Water Quality Trend and Change-Point Analyses Using Integration of Locally Weighted Polynomial Regression and Segmented Regression
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How to Assess the Impact of Quality and Patient Safety Interventions with Routinely Collected Longitudinal Data
How to Assess the Impact of Quality and Patient Safety Interventions with Routinely Collected Longitudinal Data Diego A. Martinez, PhD, Assistant Professor of Emergency Medicine, Johns Hopkins University School of Medicine, Baltimore, MD Mehdi Jalalpour, PhD, Assistant Professor of Civil and Environmental Engineering, Cleveland State University, Cleveland, Ohio, USA. David T. Efron, MD, FACS, Professor of Surgery, Johns Hopkins University School of Medicine, Baltimore, MD Scott R. Levin, PhD, Associate Professor of Emergency Medicine, Johns Hopkins University School of Medicine, Baltimore, MD ABSTRACT Objectives: Measuring the effect of patient safety improvement efforts is needed to determine their value but is difficult due to the inherent complexities of hospital operations. In this paper, we show by case study how interrupted time series design can be used to isolate and measure the impact of interventions while accounting for confounders often present in complex health delivery systems. Methods: We searched for time-stamped data from electronic medical records and operating room information systems associated with perioperative patient flow in a large, urban, academic hospital in Baltimore, Maryland. We limited the searched to those adult cases performed between January 2015 and March 2017. We used segmented regression and Box-Jenkins methods to measure the effect of perioperative throughput improvement efforts and account for the loss of high volume surgeons, surgical volume, and occupancy. Results: We identified a significant decline of operating room exit delays of about 50%, achieved in 6 months and sustained over 14 months. Conclusions: By longitudinal assessment of intervention effects, rather than cross-sectional comparison, our measurement tool estimated and provided inferences of change-points over time while taking into account the magnitude of other latent systems factors. -
Process Control Charts and ITS Analysis of Epworth MEER Trial
Supplementary material BMJ Open Qual Process control charts and ITS analysis of Epworth MEER trial Contents Introduction 2 References............................................. 2 Load R packages 3 Useful functions 3 Import .csv data file for standard 5 incident counts 4 Read in the standard 5 data and add field for incident rate: . 4 Display the data . 5 Summarise the data . 7 View the data 8 Plot patient activity levels . 8 Plot RiskMan incident rates for standard 5 . 9 Probablity distributions for the culpcount data 10 Poisson distribution . 10 Negative binomial distribution . 11 CHART AND ANALYSIS FUNCTIONS 12 Process control chart . 12 Segmented regression model function . 13 Segmented regression full analysis function . 13 ANALYSIS & FIGURES 15 ED+4G vs Other . 15 glm analyses . 15 Residual & autocorrelation plots for negative binomial analysis . 17 Generate u-charts and ITS plot . 19 1 Curtin AG, et al. BMJ Open Qual 2020; 9:e000741. doi: 10.1136/bmjoq-2019-000741 Supplementary material BMJ Open Qual Introduction This notebook file provides R code and results for process control charts (u-charts) and Interrupted Time Series (ITS) analyses of an intervention trial at the Epworth Richmond hospital in Melbourne which was applied to two units at the Epworth hospital in Richmond, 4 Gray (4G) and Emergency (ED), from Jan 2018 to Oct 2018. The intervention was the application of a quality improvement approach called MEER. The effectiveness of the MEER intervention was gauged by its influence on reported adverse adverse incidents at the Epworth Richmond hospital as recorded by an electronic reporting system called RiskMan. The RiskMan incidents analysed in this study can be categorised according to which of five National Safety and Quality Health Standards (NSQHS) they pertain to. -
Original Research Article Analysing Interrupted Time Series with A
Original Research Article Analysing interrupted time series with a control Authors Bottomley C 1,2* , Scott JAG 2,3 , Isham V 4 Institutions 1. MRC Tropical Epidemiology Group, London School of Hygiene & Tropical Medicine, London, UK 2. Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK 3. KEMRI-Wellcome Trust Research Programme, Kilifi, Kenya 4. Department of Statistical Science, University College London, London, UK * Corresponding Author: [email protected] London School of Hygiene & Tropical Medicine, Keppel Street, London, UK Tel: +44 207 927 2533 1 Abstract Interrupted time series are increasingly being used to evaluate the population-wide implementation of public health interventions. However, the resulting estimates of intervention impact can be severely biased if underlying disease trends are not adequately accounted for. Control series offer a potential solution to this problem, but there is little guidance on how to use them to produce trend-adjusted estimates. To address this lack of guidance, we show how interrupted time series can be analysed when the control and intervention series share confounders, i.e., when they share a common trend. We show that the intervention effect can be estimated by subtracting the control series from the intervention series and analysing the difference using linear regression or, if a log-linear model is assumed, by including the control series as an offset in a Poisson regression with robust standard errors. The methods are illustrated with two examples. Key words: interrupted time series, segmented regression, common trend model 2 Introduction Interrupted time series (ITS) analysis is an increasingly popular method for evaluating public health interventions [1]. -
