DOCSLIB.ORG

Comparison of Six Statistical Methods for Interrupted Time Series Studies: Empirical Evaluation of 190 Published Series

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Comparison of Six Statistical Methods for Interrupted Time Series Studies: Empirical Evaluation of 190 Published Series Comparison of Six Statistical Methods for Interrupted time Series Studies: Empirical Evaluation of 190 Published Series Simon Turner Monash University Amalia Karahalios Monash University Andrew Forbes Monash University Monica Taljaard University of Ottawa Jeremy Grimshaw University of Ottawa Joanne McKenzie ( [email protected] ) Monash University Research Article Keywords: Autocorrelation, Interrupted Time Series, Public Health, Segmented Regression, Statistical Methods, Empirical study Posted Date: December 7th, 2020 DOI: https://doi.org/10.21203/rs.3.rs-118335/v1 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License 1 Comparison of six statistical methods for interrupted time 2 series studies: empirical evaluation of 190 published series 3 Simon L Turner1, Amalia Karahalios1, Andrew B Forbes1, Monica Taljaard2,3, Jeremy 4 M Grimshaw2,3,4, Joanne E McKenzie1* 5 1School of Public Health and Preventive Medicine, Monash University, Melbourne, 6 Victoria, Australia. 7 2Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, 8 Ontario, Canada. 1053 Carling Ave, Ottawa. 9 3School of Epidemiology and Public Health, University of Ottawa, Ottawa, Ontario, 10 Canada. 600 Peter Morand Crescent, Ottawa, Ontario K1G 5Z3. 11 4Department of Medicine, University of Ottawa, Ottawa, Ontario, Canada. Roger 12 Guindon Hall, 451 Smyth Rd. 13 *Corresponding Author: 14 Joanne McKenzie 15 mail: Level 4, 553 St. Kilda Road, Melbourne, 3004, Australia 16 email: [email protected] 17 ph: +61 3 9903 0380 18 Abstract 19 Background 20 The Interrupted Time Series (ITS) is a quasi-experimental design commonly used in 21 public health to evaluate the impact of interventions or exposures. Multiple statistical 22 methods are available to analyse data from ITS studies, but no empirical 1 23 investigation has examined how the different methods compare when applied to real- 24 world datasets. 25 Methods 26 A random sample of 200 ITS studies identified in a previous methods review were 27 included. Time series data from each of these studies was sought. Each dataset was 28 re-analysed using six statistical methods. Point and confidence interval estimates for 29 level and slope changes, standard errors, p-values and estimates of autocorrelation 30 were compared between methods. 31 Results 32 From the 200 ITS studies, including 230 time series, 190 datasets were obtained. 33 We found that the choice of statistical method can importantly affect the level and 34 slope change point estimates, their standard errors, width of confidence intervals and 35 p-values. Statistical significance (categorised at the 5% level) often differed across 36 the pairwise comparisons of methods, ranging from 4% to 25% disagreement. 37 Estimates of autocorrelation differed depending on the method used and the length 38 of the series. 39 Conclusions 40 The choice of statistical method in ITS studies can lead to substantially different 41 conclusions about the impact of the interruption. Pre-specification of the statistical 42 method is encouraged, and naive conclusions based on statistical significance 43 should be avoided. 2 44 Keywords 45 Autocorrelation, Interrupted Time Series, Public Health, Segmented Regression, 46 Statistical Methods, Empirical study 47 1 Background 48 Randomised trials are the gold standard design for investigating the impact of public 49 health interventions, however, they cannot always be used. For example, 50 interventions that impact an entire country, or those that have occurred historically, 51 may preclude the ability to randomize or include control groups (1). An alternative 52 non-randomised design that may be considered in such circumstances is an 53 interrupted time series (ITS) (2-4). In an ITS design, data are collected at multiple 54 time points both before and after an interruption (i.e. an intervention or exposure). 55 Modelling of the data in the pre-interruption period allows estimation of the 56 underlying secular trend, which when modelled correctly and extrapolated into the 57 post-interruption time period, yields a counterfactual for what would have occurred in 58 the absence of the interruption. Differences between the counterfactual and 59 observed data at various points post interruption can be estimated (e.g. immediate 60 and long-term effects), having accounted for the underlying secular trend. 61 A characteristic of data collected over time is that the data points tend to be 62 correlated (5). This correlation – referred to as autocorrelation or serial correlation – 63 can be positive (whereby data points close together in time are more similar than 64 data points further apart) or, infrequently, negative (whereby data points close 65 together are more dissimilar than data points further apart). Autocorrelation may be 66 observed between consecutive data points or over longer periods of time (e.g. 67 seasonal effects). This characteristic of the data needs to be considered when 3 68 designing and analysing ITS studies. If positive autocorrelation is present, larger 69 sample sizes are required to provide power at the desired level (6) and if 70 autocorrelation is not accounted for in the statistical analysis, standard errors may be 71 underestimated (7). 