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Statistical methods in spatial epidemiology

01 Jan 2001-Iss: 1, pp 1
TL;DR: The nature of Spatial Epidemiology, the nature of modelling, and some of the approaches explored: Exploratory Approaches, Parametric Estimation and Inference.
Abstract: Preface and Acknowledgements to Second Edition Preface and Acknowledgements I: The Nature of Spatial Epidemiology 1 Definitions, Terminolgy and Data Sets 11 Map Hypotheses and Modelling Approaches 12 Definitions and Data Examples 13 Further definitions 14 Some Data Examples 2Scales of Measurement and Data Availability 21 Small Scale 22 Large Scale 23 Rate Dependence 24 DataQuality and the Ecological Fallacy 25 Edge Eects 3Geographical Representation and Mapping 31 Introduction and Definitions 32 Maps and Mapping 33 Statistical Accuracy 34 Aggregation 35 Mapping Issues related toAggregated Data 36 Conclusions 4Basic Models 41 Sampling Considerations 42 Likelihood-based and Bayesian Approaches 43 Point EventModels 44 CountModels 5Exploratory Approaches, Parametric Estimation and Inference 51 ExploratoryMethods 52 Parameter Estimation 53 Residual Diagnostics 54 Hypothesis Testing 55 Edge Eects II:Important Problems in Spatial Epidemiology 6Small Scale: Disease Clustering 61 Definition of Clusters and Clustering 62 Modelling Issues 63 Hypothesis Tests for Clustering 64 Space-Time Clustering 65 Clustering Examples 66 OtherMethods related to clustering 7Small Scale: Putative Sources of Hazard 71 Introduction 72 StudyDesign 73 Problems of Inference 74 Modelling the Hazard Exposure Risk 75 Models for Case Event Data 76 ACase Event Example 77 Models for CountData 78 ACountData Example 79 OtherDirections 8 Large Scale: Disease Mapping 81 Introduction 82 Simple Statistical Representation 83 BasicModels 84 AdvancedMethods 85 Model Variants and Extensions 86 ApproximateMethods 87 MultivariateMethods 88 Evaluation ofModel Performance 89 Hypothesis Testing in DiseaseMapping 810 Space-Time DiseaseMapping 811 Spatial Survival and longitudinal data 812 DiseaseMapping: Case Studies 9Ecological Analysis and Scale Change 91 Ecological Analysis: Introduction 92 Small-ScaleModelling Issues 93 Changes of Scale andMAUP 94 A Simple Example: Sudden Infant Death in North Carolina 95 ACase Study: Malaria and IDDM 10Infectious Disease Modelling 101 Introduction 102 GeneralModelDevelopment 103 SpatialModelDevelopment 104 Modelling Special Cases for Individual Level Data 105 Survival Analysis with spatial dependence 106 Individual level data example 107 Underascertainment and Censoring 108 Conclusions 11Large Scale: Surveillance 111 Process ControlMethodology 112 Spatio-Temporal Modelling 113 Spatio-TemporalMonitoring 114 Syndromic Surveillance 115 Multivariate-Mulitfocus Surveillance 116 Bayesian Approaches 117 Computational Considerations 118 Infectious Diseases 119 Conclusions Appendix A:Monte Carlo Testing, Parametric Bootstrap and Simulation Envelopes Appendix B:Markov ChainMonte Carlo Methods Appendix C:Algorithms and Software Appendix D: Glossary of Estimators Appendix E:Software Bibliography Index
Citations
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Journal ArticleDOI
TL;DR: A number of conceptual issues pertaining to the implementation of an explicit "spatial" perspective in applied econometrics are reviewed, both from a theory-driven as well as from a data-driven perspective.

1,250 citations


Cites background from "Statistical methods in spatial epid..."

  • ...Examples can be found in Gotway and Stroup (1997), Waller et al. (1997b), Best et al. (1999), Lawson (2001), MacNab and Dean (2002), among others....

