Heterogeneity, or mixtures, are ubiquitous in genetics. Even for data as simple as mono-genic diseases, populations are a mixture of affected and unaffected individuals. Still, most statistical genetic association analyses, designed to map genes for diseases and other genetic traits, ignore this phenomenon. In this book, we document methods that incorporate heterogeneity into the design and analysis of genetic and genomic association data. Among the key qualities of our developed statistics is that they include mixture parameters as part of the statistic, a unique component for tests of association. A critical feature of this work is the inclusion of at least one heterogeneity parameter when performing statistical power and sample size calculations for tests of genetic association. We anticipate that this book will be useful to researchers who want to estimate heterogeneity in their data, develop or apply genetic association statistics where heterogeneity exists, and accurately evaluate statistical power and sample size for genetic association through the application of robust experimental design.

This User’s Guide is a resource for investigators and stakeholders who develop and review observational comparative effectiveness research protocols. It explains how to (1) identify key considerations and best practices for research design; (2) build a protocol based on these standards and best practices; and (3) judge the adequacy and completeness of a protocol. Eleven chapters cover all aspects of research design, including: developing study objectives, defining and refining study questions, addressing the heterogeneity of treatment effect, characterizing exposure, selecting a comparator, defining and measuring outcomes, and identifying optimal data sources. Checklists of guidance and key considerations for protocols are provided at the end of each chapter. The User’s Guide was created by researchers affiliated with AHRQ’s Effective Health Care Program, particularly those who participated in AHRQ’s DEcIDE (Developing Evidence to Inform Decisions About Effectiveness) program. Chapters were subject to multiple internal and external independent reviews. More more information, please consult the Agency website: www.effectivehealthcare.ahrq.gov)

An attractive, promising, and frustrating feature of ecology is its complex ity, both conceptual and observational. Increasing acknowledgment of the importance of scale testifies to the shifting focus in large areas of ecology. In the rush to explore problems of scale, another general aspect of ecolog ical systems has been given less attention. This aspect, equally important, is heterogeneity. Its importance lies in the ubiquity of heterogeneity as a feature of ecological systems and in the number of questions it raises questions to which answers are not readily available. What is heterogeneity? Does it differ from complexity? What dimensions need be considered to evaluate heterogeneity ade quately? Can heterogeneity be measured at various scales? Is heterogeneity apart of organization of ecological systems? How does it change in time and space? What are the causes of heterogeneity and causes of its change? This volume attempts to answer these questions. It is devoted to iden tification of the meaning, range of applications, problems, and methodol ogy associated with the study of heterogeneity. The coverage is thus broad and rich, and the contributing authors have been encouraged to range widely in discussions and reflections. vi Preface The chapters are grouped into themes. The first group focuses on the conceptual foundations (Chapters 1-5). These papers exarnine the meaning of the term, historical developments, and relations to scale. The second theme is modeling population and interspecific interactions in hetero geneous environments (Chapters 6 and 7).

This book presents a multi-market framework of market and policy analysis that explicitly accounts for the empirically relevant heterogeneity in consumer preferences and producer characteristics. The explicit consideration of consumer and producer heterogeneity represents a significant departure from the representative consumer and producer that have been at the center of most of the literature on market and policy analysis, and enables the distributional impacts of changes in market conditions and policies to be fully identified. The framework is used to analyze the system-wide market and welfare impacts of a number of changes in market conditions (like changes in consumer preferences, costs and market structure) and policies (like subsidies and taxes) on one of the products in the system. Consistent with a priori expectations, the use of the framework unveils impacts masked by the conventional market and policy analysis.

The papers in this volume present an excellent sampling of the best of current research in labor economics, combining the most sophisticated theory and econometric methods with high-quality data on a variety of problems. Originally presented at a Universities-National Bureau Committee for Economic Research conference on labor markets in 1978, and not published elsewhere, the thirteen papers treat four interrelated themes: labor mobility, job turnover, and life-cycle dynamics; the analysis of unemployment compensation and employment policy; labor market discrimination; and labor market information and investment. The Introduction by Sherwin Rosen provides a thoughtful guide to the contents of the papers and offers suggestions for continuing research.

