Mathematics

SUMMARY The common approach to the multiplicity problem calls for controlling the familywise error rate (FWER). This approach, though, has faults, and we point out a few. A different approach to problems of multiple significance testing is presented. It calls for controlling the expected proportion of falsely rejected hypotheses — the false discovery rate. This error rate is equivalent to the FWER when all hypotheses are true but is smaller otherwise. Therefore, in problems where the control of the false discovery rate rather than that of the FWER is desired, there is potential for a gain in power. A simple sequential Bonferronitype procedure is proved to control the false discovery rate for independent test statistics, and a simulation study shows that the gain in power is substantial. Th

Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the st

This paper presents a general statistical methodology for the analysis of multivariate categorical data arising from observer reliability studies. The procedure essentially involves the construction of functions of the observed proportions which are directed at the extent to which the observers agree among themselves and the construction of test statistics for hypotheses involving these functions. Tests for interobserver bias are presented in terms of first-order marginal homogeneity and measures of interobserver agreement are developed as generalized kappa-type statistics. These procedures are illustrated with a clinical diagnosis example from the epidemiological literature.

In this Section: 1. Brief Table of Contents 2. Full Table of Contents 1. BRIEF TABLE OF CONTENTS Chapter 1 Introduction Chapter 2 A Guide to Statistical Techniques: Using the Book Chapter 3 Review of Univariate and Bivariate Statistics Chapter 4 Cleaning Up Your Act: Screening Data Prior to Analysis Chapter 5 Multiple Regression Chapter 6 Analysis of Covariance Chapter 7 Multivariate Analysis of Variance and Covariance Chapter 8 Profile Analysis: The Multivariate Approach to Repeated Measures Chapter 9 Discriminant Analysis Chapter 10 Logistic Regression Chapter 11 Survival/Failure Analysis Chapter 12 Canonical Correlation Chapter 13 Principal Components and Factor Analysis Chapter 14 Structural Equation Modeling Chapter 15 Multilevel Linear Modeling Chapter 16 Multiway Frequency Analysis

The statistical tests used in the analysis of structural equation models with unobservable variables and measurement error are examined. A drawback of the commonly applied chi square test, in addition to the known problems related to sample size and power, is that it may indicate an increasing correspondence between the hypothesized model and the observed data as both the measurement properties and the relationship between constructs decline. Further, and contrary to common assertion, the risk of making a Type II error can be substantial even when the sample size is large. Moreover, the present testing methods are unable to assess a model's explanatory power. To overcome these problems, the authors develop and apply a testing system based on measures of shared variance within the structura

Abstract Objective: Funnel plots (plots of effect estimates against sample size) may be useful to detect bias in meta-analyses that were later contradicted by large trials. We examined whether a simple test of asymmetry of funnel plots predicts discordance of results when meta-analyses are compared to large trials, and we assessed the prevalence of bias in published meta-analyses. Design: Medline search to identify pairs consisting of a meta-analysis and a single large trial (concordance of results was assumed if effects were in the same direction and the meta-analytic estimate was within 30% of the trial); analysis of funnel plots from 37 meta-analyses identified from a hand search of four leading general medicine journals 1993-6 and 38 meta-analyses from the second 1996 issue of the Coch

SUMMARY We propose a new method for estimation in linear models. The ‘lasso’ minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It produces interpretable models like subset selection and exhibits the stability of ridge regression. There is also an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to genera

Designing complex, dynamic yet multi-functional materials and devices is challenging because the design spaces for these materials have numerous interdependent and often conflicting constraints. Taking inspiration from advances in artificial intelligence and their applications in material discovery, we propose a computational method for designing metamorphic DNA-co-polymerized hydrogel structures. The method consists of a coarse-grained simulation and a deep learning-guided optimization system for exploring the immense design space of these structures. Here, we develop a simple numeric simulation of DNA-co-polymerized hydrogel shape change and seek to find designs for structured hydrogels that can fold into the shapes of different Arabic numerals in different actuation states. We train a c

Summary A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis.