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Journal ArticleDOI
TL;DR: This 2007 global P. falciparum malaria endemicity map is the first of a series with which it will be possible to monitor and evaluate the progress of this intervention process, and shows significant opportunities for malaria control in Africa and for malaria elimination elsewhere.
Abstract: Transmission intensity affects almost all aspects of malaria epidemiology and the impact of malaria on human populations. Maps of transmission intensity are necessary to identify populations at different levels of risk and to evaluate objectively options for disease control. To remain relevant operationally, such maps must be updated frequently. Following the first global effort to map Plasmodium falciparum malaria endemicity in 2007, this paper describes the generation of a new world map for the year 2010. This analysis is extended to provide the first global estimates of two other metrics of transmission intensity for P. falciparum that underpin contemporary questions in malaria control: the entomological inoculation rate (Pf EIR) and the basic reproductive number (PfR). Annual parasite incidence data for 13,449 administrative units in 43 endemic countries were sourced to define the spatial limits of P. falciparum transmission in 2010 and 22,212 P. falciparum parasite rate (Pf PR) surveys were used in a model-based geostatistical (MBG) prediction to create a continuous contemporary surface of malaria endemicity within these limits. A suite of transmission models were developed that link Pf PR to Pf EIR and PfR and these were fitted to field data. These models were combined with the Pf PR map to create new global predictions of Pf EIR and PfR. All output maps included measured uncertainty. An estimated 1.13 and 1.44 billion people worldwide were at risk of unstable and stable P. falciparum malaria, respectively. The majority of the endemic world was predicted with a median Pf EIR of less than one and a median PfRc of less than two. Values of either metric exceeding 10 were almost exclusive to Africa. The uncertainty described in both Pf EIR and PfR was substantial in regions of intense transmission. The year 2010 has a particular significance as an evaluation milestone for malaria global health policy. The maps presented here contribute to a rational basis for control and elimination decisions and can serve as a baseline assessment as the global health community looks ahead to the next series of milestones targeted at 2015.

1,161 citations


Cites methods from "Statistical methods in spatial epid..."

  • ...MBG provides a formal statistical interpretation of classical geostatistical tools for spatial prediction [39–41] and allows the incorporation of Bayesian methods of statistical inference [42,43]....

