A Bayesian hierarchical surrogate outcome model for multiple sclerosis


 Victoria Wilcox
 2 years ago
 Views:
Transcription
1 A Bayesian hierarchical surrogate outcome model for multiple sclerosis 3 rd Annual ASA New Jersey Chapter / Bayer Statistics Workshop David Ohlssen (Novartis), Luca Pozzi and Heinz Schmidli (Novartis) November 13, 2015
2 Overview of presentation Brief review of metaanalysis methods in clinical trials What methods are attempting to do Quick overview of Bayesian methods Extension to Bayesian hierarchical surrogate outcome model Application related to drug development in MS Clinical background Previous research by Sormani and colleagues Applying the Bayesian surrogate outcome model Discussion and conclusions 2
3 3 Overview of metaanalysis models and methods
4 Introduction to metaanalysis methods and models A technique to adjust for imbalances When combining data from several clinical trials, metaanalysis is a technique that aims at adjusting for differences in background risk of patients in the analysis of the effects of treatments Within a single clinical trial this is accomplished by randomization Therefore, if all trials have the same randomization (e.g. 1:1), estimating the treatment effect from a pool of all observations will not introduce bias (although it might not be the most efficient approach) If trials have different unbalanced randomization, treatments recovered from the pool of all patients from all trials will no longer correspond to a common randomized assignment. This potentially leads to biased treatment effects if it is not accounted for in the analysis 4
5 Simpsons paradox A simple illustration of the need for metaanalysis Trial1 2:1 randomization Trial 2: 1:2 randomization In both cases, a consistent moderate improvement in the treatment effect is seen (Odds ratio of cured 1.39 and 1.40) Analysis of a pooled data results in a treatment effect that appears detrimental (Odds ratio of cured is 0.96) Trial 1 (very sick patients) Cured Died Total New Control Trial 2 (less sick patients) Cured Died Total New Control Pooled Cured Died Total New Control
6 Metaanalysis adjustment Adjustment that can be accomplished with summary data Adjustment could be based on building a model to adjust for difference in potential confounding factors based on individual patient baseline characteristics However, in the randomized control trial setting, most metaanalysis methods only apply some kind of adjustment or stratification for study Because each individual study is randomized, this alone can take care of the main potential source of bias In this sense "study" is a surrogate for all differences between the populations tested in different trials 6
7 Some notation for metaanalysis Generic notation for summary or IP data Let T represent the experimental treatment group and C the control group Suppose y i is the data from N studies (i=1,...,n) y i could be: individual patient outcome data associated with the study Could represent summary data (sufficient statistics) from each treatment group (e.g binary outcome data (y it, n it ) (y ic, n ic ) ) Could represent a treatment effect estimate and corresponding standard error (q i s i ) 7
8 Model parameters for an individual study Let C be the control group parameter (e.g background rate or population mean) and T be the corresponding treatment group parameter T Let q Parameter of interest compares T with C absolute metric: e.g. mean difference T C relative metric: Ratio: T / C (risk ratio, oddsratio, hazard ratio) logratio: log( T / C ) 8
9 Multiple studies Parameters and assumptions Modeling structures for the two treatment case Parameters 1,..., N response rate for C (control parameters) in studies 1,...,N q 1,..., q N (e.g logoddsratios (T vs. C, effects) for studies 1,...,N Assumptions for for control parameters ( 1,..., N )  a common (across studies) parameter c  N unrelated (stratification) parameters u  logit( i ) N(, 2 ): N parameters are similar/related r for effect parameters (q 1,..., q N ) (T vs. C)  a common effect parameter C  N unrelated effect parameters (no synthesis!) U  q i N(, 2 ): N effect parameters are similar/related R 9
10 Models assumptions A picture summarizing possible assumptions 10
11 Summary data metaanalysis Normal likelihood Fixed effects metaanalysis model (uc) q i q i ~ N(q i, s i2 ) q 1 =...=q N = q (uc) Random effects metaanalysis model (ur) q i q i ~ N(q i, s i2 ) q i ~ N(q, 2 ) (ur) 11 q i is the estimated treatment effect associated with study i s i is the corresponding standard error q is the overall treatment effect parameter is the standard deviation among the treatment effect parameters in the random effects model
12 12 Bayesian methods quick review