A general formula ( α ) of which a special case is the Kuder-Richardson coefficient of equivalence is shown to be the mean of all split-half coefficients resulting from different splittings of a test. α is therefore an estimate of the correlation between two random samples of items from a universe of items like those in the test. α is found to be an appropriate index of equivalence and, except for very short tests, of the first-factor concentration in the test. Tests divisible into distinct subtests should be so divided before using the formula. The index \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\bar r_

The recently-developed statistical method known as the "bootstrap" can be used to place confidence intervals on phylogenies. It involves resampling points from one's own data, with replacement, to create a series of bootstrap samples of the same size as the original data. Each of these is analyzed, and the variation among the resulting estimates taken to indicate the size of the error involved in making estimates from the original data. In the case of phylogenies, it is argued that the proper method of resampling is to keep all of the original species while sampling characters with replacement, under the assumption that the characters have been independently drawn by the systematist and have evolved independently. Majority-rule consensus trees can be used to construct a phylogeny showing a

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An Introduction to the Bootstrap arms scientists and engineers as well as statisticians with the computational techniques they need to analyze and understand complicated data sets. The bootstrap is a computer-based method of statistical inference that answers statistical questions without formulas and gives a direct appreciation of variance, bias, coverage, and other probabilistic phenomena. This book presents an overview of the bootstrap and related methods for assessing statistical accuracy, concentrating on the ideas rather than their mathematical justification. Not just for beginners, the presentation starts off slowly, but builds in both scope and depth to ideas that are quite sophisticated.

Abstract In lifetesting, medical follow-up, and other fields the observation of the time of occurrence of the event of interest (called a death) may be prevented for some of the items of the sample by the previous occurrence of some other event (called a loss). Losses may be either accidental or controlled, the latter resulting from a decision to terminate certain observations. In either case it is usually assumed in this paper that the lifetime (age at death) is independent of the potential loss time; in practice this assumption deserves careful scrutiny. Despite the resulting incompleteness of the data, it is desired to estimate the proportion P(t) of items in the population whose lifetimes would exceed t (in the absence of such losses), without making any assumption about the form of th

Academia and Clinic18 August 2009Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The PRISMA StatementFREEDavid Moher, PhD, Alessandro Liberati, MD, DrPH, Jennifer Tetzlaff, BSc, and Douglas G. Altman, DSc, the PRISMA Group*David Moher, PhDFrom Ottawa Methods Centre, Ottawa Hospital Research Institute, University of Ottawa, Ottawa, Ontario, Canada; Università di Modena e Reggio Emilia, Modena, Italy; Centro Cochrane Italiano, Istituto Ricerche Farmacologiche Mario Negri, Milan, Italy; and Centre for Statistics in Medicine, University of Oxford, Oxford, United Kingdom.Search for more papers by this author, Alessandro Liberati, MD, DrPHFrom Ottawa Methods Centre, Ottawa Hospital Research Institute, University of Ottawa, Ottawa, Ontario, Canada; Università di Modena e Reggi

Introduction Interactions between Continuous Predictors in Multiple Regression The Effects of Predictor Scaling on Coefficients of Regression Equations Testing and Probing Three-Way Interactions Structuring Regression Equations to Reflect Higher Order Relationships Model and Effect Testing with Higher Order Terms Interactions between Categorical and Continuous Variables Reliability and Statistical Power Conclusion Some Contrasts Between ANOVA and MR in Practice

The extent of heterogeneity in a meta-analysis partly determines the difficulty in drawing overall conclusions. This extent may be measured by estimating a between-study variance, but interpretation is then specific to a particular treatment effect metric. A test for the existence of heterogeneity exists, but depends on the number of studies in the meta-analysis. We develop measures of the impact of heterogeneity on a meta-analysis, from mathematical criteria, that are independent of the number of studies and the treatment effect metric. We derive and propose three suitable statistics: H is the square root of the chi2 heterogeneity statistic divided by its degrees of freedom; R is the ratio of the standard error of the underlying mean from a random effects meta-analysis to the standard err

Offers an applications-oriented approach to multivariate data analysis, focusing on the use of each technique, rather than its mathematical derivation. The text introduces a six-step framework for organizing and discussing techniques with flowcharts for each. Well-suited for the non-statistician, this applications-oriented introduction to multivariate analysis focuses on the fundamental concepts that affect the use of specific techniques rather than the mathematical derivation of the technique. Provides an overview of several techniques and approaches that are available to analysts today - e.g., data warehousing and data mining, neural networks and resampling/bootstrapping. Chapters are organized to provide a practical, logical progression of the phases of analysis and to group similar ty

A new edition of the definitive guide to logistic regression modeling for health science and other applications This 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-

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and home