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Book
15 Jul 2004
TL;DR: In this paper, the authors present a method for estimating risk and risk of cancer in public health data using statistical methods for spatial data in the context of geographic information systems (GISs).
Abstract: Preface.Acknowledgments.1 Introduction.1.1 Why Spatial Data in Public Health?1.2 Why Statistical Methods for Spatial Data?1.3 Intersection of Three Fields of Study.1.4 Organization of the Book.2 Analyzing Public Health Data.2.1 Observational vs. Experimental Data.2.2 Risk and Rates.2.2.1 Incidence and Prevalence.2.2.2 Risk.2.2.3 Estimating Risk: Rates and Proportions.2.2.4 Relative and Attributable Risks.2.3 Making Rates Comparable: Standardized Rates.2.3.1 Direct Standardization.2.3.2 Indirect Standardization.2.3.3 Direct or Indirect?2.3.4 Standardizing to What Standard?2.3.5 Cautions with Standardized Rates.2.4 Basic Epidemiological Study Designs.2.4.1 Prospective Cohort Studies.2.4.2 Retrospective Case-Control Studies.2.4.3 Other Types of Epidemiological Studies.2.5 Basic Analytic Tool: The Odds Ratio.2.6 Modeling Counts and Rates.2.6.1 Generalized Linear Models.2.6.2 Logistic Regression.2.6.3 Poisson Regression.2.7 Challenges in the Analysis of Observational Data.2.7.1 Bias.2.7.2 Confounding.2.7.3 Effect Modification.2.7.4 Ecological Inference and the Ecological Fallacy.2.8 Additional Topics and Further Reading.2.9 Exercises.3 Spatial Data.3.1 Components of Spatial Data.3.2 An Odyssey into Geodesy.3.2.1 Measuring Location: Geographical Coordinates.3.2.2 Flattening the Globe: Map Projections and Coordinate Systems.3.2.3 Mathematics of Location: Vector and Polygon Geometry.3.3 Sources of Spatial Data.3.3.1 Health Data.3.3.2 Census-Related Data.3.3.3 Geocoding.3.3.4 Digital Cartographic Data.3.3.5 Environmental and Natural Resource Data.3.3.6 Remotely Sensed Data.3.3.7 Digitizing.3.3.8 Collect Your Own!3.4 Geographic Information Systems.3.4.1 Vector and Raster GISs.3.4.2 Basic GIS Operations.3.4.3 Spatial Analysis within GIS.3.5 Problems with Spatial Data and GIS.3.5.1 Inaccurate and Incomplete Databases.3.5.2 Confidentiality.3.5.3 Use of ZIP Codes.3.5.4 Geocoding Issues.3.5.5 Location Uncertainty.4 Visualizing Spatial Data.4.1 Cartography: The Art and Science of Mapmaking.4.2 Types of Statistical Maps.MAP STUDY: Very Low Birth Weights in Georgia Health Care District 9.4.2.1 Maps for Point Features.4.2.2 Maps for Areal Features.4.3 Symbolization.4.3.1 Map Generalization.4.3.2 Visual Variables.4.3.3 Color.4.4 Mapping Smoothed Rates and Probabilities.4.4.1 Locally Weighted Averages.4.4.2 Nonparametric Regression.4.4.3 Empirical Bayes Smoothing.4.4.4 Probability Mapping.4.4.5 Practical Notes and Recommendations.CASE STUDY: Smoothing New York Leukemia Data.4.5 Modifiable Areal Unit Problem.4.6 Additional Topics and Further Reading.4.6.1 Visualization.4.6.2 Additional Types of Maps.4.6.3 Exploratory Spatial Data Analysis.4.6.4 Other Smoothing Approaches.4.6.5 Edge Effects.4.7 Exercises.5 Analysis of Spatial Point Patterns.5.1 Types of Patterns.5.2 Spatial Point Processes.5.2.1 Stationarity and Isotropy.5.2.2 Spatial Poisson Processes and CSR.5.2.3 Hypothesis Tests of CSR via Monte Carlo Methods.5.2.4 Heterogeneous Poisson Processes.5.2.5 Estimating Intensity Functions.DATA BREAK: Early Medieval Grave Sites.5.3 K Function.5.3.1 Estimating the K Function.5.3.2 Diagnostic Plots Based on the K Function.5.3.3 Monte Carlo Assessments of CSR Based on the K Function.DATA BREAK: Early Medieval Grave Sites.5.3.4 Roles of First- and Second-Order Properties.5.4 Other Spatial Point Processes.5.4.1 Poisson Cluster Processes.5.4.2 Contagion/Inhibition Processes.5.4.3 Cox Processes.5.4.4 Distinguishing Processes.5.5 Additional Topics and Further Reading.5.6 Exercises.6 Spatial Clusters of Health Events: Point Data for Cases and Controls.6.1 What Do We Have? Data Types and Related Issues.6.2 What Do We Want? Null and Alternative Hypotheses.6.3 Categorization of Methods.6.4 Comparing Point Process Summaries.6.4.1 Goals.6.4.2 Assumptions and Typical Output.6.4.3 Method: Ratio of Kernel Intensity Estimates.DATA BREAK: Early Medieval Grave Sites.6.4.4 Method: Difference between K Functions.DATA BREAK: Early Medieval Grave Sites.6.5 Scanning Local Rates.6.5.1 