13 Introduction Bayesian methods Summary Historical Data Publications Expert Knowledge Bayesian Statistics All uncertainty is expressed probabilistically Critical input: Likelihood (Statistical Model) and Prior Bayes Theorem: Posterior Likelihood Prior Bayes (probability calculus) + Contextual Evidence Observed Data Updated Evidence + = Predictions Decisions + = 13
14 Some comments on Bayesian methods A personal perspective For a given problem, Bayesian statistics provides: A framework to combine relevant sources of information, using a realistically complex probability model In addition, if this model is useful: it should be reasonably well calibrated and lead to predictions that can form the basis for rational decision making However, the big challenge for a Bayesian, is convincing others that their model(s) are useful In other words, the posterior distributions and predictive distributions are approximately correct 14
15 The Bayesian modeling strategy used here Priors are carefully selected that we hope are dominated by the data Models fitted using Markov chain Monte Carlo (MCMC) estimation A variety of modeling structures examined Model support measured using the deviance information criteria (DIC) Model diagnostics with frequentist properties used to help show whether a model has good calibration Examine if similar conclusions are reached from well supported models to check inference robustness This work follows the ideas of Box (1980), who advocated the use of an iterative cycle of model criticism and estimation 15
16 16 Case study background
17 Multiple Sclerosis (MS) is a debilitating progressive disease Chronic, inflammatory, degenerative neurological autoimmune disease No known cure; affecting people in the prime of their lives (diagnosis years) Over 1 million sufferers worldwide Disproportionately affects women (70%), Caucasians and those in temperate climates 80% eventually need cane or wheelchair 17
18 MS disease background Multiple sclerosis (MS) is one area where a range of surrogate outcomes are used in various stages of clinical research The aim of treatments in MS is to prevent long term irreversible disability A clinical trial for evaluating a disability progression would require a large sample of patients with many years of followup In early stages, the vast majority of MS cases typically present as relapsing disease (Relapsing Remitting MS, RRMS) 18
19 Phase II and Phase III outcomes Relapsing Remitting MS Multiple Sclerosis In phase II MS trials, primary outcomes are typically based on magnetic resonance imaging (MRI) in the form of lesion counts Accepted surrogate marker for learn phase trials in RRMS: objective measure of the inflammatory activity of MS (detects 510x more events compared with clinical relapses) effect seen within weeks or a few months In Phase III primary outcomes are typically clinical relapses (count or time to event) and/or time to confirmed disability progression 19
20 log(rrrel) Clinical translation of MRI response R 2 = log(rr MRI ) Adapted from Sormani et al, Ann Neurol
21 Extract from the Motivating data Based on a systematic review by Sormani and colleagues (2010) 21
22 Clinical translation response (y) MRI> disability Relapse to disability; MRI to disability Adapted from Sormani et al, Neurolgy
23 Previous work by Sormani and colleagues a systematic review and metaanalysis Two separate weighted leastsquares regressions were fitted. The first relating the observed treatment effect on MRI lesions to the observed treatment effect on disability (adjusted R 2 =0:57), The second relating the observed treatment effect on relapses to the observed treatment effect on disability (adjusted R 2 = 0:71). The analyses ignored the measurement error with the relapse and MRI treatment effects Combining information from both MRI lesions and relapses may be a better surrogate for disability than each of them alone 23
24 24 Metaanalysis using a Bayesian hierarchical surrogate outcome model
25 Introduction to statistical techniques for surrogate outcomes The seminal work by Prentice subsequently lead to large literature examining statistical evaluation of surrogate outcomes Within this area statistical methods have been divided into three groups:  Those focusing on data from a single trial such as the Prentice criteria;  Those which use metaanalysis to combine summary information from multiple trials  Techniques that use a combination of triallevel and individuallevel data In this talk we will provide an analysis of summary data from multiple clinical trials, with the aim of understanding uncertainty associated with drug development decisions rather than formal validation, we shall solely focus on the Bayesian metaanalytic approach that was developed by Daniels and Hughes (1997) 25