An Exact Algorithm for Estimating Breakpoints in Segmented Generalized Linear Models
Küchenhoff: An exact algorithm for estimating breakpoints in segmented generalized linear models Sonderforschungsbereich 386, Paper 27 (1996) Online unter: http://epub.ub.uni-muenchen.de/ Projektpartner An exact algorithm for estimating breakp oints in segmented generalized linear mo dels Helmut Kuc henho University of Munich Institute of Statistics Akademiestrasse D Munc hen Summary We consider the problem of estimating the unknown breakp oints in seg mented generalized linear mo dels Exact algorithms for calculating maxi mum likeliho o d estimators are derived for dierenttyp es of mo dels After discussing the case of a GLM with a single covariate having one breakp oint a new algorithm is presented when further covariates are included in the mo del The essential idea of this approach is then used for the case of more than one breakp oint As further extension an algorithm for the situation of two regressors eachhaving a breakp oint is prop osed These techniques are applied for analysing the data of the Munichrental table It can b e seen that these algorithms are easy to handle without to o much computational eort The algorithms are available as GAUSSprograms Keywords Breakp oint generalized linear mo del segmented regression Intro duction In many practical regressiontyp e problems we cannot t one uniform re gression function to the data since the functional relationship b etween the resp onse Y and the regressor X changes at certain p oints of the domain of X These p oints are usually called breakp oints or changep oints One imp -
Fitting Segmented Regression Curves
University of Montana ScholarWorks at University of Montana Graduate Student Theses, Dissertations, & Professional Papers Graduate School 1968 Fitting segmented regression curves Kenneth P. Johnson The University of Montana Follow this and additional works at: https://scholarworks.umt.edu/etd Let us know how access to this document benefits ou.y Recommended Citation Johnson, Kenneth P., "Fitting segmented regression curves" (1968). Graduate Student Theses, Dissertations, & Professional Papers. 8324. https://scholarworks.umt.edu/etd/8324 This Thesis is brought to you for free and open access by the Graduate School at ScholarWorks at University of Montana. It has been accepted for inclusion in Graduate Student Theses, Dissertations, & Professional Papers by an authorized administrator of ScholarWorks at University of Montana. For more information, please contact [email protected]. FITTING SEGMENTED REGRESSION CURVES By Kenneth P. Johnson B.A., University of Montana, l965 Presented in partial fulfillment of the requirements for the degree of Master of Arts UNIVERSITY OF MONTANA 1968 Approved by: Chairman, Board of Examiners /C'..,,_^ De ^ , Graduate' School Date Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: EP39125 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMT DMSsdation PublisNng UMI EP39125 Published by ProQuest LLC (2013). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. -
Computing Primer for Applied Linear Regression, Third Edition Using R and S-Plus
Computing Primer for Applied Linear Regression, Third Edition Using R and S-Plus Sanford Weisberg University of Minnesota School of Statistics February 8, 2010 c 2005, Sanford Weisberg Home Website: www.stat.umn.edu/alr Contents Introduction 1 0.1 Organizationofthisprimer 4 0.2 Data files 5 0.2.1 Documentation 5 0.2.2 R datafilesandapackage 6 0.2.3 Two files missing from the R library 6 0.2.4 S-Plus data files and library 7 0.2.5 Getting the data in text files 7 0.2.6 Anexceptionalfile 7 0.3 Scripts 7 0.4 The very basics 8 0.4.1 Readingadatafile 8 0.4.2 ReadingExcelFiles 9 0.4.3 Savingtextoutputandgraphs 10 0.4.4 Normal, F , t and χ2 tables 11 0.5 Abbreviationstoremember 12 0.6 Packages/Libraries for R and S-Plus 12 0.7 CopyrightandPrintingthisPrimer 13 1 Scatterplots and Regression 13 v vi CONTENTS 1.1 Scatterplots 13 1.2 Mean functions 16 1.3 Variance functions 16 1.4 Summary graph 16 1.5 Tools for looking at scatterplots 16 1.6 Scatterplot matrices 16 2 Simple Linear Regression 19 2.1 Ordinaryleastsquaresestimation 19 2.2 Leastsquarescriterion 19 2.3 Estimating σ2 20 2.4 Propertiesofleastsquaresestimates 20 2.5 Estimatedvariances 20 2.6 Comparing models: The analysis of variance 21 2.7 The coefficient of determination, R2 22 2.8 Confidence intervals and tests 23 2.9 The Residuals 26 3 Multiple Regression 27 3.1 Adding a term to a simple linear regression model 27 3.2 The Multiple Linear Regression Model 27 3.3 Terms and Predictors 27 3.4 Ordinaryleastsquares 28 3.5 Theanalysisofvariance 30 3.6 Predictions and fitted values 31 4 Drawing Conclusions -