Goals.6.5.2 Assumptions and Typical Output.6.5.3 Method: Geographical Analysis Machine.6.5.4 Method: Overlapping Local Case Proportions.DATA BREAK: Early Medieval Grave Sites.6.5.5 Method: Spatial Scan Statistics.DATA BREAK: Early Medieval Grave Sites.6.6 Nearest-Neighbor Statistics.6.6.1 Goals.6.6.2 Assumptions and Typical Output.6.6.3 Method: q Nearest Neighbors of Cases.CASE STUDY: San Diego Asthma.6.7 Further Reading.6.8 Exercises.7 Spatial Clustering of Health Events: Regional Count Data.7.1 What Do We Have and What Do We Want?7.1.1 Data Structure.7.1.2 Null Hypotheses.7.1.3 Alternative Hypotheses.7.2 Categorization of Methods.7.3 Scanning Local Rates.7.3.1 Goals.7.3.2 Assumptions.7.3.3 Method: Overlapping Local Rates.DATA BREAK: New York Leukemia Data.7.3.4 Method: Turnbull et al.'s CEPP.7.3.5 Method: Besag and Newell Approach.7.3.6 Method: Spatial Scan Statistics.7.4 Global Indexes of Spatial Autocorrelation.7.4.1 Goals.7.4.2 Assumptions and Typical Output.7.4.3 Method: Moran's I .7.4.4 Method: Geary's c.7.5 Local Indicators of Spatial Association.7.5.1 Goals.7.5.2 Assumptions and Typical Output.7.5.3 Method: Local Moran's I.7.6 Goodness-of-Fit Statistics.7.6.1 Goals.7.6.2 Assumptions and Typical Output.7.6.3 Method: Pearson's chi2.7.6.4 Method: Tango's Index.7.6.5 Method: Focused Score Tests of Trend.7.7 Statistical Power and Related Considerations.7.7.1 Power Depends on the Alternative Hypothesis.7.7.2 Power Depends on the Data Structure.7.7.3 Theoretical Assessment of Power.7.7.4 Monte Carlo Assessment of Power.7.7.5 Benchmark Data and Conditional Power Assessments.7.8 Additional Topics and Further Reading.7.8.1 Related Research Regarding Indexes of Spatial Association.7.8.2 Additional Approaches for Detecting Clusters and/or Clustering.7.8.3 Space-Time Clustering and Disease Surveillance.7.9 Exercises.8 Spatial Exposure Data.8.1 Random Fields and Stationarity.8.2 Semivariograms.8.2.1 Relationship to Covariance Function and Correlogram.8.2.2 Parametric Isotropic Semivariogram Models.8.2.3 Estimating the Semivariogram.DATA BREAK: Smoky Mountain pH Data.8.2.4 Fitting Semivariogram Models.8.2.5 Anisotropic Semivariogram Modeling.8.3 Interpolation and Spatial Prediction.8.3.1 Inverse-Distance Interpolation.8.3.2 Kriging.CASE STUDY: Hazardous Waste Site Remediation.8.4 Additional Topics and Further Reading.8.4.1 Erratic Experimental Semivariograms.8.4.2 Sampling Distribution of the Classical Semivariogram Estimator.8.4.3 Nonparametric Semivariogram Models.8.4.4 Kriging Non-Gaussian Data.8.4.5 Geostatistical Simulation.8.4.6 Use of Non-Euclidean Distances in Geostatistics.8.4.7 Spatial Sampling and Network Design.8.5 Exercises.9 Linking Spatial Exposure Data to Health Events.9.1 Linear Regression Models for Independent Data.9.1.1 Estimation and Inference.9.1.2 Interpretation and Use with Spatial Data.DATA BREAK: Raccoon Rabies in Connecticut.9.2 Linear Regression Models for Spatially Autocorrelated Data.9.2.1 Estimation and Inference.9.2.2 Interpretation and Use with Spatial Data.9.2.3 Predicting New Observations: Universal Kriging.DATA BREAK: New York Leukemia Data.9.3 Spatial Autoregressive Models.9.3.1 Simultaneous Autoregressive Models.9.3.2 Conditional Autoregressive Models.9.3.3 Concluding Remarks on Conditional Autoregressions.9.3.4 Concluding Remarks on Spatial Autoregressions.9.4 Generalized Linear Models.9.4.1 Fixed Effects and the Marginal Specification.9.4.2 Mixed Models and Conditional Specification.9.4.3 Estimation in Spatial GLMs and GLMMs.DATA BREAK: Modeling Lip Cancer Morbidity in Scotland.9.4.4 Additional Considerations in Spatial GLMs.CASE STUDY: Very Low Birth Weights in Georgia Health Care District 9.9.5 Bayesian Models for Disease Mapping.9.5.1 Hierarchical Structure.9.5.2 Estimation and Inference.9.5.3 Interpretation and Use with Spatial Data.9.6 Parting Thoughts.9.7 Additional Topics and Further Reading.9.7.1 General References.9.7.2 Restricted Maximum Likelihood Estimation.9.7.3 Residual Analysis with Spatially Correlated Error Terms.9.7.4 Two-Parameter Autoregressive Models.9.7.5 Non-Gaussian Spatial Autoregressive Models.9.7.6 Classical/Bayesian GLMMs.9.7.7 Prediction with GLMs.9.7.8 Bayesian Hierarchical Models for Spatial Data.9.8 Exercises.References.Author Index.Subject Index.

