
I
ndices
Authors: Dobbie Melissa J. , Dail David
Published: September 2014

An environmental index is the combination of multiple sources of information (i.e., indicators of ecological responses) about an environmental system (e.g., a stream) from potentially varying attributes of that system (e.g., instream processes, ecological processes, species richness, riparian vegetation, etc.). Environmental indices are typically developed to provide an overall snapshot of some feature of the environmental system but they are also used to compare similar environmental systems. The construction of an environmental index requires careful consideration of several important aspects of the individual environmental indicators that contribute to it, namely,

defining a theoretical framework for supporting indicator selection;

data preparation;

standardization of the potentially disparate indicators so that they can easily be combined into an index;

weighting and aggregation of the individual indicators; and

robustness and sensitivity of the decisions made in constructing an environmental index.

By considering all five steps, there is a better chance of producing a transparent, objective, and defensible summary of the attribute of the environmental system.
Escape Trajectory
Authors: Domenici Paolo
Published: September 2014

Escape responses consist of sudden accelerations as reactions to threatening stimuli and are present in most animals as a means of avoiding predation. Escape responses are currently receiving increased attention as valuable models for animal behavior, ecology, and neurobiology. The path along which an animal moves during an escape response (its escape trajectory) has attracted the interest of ecologists and behaviorists in relation to its functional role in predator–prey interactions. Escape trajectories (ETs) as considered in this article refer to the initial prey response to a predator's attack. Such a trajectory should be measured at the end of the main rotational motion present during the escape response, which usually corresponds to a specific kinematic stage of the animal's locomotion. Beyond this stage, prey may continue escaping along a zigzag path, especially if predators follow up their attack with a chase.
Forest‐Fire Models
Authors: Preisler Haiganoush K. , Ager Alan A.
Published: September 2014

For applied mathematicians forest‐fire models refer mainly to a nonlinear dynamic system often used to simulate spread of fire. For forest managers forest‐fire models may pertain to any of the three phases of fire management: prefire planning (fire risk models), fire suppression (fire behavior models), and postfire evaluation (fire effects models). In this context forest‐fire models may be statistical, rule‐based, process‐based, or a combination of all three.
Hydrological Extremes
Authors: Katz Richard W.
Published: September 2014

An accurate estimation of the probability of occurrence of an extreme hydrological event is often required for the effective development and management of water resources. Examples include characterizing extreme rainfall event magnitudes to predict urban runoff, determining river flow magnitudes to design a culvert or bridge opening at a road crossing, and determining the likely severity of a drought event during the design life of a water supply system. In each of these examples, an understanding of the hydrological response of a watershed is essential in order to obtain a reliable estimate of the relationship between extreme hydrological event magnitudes and the probability of these events occurring. The role of the statistical theory of extreme values is emphasized.
Impact Assessment: Assessing a Local Biological Effect With Before and After Data
Authors: Stewart‐oaten Allan
Published: September 2014

The design and analysis of monitoring studies to assess chronic biological effects of anthropogenic environmental change when data can be gathered before the change are discussed. Intervention Analysis compares Before and After time series at an Impact site. A special case, sometimes useful when the anticipated effects are “local,” is Before‐After, Control‐Impact (BACI), using comparison sites as covariates to reduce extraneous variance and serial correlation. Both sampling error and natural temporal processes cause uncertainty in inferences: both must be modeled. The models are themselves uncertain. The Impact site is not randomly selected, so these are observational studies, not experiments. Whether and how the change caused the “effects” must be based on their timing and on studies of mechanisms.