72 Segmented linear regression models are often fitted to ITS data using a range of 73 estimation methods (8-11). Commonly ordinary least squares (OLS) is used to 74 estimate the model parameters (10); however, the method does not account for 75 autocorrelation. Other statistical methods are available that attempt to account for 76 autocorrelation in different ways (e.g. correction of standard errors, directly modelling 77 the errors). 78 Turner et al undertook a statistical simulation study examining the performance of 79 statistical methods for analysing ITS data, where the methods were those commonly 80 used in practice or had shown potential to perform well (12). This simulation study 81 provided insight into how these statistical methods performed under different 82 scenarios, including different level and slope changes, varying magnitudes of 83 underlying autocorrelation and series lengths. In combination with these findings, 84 evidence from an empirical evaluation can provide a more comprehensive 85 understanding of how the methods operate. In particular, empirical evaluations – in 86 which methods are applied to real-world data sets and the results are compared – 87 allow assessment of whether the choice of method matters in practice, and the 88 degree to which they may do so. 89 To our knowledge, there has been no study that has empirically compared different 90 methods for analysing ITS data when applied to a large sample of real-world data 91 sets. We therefore undertook such an evaluation, where we aimed to compare level 4 92 and slope change estimates, their standard errors, confidence intervals and p- 93 values, and estimates of autocorrelation, obtained from the set of statistical methods 94 used in the Turner et al simulation study (12). 95 2 Methods 96 2.1 Repository of ITS studies 97 A sample of 200 ITS studies identified in a previous methods review were eligible for 98 inclusion in the current study (10). In brief, we randomly selected ITS studies 99 indexed on PubMed between the years 2013 to 2017. The criteria for inclusion were: 100 1) studies in which there were at least two segments separated by a clearly defined 101 interruption with at least three points in each segment; 2) observations were 102 collected on a group of individuals at each time point; and 3) the study investigated 103 the impact of an interruption that had public health implications. 104 For each of the 200 studies, the first reported ITS of each outcome type (binary, 105 continuous, count or proportion) was included, resulting in 230 ITS. Data were 106 collected on the study characteristics and design of the ITS studies, types of 107 outcomes, models used, statistical methods employed, effect measures reported, 108 and the properties of included graphs. Further details of the study methods are 109 available in the study protocol and results papers (10, 13). 110 2.2 Methods to obtain time series data 111 Time series data from the included studies were obtained using three methods. First, 112 we collated datasets that were reported in the published paper or its supplement 113 (e.g. time series data reported in tables, or as text files). Second, we contacted all 114 authors for whom we were able to obtain contact details to request datasets. We 115 requested only aggregate level data (i.e. not individual participant data) and in the 5 116 circumstance where a study included multiple series, we only sought data from the 117 first time series reported in the paper to reduce respondent burden. We sent an initial 118 email request on the 13th December 2018 and a follow-up email on the 24th January 119 2019. Third, we digitally extracted datasets from published graphs using the software 120 WebPlotDigitizer (14). This graphical data extraction tool has been found to 121 accurately estimate the position of points on a graph (15). 122 If multiple datasets from the above methods were available for a particular time 123 series, we selected the dataset generated using the following hierarchy: (i) published 124 data, (ii) contact with authors, and (iii) digitally extracted. We checked the data 125 provided by authors against the information reported in the publication. Where there 126 was a discrepancy, we re-contacted the authors to query the provided data. 127 2.3 Interrupted time series model 128 We fitted segmented linear regression models to each dataset using the 129 parameterisation of Huitema and McKean (7) (Equation1, 130 Figure 1): (1) 131 where푌푡 = 훽0 +represents 훽1푡 + 훽2퐷 the푡 + 훽outcome3[푡 − 푇퐼] 퐷that푡 + is 휀푡 measured at time point t of N time points (1 132 to measurements푌푡 during the pre-interruption stage, and to 133 measurements푛1 in the post-interruption stage), with the interruption푛1 + 1 occurring푛2 at time 134 .
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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].