1,134 citations

Journal ArticleDOI
TL;DR: It is shown that identifying useful independent neighborhood effect parameters is impossible, as currently conceptualized with observational data, and randomized community trials are advocated as a superior research strategy.

710 citations


Cites background or methods from "Statistical methods in spatial epid..."

  • ...Yet another alternative is to apply techniques that capitalize on spatial autocorrelation, such as those used in spatial statistics (Doreian, 1981; Haining, 1990; Lawson, 2001)....

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  • ...Epidemiologists have long recognized that people residing in different areas have differing health outcomes (cf. Macintyre, Maciver, & Sooman, 1993; McMichael, 1999; Catalono & Pickett, 2000; Lawson, 2001)....

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  • ...…Susser & Susser, 1996; see DiezRoux, 1998), though one need not distinguish between them.1 Epidemiologists have long recognized that people residing in different areas have differing health outcomes (cf. Macintyre, Maciver, & Sooman, 1993; McMichael, 1999; Catalono & Pickett, 2000; Lawson, 2001)....

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  • ...Lawson, A. B. (2001). Statistical methods in spatial epidemiol-...

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  • ...34Yet another alternative is to apply techniques that capitalize on spatial autocorrelation, such as those used in spatial statistics (Doreian, 1981; Haining, 1990; Lawson, 2001)....

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Posted Content
TL;DR: A new concept for constructing prior distributions that is invariant to reparameterisations, have a natural connection to Jeffreys’ priors, seem to have excellent robustness properties, and allow this approach to define default prior distributions.
Abstract: In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys' priors, are designed to support Occam's razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations.

579 citations


Cites background from "Statistical methods in spatial epid..."

  • ...the sequence of base models interpretable and the parameters more orthogonal. Mapping disease incidence is a huge field within public health and epidemiology, and good introductions to the field exist (Lawson, 2006, 2013; Wakefield et al., 2000; Waller and Carlin, 2010). 13 1.0 10 Lag-one correlation Density 400 0.8 e time .hazard (a) (b) Figure 5: Panel (a) displays the posterior density (solid) and prior densi...

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References
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Book
12 Dec 2014
TL;DR: Applied mixed models in medicine, Applied mixed model in medicine , کتابخانه دیجیتال جندی شاپور اهواز
Abstract: Applied mixed models in medicine , Applied mixed models in medicine , کتابخانه دیجیتال جندی شاپور اهواز

1,629 citations

Journal ArticleDOI
TL;DR: A General Approach to Pooling Investigating Heterogeneity Pooling Tabular Data Individual Participant Data Dealing with Aspects of Study Quality Publication Bias Is Meta-Analysis a Valid Tool in Epidemiology?
Abstract: PREFACE FUNDAMENTAL ISSUES What is Epidemiology? Case Studies: The Work of Doll and Hill Populations and Samples Measuring Disease Measuring the Risk Factor Causality Studies Using Routine Data Study Design Data Analysis Exercises BASIC ANALYTICAL PROCEDURES Introduction Case Study Types of Variables Tables and Charts Inferential Techniques for Categorical Variables Descriptive Techniques for Quantitative Variables Inferences about Means Inferential Techniques for Non-Normal Data Measuring Agreement Assessing Diagnostic Tests Exercises ASSESSING RISK FACTORS Risk and Relative Risk Odds and Odds Ratio Relative Risk or Odds Ratio? Prevalence Studies Testing Association Risk Factors Measured at Several Levels Attributable Risk Rate and Relative Rate Measures of Difference Exercises CONFOUNDING AND INTERACTION Introduction The Concept of Confounding Identification of Confounders Assessing Confounding Standardization Mantel-Haenszel Methods The Concept of Interaction Testing for Interaction Dealing with Interaction Exercises COHORT STUDIES Design Considerations Analytical Considerations Cohort Life Tables Kaplan-Meier Estimation Comparison of Two Sets of Survival Probabilities The Person-Years Method Period-Cohort Analysis Exercises CASE-CONTROL STUDIES Basic Design Concepts Basic Methods of Analysis Selection of Cases Selection of Controls Matching The Analysis of Matched Studies Nested Case-Control Studies Case-Cohort Studies Case-Crossover Studies Exercises INTERVENTION STUDIES Introduction Ethical Considerations Avoidance of Bias Parallel Group Studies Cross-Over Studies Sequential Studies Allocation to Treatment Group Exercises SAMPLE SIZE DETERMINATION Introduction Power Testing a Mean Value Testing a Difference Between Means Testing a Proportion Testing a Relative Risk Case-Control Studies Complex Sampling Designs Concluding Remarks Exercises MODELLING QUANTITATIVE OUTCOME VARIABLES Statistical Models One Categorical Explanatory Variable One Quantitative Explanatory Variable Two Categorical Explanatory Variables Model Building General Linear Models Several Explanatory Variables Model Checking Confounding Longitudinal Data Non-Normal Alternatives Exercises MODELLING BINARY OUTCOME DATA Introduction Problems with Standard Regression Models Logistic Regression Interpretation of Logistic Regression Coefficients Generic Data Multiple Logistic Regression Models Tests of Hypotheses Confounding Interaction Model Checking Regression Dilution Case-Control Studies Outcomes with Several Ordered Levels Longitudinal Data Complex Sampling Designs Exercises MODELLING FOLLOW-UP DATA Introduction Basic Functions of Survival Time Estimating the Hazard Function Probability Models Proportional Hazards Regression Models The Cox Proportional Hazards Model The Weibull Proportional Hazards Model Model Checking Poisson Regression Pooled Logistic Regression Exercises META-ANALYSIS Reviewing Evidence Systematic Review A General Approach to Pooling Investigating Heterogeneity Pooling Tabular Data Individual Participant Data Dealing with Aspects of Study Quality Publication Bias Is Meta-Analysis a Valid Tool in Epidemiology? Exercises APPENDIX A: MATERIALS AVAILABLE FROM THE WEBSITE APPENDIX B: STATISTICAL TABLES APPENDIX C: EXAMPLE DATA SETS SOLUTIONS TO EXERCISES REFERENCES INDEX

