Classification and regression trees are machine-learning methods for constructing prediction models from data. The models are obtained by recursively partitioning the data space and fitting a simple prediction model within each partition. As a result, the partitioning can be represented graphically as a decision tree. Classification trees are designed for dependent variables that take a finite number of unordered values, with prediction error measured in terms of misclassification cost. Regression trees are for dependent variables that take continuous or ordered discrete values, with prediction error typically measured by the squared difference between the observed and predicted values. This article gives an introduction to the subject by reviewing some widely available algorithms and comparing their capabilities, strengths, and weakness in two examples. © 2011 John Wiley & Sons, Inc. WIREs Data Mining Knowl Discov 2011 1 14-23 DOI: 10.1002/widm.8

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Technologies > Classification
Technologies > Machine Learning
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Technologies > Statistical Fundamentals

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Classification and regression trees

Importance Definitions of sepsis and septic shock were last revised in 2001. Considerable advances have since been made into the pathobiology (changes in organ function, morphology, cell biology, biochemistry, immunology, and circulation), management, and epidemiology of sepsis, suggesting the need for reexamination. Objective To evaluate and, as needed, update definitions for sepsis and septic shock. Process A task force (n = 19) with expertise in sepsis pathobiology, clinical trials, and epidemiology was convened by the Society of Critical Care Medicine and the European Society of Intensive Care Medicine. Definitions and clinical criteria were generated through meetings, Delphi processes, analysis of electronic health record databases, and voting, followed by circulation to international professional societies, requesting peer review and endorsement (by 31 societies listed in the Acknowledgment). Key Findings From Evidence Synthesis Limitations of previous definitions included an excessive focus on inflammation, the misleading model that sepsis follows a continuum through severe sepsis to shock, and inadequate specificity and sensitivity of the systemic inflammatory response syndrome (SIRS) criteria. Multiple definitions and terminologies are currently in use for sepsis, septic shock, and organ dysfunction, leading to discrepancies in reported incidence and observed mortality. The task force concluded the term severe sepsis was redundant. Recommendations Sepsis should be defined as life-threatening organ dysfunction caused by a dysregulated host response to infection. For clinical operationalization, organ dysfunction can be represented by an increase in the Sequential [Sepsis-related] Organ Failure Assessment (SOFA) score of 2 points or more, which is associated with an in-hospital mortality greater than 10%. Septic shock should be defined as a subset of sepsis in which particularly profound circulatory, cellular, and metabolic abnormalities are associated with a greater risk of mortality than with sepsis alone. Patients with septic shock can be clinically identified by a vasopressor requirement to maintain a mean arterial pressure of 65 mm Hg or greater and serum lactate level greater than 2 mmol/L (>18 mg/dL) in the absence of hypovolemia. This combination is associated with hospital mortality rates greater than 40%. In out-of-hospital, emergency department, or general hospital ward settings, adult patients with suspected infection can be rapidly identified as being more likely to have poor outcomes typical of sepsis if they have at least 2 of the following clinical criteria that together constitute a new bedside clinical score termed quickSOFA (qSOFA): respiratory rate of 22/min or greater, altered mentation, or systolic blood pressure of 100 mm Hg or less. Conclusions and Relevance These updated definitions and clinical criteria should replace previous definitions, offer greater consistency for epidemiologic studies and clinical trials, and facilitate earlier recognition and more timely management of patients with sepsis or at risk of developing sepsis.

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The Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Background: This study presents estimates of lifetime and 12-month prevalence of 14 DSM-III-R psychiatric disorders from the National Comorbidity Survey, the first survey to administer a structured psychiatric interview to a national probability sample in the United States. Methods: The DSM-III-R psychiatric disorders among persons aged 15 to 54 years in the noninstitutionalized civilian population of the United States were assessed with data collected by lay interviewers using a revised version of the Composite International Diagnostic Interview. Results: Nearly 50% of respondents reported at least one lifetime disorder, and close to 30% reported at least one 12-month disorder. The most common disorders were major depressive episode, alcohol dependence, social phobia, and simple phobia. More than half of all lifetime disorders occurred in the 14% of the population who had a history of three or more comorbid disorders. These highly comorbid people also included the vast majority of people with severe disorders. Less than 40% of those with a lifetime disorder had ever received professional treatment, and less than 20% of those with a recent disorder had been in treatment during the past 12 months. Consistent with previous risk factor research, it was found that women had elevated rates of affective disorders and anxiety disorders, that men had elevated rates of substance use disorders and antisocial personality disorder, and that most disorders declined with age and with higher socioeconomic status. Conclusions: The prevalence of psychiatric disorders is greater than previously thought to be the case. Furthermore, this morbidity is more highly concentrated than previously recognized in roughly one sixth of the population who have a history of three or more comorbid disorders. This suggests that the causes and consequences of high comorbidity should be the focus of research attention. The majority of people with psychiatric disorders fail to obtain professional treatment. Even among people with a lifetime history of three or more comorbid disorders, the proportion who ever obtain specialty sector mental health treatment is less than 50%. These results argue for the importance of more outreach and more research on barriers to professional help-seeking.