Testing the Significance of the Improvement of Cubic Regression
Testing the statistical significance of the improvement of cubic regression compared to quadratic regression using analysis of variance (ANOVA) R.J. Oosterbaan on www.waterlog.info , public domain. Abstract When performing a regression analysis, it is recommendable to test the statistical significance of the result by means of an analysis of variance (ANOVA). In a previous article, the significance of the improvement of segmented regression, as done by the SegReg calculator program, compared to simple linear regression was tested using analysis of variance (ANOVA). The significance of the improvement of a quadratic (2nd degree) regression over a simple linear regression is tested in the SegRegA program (A stands for “amplified”) by means of ANOVA. Also, here the significance of the improvement of a cubic (3rd degree) over a simple linear regression is tested in the same way. In this article, the significance test of the improvement of a cubic regression over a quadratic regression will be dealt with. Contents 1. Introduction 2. ANOVA symbols used 3. Explanatory examples A. Quadratic regression B. Cubic regression C. Comparing quadratic and cubic regression 4. Summary 5. References 1. Introduction When performing a regression analysis, it is recommendable to test the statistical significance of the result by means of an analysis of variance (ANOVA). In a previous article [Ref. 1], the significance of the improvement of segmented regression, as done by the SegReg program [Ref. 2], compared to simple linear regression was dealt with using analysis of variance. The significance of the improvement of a quadratic (2nd degree) regression over a simple linear regression is tested in the SegRegA program (the A stands for “amplified”), also by means of ANOVA [Ref. -
Correctional Data Analysis Systems. INSTITUTION Sam Honston State Univ., Huntsville, Tex
I DocdnENT RESUME ED 209 425 CE 029 723 AUTHOR Friel, Charles R.: And Others TITLE Correctional Data Analysis Systems. INSTITUTION Sam Honston State Univ., Huntsville, Tex. Criminal 1 , Justice Center. SPONS AGENCY Department of Justice, Washington, D.C. Bureau of Justice Statistics. PUB DATE 80 GRANT D0J-78-SSAX-0046 NOTE 101p. EDRS PRICE MF01fPC05Plus Postage. DESCRIPTORS Computer Programs; Computers; *Computer Science; Computer Storage Devices; *Correctional Institutions; *Data .Analysis;Data Bases; Data Collection; Data Processing; *Information Dissemination; *Iaformation Needs; *Information Retrieval; Information Storage; Information Systems; Models; State of the Art Reviews ABSTRACT Designed to help the-correctional administrator meet external demands for information, this detailed analysis or the demank information problem identifies the Sources of teguests f6r and the nature of the information required from correctional institutions' and discusses the kinds of analytic capabilities required to satisfy . most 'demand informhtion requests. The goals and objectives of correctional data analysis systems are ontliled. Examined next are the content and sources of demand information inquiries. A correctional case law demand'information model is provided. Analyzed next are such aspects of the state of the art of demand information as policy considerations, procedural techniques, administrative organizations, technology, personnel, and quantitative analysis of 'processing. Availa4ie software, report generators, and statistical packages -
Parameter Estimation in Linear-Linear Segmented Regression
Brigham Young University BYU ScholarsArchive Theses and Dissertations 2010-04-20 Parameter Estimation in Linear-Linear Segmented Regression Erika Lyn Hernandez Brigham Young University - Provo Follow this and additional works at: https://scholarsarchive.byu.edu/etd Part of the Statistics and Probability Commons BYU ScholarsArchive Citation Hernandez, Erika Lyn, "Parameter Estimation in Linear-Linear Segmented Regression" (2010). Theses and Dissertations. 2113. https://scholarsarchive.byu.edu/etd/2113 This Selected Project is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. Parameter Estimation in Linear-Linear Segmented Regression Erika L. Hernandez A project submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Master of Science C. Shane Reese, Chair Scott D. Grimshaw Gilbert W. Fellingham Department of Statistics Brigham Young University August 2010 Copyright c 2010 Erika L. Hernandez All Rights Reserved ABSTRACT Parameter Estimation in Linear-Linear Segmented Regression Erika L. Hernandez Department of Statistics Master of Science Segmented regression is a type of nonlinear regression that allows differing functional forms to be fit over different ranges of the explanatory variable. This paper considers the simple segmented regression case of two linear segments that are constrained to meet, often called the linear-linear model. Parameter estimation in the case where the joinpoint between the regimes is unknown can be tricky. Using a simulation study, four estimators for the parameters of the linear-linear model are evaluated. -