811 citations

Book
13 Dec 1990
TL;DR: In this paper, a description of variable material sampling and estimation generalization, prediction, and classification relations between variables, covariance and correlation regression relations between individuals, similarity ordination analysis of dispersion and discrimination numerical classification, hierarchical systems numerical classification - non hierarchical methods spatial dependence nested sampling and analysis local estimation, kriging.
Abstract: Quantitative description of variable material sampling and estimation generalization, prediction, and classification relations between variables - covariance and correlation regression relations between individuals - similarity ordination analysis of dispersion and discrimination numerical classification - hierarchical systems numerical classification - non hierarchical methods spatial dependence nested sampling and analysis local estimation - kriging.

775 citations


"Statistical methods in spatial epid..." refers methods in this paper

  • ...the book by Webster and Oliver (1990), which was reviewed in Technometrics...

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Journal ArticleDOI
TL;DR: This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data and attempts to target applied statisticians and biomedical researchers in industry, public health organizations, contract research organizations, and academia.
Abstract: Mixed-effects models (or mixed models) provide a  exible and powerful tool for the analysis of data with a complex variance structure, such as correlated data. Linear mixed models originated speciŽ cally in the area of application. The motivation of this book is to satisfy the great demand by users from various applied backgrounds for clearer guidance on using the available methodology (e.g., theoretical concepts and their software implementation) more effectively. The authors refer to this book as a second version of their Ž rst book Linear Mixed Models in Practice (Verbeke and Molenberghs 1997). This book, however, is not presented as a second edition since a large range of new topics has been added and material kept from the Ž rst version has been reworked. The authors adopt the view that each type of outcome should be analyzed using instruments that exploit the nature of the data (i.e., each model family requires its own speciŽ c software tools). This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data. Over 125 illustrations are included in the book. This book gives emphasis to practice rather than mathematical rigor. Although enough theory is covered in the text to understand the strengths and weaknesses of mixed models, the authors emphasize the applied aspects of these. Hence, this book is explanatory rather than research oriented. It is mentioned that the authors attempt to target applied statisticians and biomedical researchers in industry, public health organizations, contract research organizations, and academia. I do believe that the book may serve as a useful reference to a broader audience (e.g., researchers in reliability engineering). Since practical examples are provided as well as discussion of the leading software utilization, it may also be appropriate as a textbook in an advanced undergraduate-level or a graduate-level course in an applied statistics program. This book is organized into 24 chapters. Excluding the Ž rst two and the last two chapters, it may also be divided into two parts. In the Ž rst part, comprising Chapters 3–13, emphasis is on the formulation and the Ž tting of, as well as on inference and diagnostics for, mixed models in general. In the second part, comprising Chapters 14–22, the problem of missing data is discussed in full detail, with emphasis on how to obtain valid inferences from observed longitudinal data and how to perform sensitivity analyses with respect to assumptions made about the dropout process. A more detailed structure follows. Chapter 1 introduces the scope, while Chapter 2 presents the examples used throughout the book. Chapters 3–9 provide the core about the linear mixed model. Chapters 10–13 discuss extensions to the original model and more advanced tools for model exploration and in uence diagnostics. Chapters 14–16 introduce the reader to basic incomplete longitudinal data concepts, such as dropout, which refers to the case in which all observations on a subject are obtained