    [Show full text]
  • 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
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • Water Quality Trend and Change-Point Analyses Using Integration of Locally Weighted Polynomial Regression and Segmented Regression
    Environ Sci Pollut Res DOI 10.1007/s11356-017-9188-x RESEARCH ARTICLE Water quality trend and change-point analyses using integration of locally weighted polynomial regression and segmented regression Hong Huang1,2 & Zhenfeng Wang1,2 & Fang Xia1,2 & Xu Shang1,2 & YuanYuan Liu 3 & Minghua Zhang1,2 & Randy A. Dahlgren1,2,4 & Kun Mei1,2 Received: 11 January 2017 /Accepted: 2 May 2017 # Springer-Verlag Berlin Heidelberg 2017 Abstract Trend and change-point analyses of water quality The reliability was verified by statistical tests and prac- time series data have important implications for pollution con- tical considerations for Shanxi Reservoir watershed. The trol and environmental decision-making. This paper devel- newly developed integrated LWPR-SegReg approach is oped a new approach to assess trends and change-points of not only limited to the assessment of trends and change-points water quality parameters by integrating locally weighted poly- of water quality parameters but also has a broad application to nomial regression (LWPR) and segmented regression other fields with long-term time series records. (SegReg). Firstly, LWPR was used to pretreat the original water quality data into a smoothed time series to represent Keywords Water quality . Long-term trend assessment . the long-term trend of water quality. Then, SegReg was used Change-point analysis . Locally weighted polynomial to identify the long-term trends and change-points of the regression . Segmented regression smoothed time series. Finally, statistical tests were applied to determine the significance of the long-term trends and change- points. The efficacy of this approach was validated using a 10- Introduction year record of total nitrogen (TN) and chemical oxygen de- mand (CODMn) from Shanxi Reservoir watershed in eastern Many countries and regions in the world suffer from chronic China.
    [Show full text]
  • Fast Algorithms for Segmented Regression
    Fast Algorithms for Segmented Regression Jayadev Acharya Ilias Diakonikolas MIT University of Southern California [email protected] [email protected] Jerry Li Ludwig Schmidt MIT MIT [email protected] [email protected] May 25, 2016 Abstract We study the fixed design segmented regression problem: Given noisy samples from a piece- wise linear function f, we want to recover f up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on dynamic programming (DP) and, while sample efficient, have running time quadratic in the sample size. As our main contribution, we provide new sample near-linear time algorithms for the problem that – while not being minimax optimal – achieve a significantly better sample-time tradeoff on large datasets compared to the DP approach. Our experimental evaluation shows that, compared with the DP approach, our algorithms provide a convergence rate that is only off by a factor of 2 to 4, while achieving speedups of three orders of magnitude. 1 Introduction We study the regression problem – a fundamental inference task with numerous applications that has received tremendous attention in machine learning and statistics during the past fifty years (see, e.g., [MT77] for a classical textbook). Roughly speaking, in a (fixed design) regression problem, we are given a set of n observations (xi; yi), where the yi’s are the dependent variables and the xi’s are the independent variables, and our goal is to model the relationship between them. The typical assumptions are that (i) there exists a simple function f that (approximately) models the underlying relation, and (ii) the dependent observations are corrupted by random noise.
    [Show full text]
  • Piecewise Linear Regression for Leaf Appearance Rate Data
    Iowa State University Capstones, Theses and Creative Components Dissertations Spring 2021 Piecewise linear regression for leaf appearance rate data Lin Quan Follow this and additional works at: https://lib.dr.iastate.edu/creativecomponents Part of the Biostatistics Commons Recommended Citation Quan, Lin, "Piecewise linear regression for leaf appearance rate data" (2021). Creative Components. 786. https://lib.dr.iastate.edu/creativecomponents/786 This Creative Component is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Creative Components by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Piecewise linear regression for leaf appearance rate data by Lin Quan A Creative Component submitted to the graduate faculty in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Major: Statistics Program of Study Committee: Dan Nettleton, Major Professor Lily Wang Peng Liu The student author, whose presentation of the scholarship herein was approved by the program of study committee, is solely responsible for the content of this creative component. The Graduate College will ensure this creative component is globally accessible and will not permit alterations after a degree is conferred. Iowa State University Ames, Iowa 2021 Copyright © Lin Quan, 2021. All rights reserved. ii TABLE OF CONTENTS Page LIST OF TABLES . iii LIST OF FIGURES . iv ABSTRACT . vi CHAPTER 1. INTRODUCTION . .1 CHAPTER 2. DATASET AND METHODS . .4 2.1 Dataset . .4 2.2 Methods . .4 2.2.1 Package segmented ................................4 2.2.2 Least-squares .