The Agency for Healthcare Research and Quality (AHRQ) commissioned the RTI International–University of North Carolina at Chapel Hill (RTI-UNC) Evidence-based Practice Center (EPC) to explore how systematic review groups have dealt with clinical heterogeneity and to seek out best practices for addressing clinical heterogeneity in systematic reviews (SRs) and comparative effectiveness reviews (CERs). Such best practices, to the extent they exist, may enable AHRQ's EPCs to address critiques from patients, clinicians, policymakers, and other proponents of health care about the extent to which “average” estimates of the benefits and harms of health care interventions apply to individual patients or to small groups of patients sharing similar characteristics. Such users of reviews often assert that EPC reviews typically focus on broad populations and, as a result, often lack information relevant to patient subgroups that are of particular concern to them. More important, even when EPCs evaluate literature on homogeneous groups, there may be varying individual treatment for no apparent reason, indicating that average treatment effect does not point to the best treatment for any given individual. Thus, the health care community is looking for better ways to develop information that may foster better medical care at a “personal” or “individual” level. To address our charge for this methods project, the EPC set out to answer six key questions (KQ). Key questions for methods report on clinical heterogeneity include: 1. What is clinical heterogeneity? a. How has it been defined by various groups? b. How is it distinct from statistical heterogeneity? c. How does it fit with other issues that have been addressed by the AHRQ Methods Manual for CERs? 2. How have systematic reviews dealt with clinical heterogeneity in the key questions? a. What questions have been asked? b. How have they pre-identified population subgroups with common clinical characteristics that modify their intervention-outcome association? c. What are best practices in key questions and how these subgroups have been identified? 3. How have systematic reviews dealt with clinical heterogeneity in the review process? a. What do guidance documents of various systematic review groups recommend? b. How have EPCs handled clinical heterogeneity in their reviews? c. What are best practices in searching for and interpreting results for particular subgroups with common clinical characteristics that may modify their intervention-outcome association? 4. What are critiques in how systematic reviews handle clinical heterogeneity? a. What are critiques from specific reviews (peer and public) on how EPCs handled clinical heterogeneity? b. What general critiques (in the literature) have been made against how systematic reviews handle clinical heterogeneity? 5. What evidence is there to support how to best address clinical heterogeneity in a systematic review? 6. What questions should an EPC work group on clinical heterogeneity address? Heterogeneity (of any type) in EPC reviews is important because its appearance suggests that included studies differed on one or more dimensions such as patient demographics, study designs, coexisting conditions, or other factors. EPCs then need to clarify for clinical and other audiences, collectively referred to as stakeholders, what are the potential causes of the heterogeneity in their results. This will allow the stakeholders to understand whether and to what degree they can apply this information to their own patients or constituents. Of greatest importance for this project was clinical heterogeneity, which we define as the variation in study population characteristics, coexisting conditions, cointerventions, and outcomes evaluated across studies included in an SR or CER that may influence or modify the magnitude of the intervention measure of effect (e.g., odds ratio, risk ratio, risk difference).

Heterogeneity of Function in Numerical Cognition presents the latest updates on ongoing research and discussions regarding numerical cognition. With great individual differences in the development or function of numerical cognition at neuroanatomical, neuropsychological, behavioral, and interactional levels, these issues are important for the achievement of a comprehensive understanding of numerical cognition, hence its brain basis, development, breakdown in brain-injured individuals, and failures to master mathematical skills. These functions are essential for the proper development of numerical cognition. - Provides an innovative reference on the emerging field of numerical cognition and the branches that converge on this diverse cognitive domain - Includes an overview of the multiple disciplines that comprise numerical cognition - Focuses on factors that influence numerical cognition, such as language, executive attention, memory and spatial processing - Features an innovative organization with each section providing a general overview, developmental research, and evidence from neurocognitive studies

Genetic alterations in cancer, in addition to being the fundamental drivers of tumorigenesis, can give rise to a variety of metabolic adaptations that allow cancer cells to survive and proliferate in diverse tumor microenvironments. This metabolic flexibility is different from normal cellular metabolic processes and leads to heterogeneity in cancer metabolism within the same cancer type or even within the same tumor. In this book, we delve into the complexity and diversity of cancer metabolism, and highlight how understanding the heterogeneity of cancer metabolism is fundamental to the development of effective metabolism-based therapeutic strategies. Deciphering how cancer cells utilize various nutrient resources will enable clinicians and researchers to pair specific chemotherapeutic agents with patients who are most likely to respond with positive outcomes, allowing for more cost-effective and personalized cancer therapeutic strategies.

This groundbreaking work connects the knowledge of system function developed in ecosystem ecology with landscape ecology's knowledge of spatial structure. The book elucidates the challenges faced by ecosystem scientists working in spatially heterogeneous systems, relevant conceptual approaches used in other disciplines and in different ecosystem types, and the importance of spatial heterogeneity in conservation resource management.

There is a new emerging interest in the effects of gaps and patches on succession and biodiversity. This innovative volume is a synthesis of studies of plant responses to temporal and spatial heterogeneity, the exploitation of resources from pulses and patches by plants, and their competition with neighbors in the face of this variability.Aboveground, the book focuses upon the nature of canopy patchiness, consequences of this heterogeneity for the light environment, and the mechanisms by which plants respond to and exploit this patchiness. Belowground, the text explores the heterogeneity of soil environments and how root systems obtain nutrients and water in the context of this temporal and spatial variability. As a new reference in an evolving and growing field, this text is sure to be a valuable tool for researchers and advanced students in plant physiology, ecology, agronomy, and forestry alike.