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Lifetime and 12-Month Prevalence of DSM-III-R Psychiatric Disorders in the United States: Results From the National Comorbidity Survey

Linear Mixed-Effects * Theory and Computational Methods for LME Models * Structure of Grouped Data * Fitting LME Models * Extending the Basic LME Model * Nonlinear Mixed-Effects * Theory and Computational Methods for NLME Models * Fitting NLME Models

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Mixed-Effects Models in S and S-PLUS

From the reviews of the First Edition. "An interesting, useful, and well-written book on logistic regression models... Hosmer and Lemeshow have used very little mathematics, have presented difficult concepts heuristically and through illustrative examples, and have included references."- Choice "Well written, clearly organized, and comprehensive... the authors carefully walk the reader through the estimation of interpretation of coefficients from a wide variety of logistic regression models . . . their careful explication of the quantitative re-expression of coefficients from these various models is excellent." - Contemporary Sociology "An extremely well-written book that will certainly prove an invaluable acquisition to the practicing statistician who finds other literature on analysis of discrete data hard to follow or heavily theoretical."-The Statistician In this revised and updated edition of their popular book, David Hosmer and Stanley Lemeshow continue to provide an amazingly accessible introduction to the logistic regression model while incorporating advances of the last decade, including a variety of software packages for the analysis of data sets. Hosmer and Lemeshow extend the discussion from biostatistics and epidemiology to cutting-edge applications in data mining and machine learning, guiding readers step-by-step through the use of modeling techniques for dichotomous data in diverse fields. Ample new topics and expanded discussions of existing material are accompanied by a wealth of real-world examples-with extensive data sets available over the Internet.

Applied Logistic Regression

\"A new edition of the definitive guide to logistic regression modeling for health science and other applicationsThis thoroughly expanded Third Edition provides an easily accessible introduction to the logistic regression (LR) model and highlights the power of this model by examining the relationship between a dichotomous outcome and a set of covariables. Applied Logistic Regression, Third Edition emphasizes applications in the health sciences and handpicks topics that best suit the use of modern statistical software. The book provides readers with state-of-the-art techniques for building, interpreting, and assessing the performance of LR models. New and updated features include: A chapter on the analysis of correlated outcome data. A wealth of additional material for topics ranging from Bayesian methods to assessing model fit Rich data sets from real-world studies that demonstrate each method under discussion. Detailed examples and interpretation of the presented results as well as exercises throughout Applied Logistic Regression, Third Edition is a must-have guide for professionals and researchers who need to model nominal or ordinal scaled outcome variables in public health, medicine, and the social sciences as well as a wide range of other fields and disciplines\"--

Applied Logistic Regression.

Objective. —To develop and validate a new Simplified Acute Physiology Score, the SAPS II, from a large sample of surgical and medical patients, and to provide a method to convert the score to a probability of hospital mortality. Design and Setting. —The SAPS II and the probability of hospital mortality were developed and validated using data from consecutive admissions to 137 adult medical and/or surgical intensive care units in 12 countries. Patients. —The 13 152 patients were randomly divided into developmental (65%) and validation (35%) samples. Patients younger than 18 years, burn patients, coronary care patients, and cardiac surgery patients were excluded. Outcome Measure. —Vital status at hospital discharge. Results. —The SAPS II includes only 17 variables: 12 physiology variables, age, type of admission (scheduled surgical, unscheduled surgical, or medical), and three underlying disease variables (acquired immunodeficiency syndrome, metastatic cancer, and hematologic malignancy). Goodness-of-fit tests indicated that the model performed well in the developmental sample and validated well in an independent sample of patients (P=.883 andP=.104 in the developmental and validation samples, respectively). The area under the receiver operating characteristic curve was 0.88 in the developmental sample and 0.86 in the validation sample. Conclusion. —The SAPS II, based on a large international sample of patients, provides an estimate of the risk of death without having to specify a primary diagnosis. This is a starting point for future evaluation of the efficiency of intensive care units. (JAMA. 1993;270:2957-2963)

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A new Simplified Acute Physiology Score (SAPS II) based on a European/North American multicenter study

THE MOST PRACTICAL, UP-TO-DATE GUIDE TO MODELLING AND ANALYZING TIME-TO-EVENT DATANOW IN A VALUABLE NEW EDITION Since publication of the first edition nearly a decade ago, analyses using time-to-event methods have increase considerably in all areas of scientific inquiry mainly as a result of model-building methods available in modern statistical software packages. However, there has been minimal coverage in the available literature to9 guide researchers, practitioners, and students who wish to apply these methods to health-related areas of study. Applied Survival Analysis, Second Edition provides a comprehensive and up-to-date introduction to regression modeling for time-to-event data in medical, epidemiological, biostatistical, and other health-related research. This book places a unique emphasis on the practical and contemporary applications of regression modeling rather than the mathematical theory. It offers a clear and accessible presentation of modern modeling techniques supplemented with real-world examples and case studies. Key topics covered include: variable selection, identification of the scale of continuous covariates, the role of interactions in the model, assessment of fit and model assumptions, regression diagnostics, recurrent event models, frailty models, additive models, competing risk models, and missing data. Features of the Second Edition include: Expanded coverage of interactions and the covariate-adjusted survival functions The use of the Worchester Heart Attack Study as the main modeling data set for illustrating discussed concepts and techniques New discussion of variable selection with multivariable fractional polynomials Further exploration of time-varying covariates, complex with examples Additional treatment of the exponential, Weibull, and log-logistic parametric regression models Increased emphasis on interpreting and using results as well as utilizing multiple imputation methods to analyze data with missing values New examples and exercises at the end of each chapter Analyses throughout the text are performed using Stata Version 9, and an accompanying FTP site contains the data sets used in the book. Applied Survival Analysis, Second Edition is an ideal book for graduate-level courses in biostatistics, statistics, and epidemiologic methods. It also serves as a valuable reference for practitioners and researchers in any health-related field or for professionals in insurance and government.

Stanley Lemeshow

Papers

Applied Logistic Regression

Applied Logistic Regression.

Applied Logistic Regression.

A new Simplified Acute Physiology Score (SAPS II) based on a European/North American multicenter study

Applied Survival Analysis: Regression Modeling of Time-to-Event Data