    [Show full text]
  • Segmented Regression Analysis of Interrupted Time Series Studies in Medication Use Research
    Journal of Clinical Pharmacy and Therapeutics (2002) 27, 299–309 RESEARCH NOTE Segmented regression analysis of interrupted time series studies in medication use research A. K. Wagner* PharmD, MPH,S.B.Soumerai*ScD, F. Zhang* MS and D. Ross-Degnan* ScD *Department of Ambulatory Care and Prevention, Harvard Medical School and Harvard Pilgrim Health Care and Department of Epidemiology, Harvard School of Public Health, Boston, MA, USA ineffective (3) or a drug with unfavourable side- SUMMARY effects can be withdrawn from the market (4). Interrupted time series design is the strongest, Interrupted time series (5, 6) is the strongest, quasi-experimental approach for evaluating lon- quasi-experimental design to evaluate longitudinal gitudinal effects of interventions. Segmented effects of such time-delimited interventions. Seg- regression analysis is a powerful statistical mented regression analysis of interrupted time method for estimating intervention effects in series data allows us to assess, in statistical terms, interrupted time series studies. In this paper, we how much an intervention changed an outcome of show how segmented regression analysis can be interest, immediately and over time; instantly or used to evaluate policy and educational inter- with delay; transiently or long-term; and whether ventions intended to improve the quality of factors other than the intervention could explain medication use and ⁄ or contain costs. the change. Segmented regression analysis is appropriate for Keywords: health policy evaluation, interrupted studying effects of interventions conducted as part time series design, longitudinal analysis, medi- of a randomized trial as well as interventions that cation use research, quasi-experimental design, constitute a natural experiment.
    [Show full text]
  • Package 'Segmented'
    Package ‘segmented’ April 22, 2021 Type Package Title Regression Models with Break-Points / Change-Points Estimation Version 1.3-4 Date 2021-04-28 Maintainer Vito M. R. Muggeo <[email protected]> Description Given a regression model, segmented `updates' it by adding one or more segmented (i.e., piece- wise linear) relationships. Several variables with multiple breakpoints are allowed. The estimation method is dis- cussed in Muggeo (2003, <doi:10.1002/sim.1545>) and illustrated in Muggeo (2008, <https://www.r-project.org/doc/Rnews/Rnews_2008- 1.pdf>). An approach for hypothesis testing is presented in Muggeo (2016, <doi:10.1080/00949655.2016.1149855>), and interval estima- tion for the breakpoint is discussed in Muggeo (2017, <doi:10.1111/anzs.12200>). License GPL NeedsCompilation no Author Vito M. R. Muggeo [aut, cre] (<https://orcid.org/0000-0002-3386-4054>) Repository CRAN Date/Publication 2021-04-22 14:00:02 UTC R topics documented: segmented-package . .2 aapc.............................................4 broken.line . .5 confint.segmented . .7 davies.test . .9 down............................................. 11 draw.history . 12 intercept . 13 lines.segmented . 14 1 2 segmented-package plant . 15 plot.segmented . 16 points.segmented . 19 predict.segmented . 20 print.segmented . 21 pscore.test . 22 seg.control . 24 seg.lm.fit . 27 segmented . 29 selgmented . 35 slope . 37 stagnant . 38 summary.segmented . 39 vcov.segmented . 41 Index 43 segmented-package Segmented relationships in regression models with breakpoints / changepoints estimation Description Estimation and Inference of Regression Models with piecewise linear relationships having a fixed number of break-points. The estimation method is described in Muggeo (2003) <doi: 10.1002/sim.1545>.
    [Show full text]
  • EMPIRICAL LIKELIHOOD METHOD for SEGMENTED LINEAR REGRESSION by Zhihua Liu a Dissertation Submitted to the Faculty of the Charles
    EMPIRICAL LIKELIHOOD METHOD FOR SEGMENTED LINEAR REGRESSION by Zhihua Liu A Dissertation Submitted to the Faculty of The Charles E. Schmidt College of Science in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Florida Atlantic University Boca Raton, FL December 2011 Copyright by Zhihua Liu 2011 ii ACKNOWLEDGEMENTS First of all, I have to confess that the thought of writing this dissertation was intimidating to me. As much as I wish to express my appreciation to all the people who have been there for me to make this dissertation possible, I know I can never include everyone, and not adequately express my immense gratitude to them in simple words. I would like to express my deepest gratitude to all my committee members, Dr. Lianfen Qian, Dr. Hongwei Long, Dr. Heinrich Niederhausen and Dr. Dragan Radulovic. I appreciate their time, interest, and valuable comments concerning my thesis. For the last few years, I had the opportunity and privilege to work with Dr. Lianfen Qian. She has given me ideas and suggestions that enlightened my under- standing of this research and gave me a better perspective on my own work. I would also want to use this opportunity to thank many faculty members and my colleagues for all their inspiration and encouragement. I am also fortunate to be surrounded by sweet people from PenServ and ERISA Pension Systems. Without their support, I would never have completed this disser- tation. In the course of writing this dissertation, I am running between a full-time job and actuarial exams. Most of the time, I wish I could have 40 hours a day.
    [Show full text]