until a certain point in time. Chapters 17 and 18 discuss strategies to model incomplete longitudinal data, based on the linear mixed model. The sensitivity of such strategies to parametric assumptions is investigated in Chapters 19 and 20 (more technical material is deferred until Appendix B). Some additional missing data topics are presented in Chapters 21 and 22. Chapter 23 is devoted to design considerations, such as designing experiments with minimal risk of high losses in efŽ ciency due to dropout. Building on the methodology developed in the book, Chapter 24 presents Ž ve case studies. Appendix A reviews a number of software tools for Ž tting mixed models. The balanced mix of real data examples, modeling software, and theory makes this book a useful reference for practitioners using mixed models in their data analysis. Researchers will also Ž nd this book appealing for its extensive literature review, for the presentation of novel methodologies, and for its discussion about needed research. In this topic (e.g., p. 237: specialized software for Ž tting nonrandom dropout models; p. 296: methods that investigate the sensitivity of the results with respect to the model assumptions; p. 374: other sensitivity analysis approaches in the pattern-mixture content). It is mentioned in the Preface that selected macros (and programs) for tools discussed in the text, as well as publicly available datasets, can be found at Springer-Verlag’s URL: http://www.springer-ny.com/. The given URL is too general, and it took some time to access the information for this book. A more efŽ cient approach is referring the reader to the following URL: http://www.luc.ac.be/censtat/members/geertmpub.html, where the datasets can be found. At this same site, macros, errata, and updates of the materials in the book should be made available. Adding the following to the Preface would have been useful to the prospective reader: prerequisites for the technical material in the book, recommended outlines for undergraduateand graduate-level courses, and typographical conventions. Some minimum prerequisites for the technical material in the book, in my opinion, include a knowledge of calculus and linear algebra and a working knowledge of probability and statistics such as provided in advanced undergraduate or graduate courses in statistics, mathematics, and related Ž elds. Some knowledge of the SAS language is deŽ nitely desirable but not a prerequisite for following the material in the book. Great care has been taken in presenting the data analyses in a software-independent fashion. The format of this book consists of (1) presenting a research question, (2) translating it into a statistical model by means of algebraic notation, and (3) implementing such a model (for most cases) using a SAS code. Although most analyses were done with the M IXED procedure of the SAS software package (discussed in detail in Chap. 8), some other commercially available packages are discussed as well. Appendix A.3, for example, describes the built-in function lme() for analyzing linear mixed models in S and S-PLUS. (The companion function for nonlinear mixed models, nlme(), is also mentioned.) On pages 493–494, the reader should not be confused with mle() and nmle(), which should have read lme() and nlme(), respectively. In summary, the increasing popularity of mixed models is explained by the  exibility they offer in modeling complex data, by the handling of balanced and unbalanced data in a uniŽ ed framework, and by the availability of reliable and efŽ cient software for Ž tting them. This book provides an overview of the theory and application of linear mixed models in the analysis of correlated data. The scope of this book is restricted to linear mixed models for continuous outcomes. This book provides guidance on using the available methodology more effectively to practitioners from a wide variety of areas. Because of its discussion and detailed reviews, advanced students and researchers may beneŽ t from it as well.

37 citations

Journal ArticleDOI
TL;DR: A review of statistical methods in Soil and Land Resource Survey is given in this article, with a focus on statistical methods for land and water resource survey, and a review of the methods used.
Abstract: (1993). A Review of: “Statistical Methods in Soil and Land Resource Survey”. International Journal of Remote Sensing: Vol. 14, No. 2, pp. 391-392.

3 citations