T2S General Functional Specifications Table of Contents
Target2-Securities General Functional Specifications V8.0 27 January 2020 T2S General Functional Specifications Table of Contents Table of Contents 1 Approach to T2S Functional Design .............................................................................. 5 1.1 Presentation of the document................................................................................ 5 1.2 Methodological elements ....................................................................................... 6 1.3 Reference documents............................................................................................. 7 1.4 Specifications references – cross-referencing URD ............................................... 7 1.5 Conventions used ................................................................................................... 7 2 General Functional Overview ........................................................................................ 8 2.1 Introduction ........................................................................................................... 8 2.1.1 Objective and scope of T2S ........................................................................... 8 2.1.2 T2S Actors.................................................................................................... 23 2.1.3 Multi-currency in T2S .................................................................................. 29 2.1.4 Other systems interacting with T2S ............................................................ 29 2.2 Overall high level -
Regression Analysis of Hydrologic Data
6 FREQUENCY AND REGRESSION ANALYSIS OF HYDROLOGIC DATA R.J. Oosterbaan PART II: REGRESSION ANALYSIS On web site www.waterlog.info For free sofware on frequency regression analysis see: www.waterlog.info/cumfreq.htm For free sofware on segmented regression analysis see: www.waterlog.info/segreg.htm Chapter 6 in: H.P.Ritzema (Ed.), Drainage Principles and Applications, Publication 16, second revised edition, 1994, International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands. ISBN 90 70754 3 39 Table of contents 6 FREQUENCY AND REGRESSION ANALYSIS .................................................................3 6.1 Introduction......................................................................................................................3 6.5 Regression Analysis..........................................................................................................4 6.5.1 Introduction................................................................................................................4 6.5.2 The Ratio Method......................................................................................................5 6.5.3 Regression of y upon x...............................................................................................9 Confidence statements, regression of y upon x.............................................................11 Example 6.2 Regression y upon x.................................................................................14 6.5.4 Linear Two-way Regression.....................................................................................16 -
Nonlinear Regression
Nonlinear Regression James H. Steiger Department of Psychology and Human Development Vanderbilt University James H. Steiger (Vanderbilt University) Nonlinear Regression 1 / 36 Nonlinear Regression 1 Introduction 2 Estimation for Nonlinear Mean Functions Iterative Estimation Technique 3 Large Sample Inference 4 An Artificial Example Turkey Growth Example Three Sources of Methionine 5 Bootstrap Inference The Temperature Example James H. Steiger (Vanderbilt University) Nonlinear Regression 2 / 36 Introduction Introduction A mean function may not necessarily be a linear combination of terms. Some examples: E(Y jX = x) = θ1 + θ2(1 − exp(−θ3x)) (1) E(Y jX = x) = β0 + β1 S (x; λ) (2) where S (x; λ) is the scaled power transformation, defined as ( (X λ − 1)/λ if λ 6= 0 S (X ; λ) = (3) log(X ) if λ = 0 Once λ has been chosen, the function becomes, in the sense we have been describing, linear in its terms, just as a quadratic in X can be viewed as linear in X and X 2. James H. Steiger (Vanderbilt University) Nonlinear Regression 3 / 36 Introduction Introduction Nonlinear mean functions often arise in practice when we have special information about the processes we are modeling. For example, consider again the function E(Y jX = x) = θ1 + θ2(1 − exp(−θ3x)). As X increases, assuming θ3 > 0, the function approaches θ1 + θ2. When X = 0, the function value is θ1, representing the average growth with no supplementation. θ3 is a rate parameter. James H. Steiger (Vanderbilt University) Nonlinear Regression 4 / 36 Estimation for Nonlinear Mean Functions Estimation for Nonlinear Mean Functions Our general notational setup is straightforward.