26 Two level Surrogate outcome Bayesian metaanalysis Where q i represents the estimated treatment effect on the main outcome of interest, g i denotes the estimated treatment effect associated with the surrogate outcome, σ 2 θi and σ 2 γi are the variances that reflect the sampling uncertainty and ρi is the correlation between the estimated treatment differences conditional on the true differences θi and γi. The simplest triallevel model to describe the relationship between θi and γi is linear: 26
27 Studies with more than two treatment groups If studies have more than two arms the analysis must account for the correlation between the multiple treatment effects within a study. This can be accomplished by adjusting the sampling model, e.g. to a 4dimensional multivariate normal model in the case of three treatment arms to: 27
28 Some notes on priors When fitting the model in the Bayesian framework prior distributions must be assumed. In the multiple sclerosis casestudy, N(0, 10 6 ) priors will be assumed for all fixed effects (α 1, β 1 and γ i i = 1,, n). In terms of the variance component τ 2 ϵ, it is well known that results can be sensitive to the choice of prior distribution Following the suggestions of Spiegelhalter et al (2003) a standard half normal prior, denoted by HalfNormal(1) will be adopted. The parameters of the covariance matrix σ θi, ρi and σ γi are typically assumed to be known in the metaanalytic literature. 28
29 Extension to a three level model In cases such as the study of relapsing remitting MS we can borrow information from two surrogates simultaneously When formulating the trial level model, a natural extension of the Daniels and Hughes model would involve two levels of linear models: 29
30 Alternative threelevel models Various alternative structures could be applied when formulating the three level model. Here, we shall consider two alternative models: Firstly, both surrogates contribute directly to the main outcome of interest Secondly, instead of formulating a conditional structure, the second level of the model could be formulated as a multivariate normal random effects metaanalysis model 30
31 Practical issues when extracting trial level data Estimated variance covariance matrix Sampling variances can usually be drawn directly from summary data included in a publication Direct estimation of the correlations among the treatment effect estimates either requires the specification of a joint model or application of a nonparametric bootstrapping technique If only summary data is available the challenge of dealing with missing sampling covariances or correlations must be addressed: Using a range of plausible values; Sensitivity analysis over the entire correlation range Use of an alternative model 31
32 MS casestudy: summary data extraction Variance associated with each treatment effect and covariance MRI Treatment effects can be taken directly from the summary data provided (lesion counts log(risk ratio) and exposure) Variance based on NB sampling model with fixed overdispersion Relapse Treatment effects taken directly from summary data log(risk ratio) Variance provided by a binomial sampling model Disability Treatment effects taken directly from summary data log(risk ratio) Variance provided by a binomial sampling model Cov Based on limited priority data (bootstrap approach) Sensitivity analysis over a range of plausible correlations 32
33 Comparison of our weighting to Sormani et al (2010) Regressor Weights Intercept (s.e.) Slope (s.e.) adjusted R2 g i Sormani 0.1 (0.055) 0.63 (0.087) 0.7 g i Inverse Variance (0.05) (0.083) y i Sormani 0.2 (0.097) 0.36 (0.085) 0.56 y i Inverse Variance (0.091) (0.085)
34 34 Results
35 Comparisons of 2level and 3level models Posterior and predictive distributions 35
36 Sensitivity analysis Assessing the impact of different values of ρ 36 Model Param eter ρ = 0.05 [95%CI] 2 level α [0.096, 0.244] β [0.476, 1.022] τ ϵ [0.027, 0.29] 3 level α [0.068, 0.256] β [0.466, 0.95] τ ϵ [0.007, 0.24] α [0.372, 0.124] β [0.28, 0.784] τ δ [0.057, 0.419] ρ = 0.1 [95%CI] 0.08 [0.095, 0.241] [0.476, 1.01] [0.024, 0.286] [0.068, 0.256] [0.466, 0.95] [0.007, 0.24] [0.369, 0.117] [0.284, 0.781] [0.063, 0.415] ρ = 0 [95%CI] 0.08 [0.097, 0.246] [0.482, 1.033] [0.026, 0.297] [0.068, 0.256] [0.466, 0.95] 0.1 [0.007, 0.24] [0.376, 0.131] [0.27, 0.788] 0.21 [0.054, 0.416]
37 Forest plot of relapse treatment effects Estimated Risk ratios associated with relapse (mean and 95% interval) 3level model (gray circle); extended 3level model (gray square) multivariate metaanalysis(gray triangle). For comparison purposes, the estimates and 95% are displayed from fixed effects model (black circle). 37
38 3level models comparison 38
39 Discussion and further work One key advantage of the Bayesian model is the ability to provide predictions for the results of future clinical trials that fully account for parameter uncertainty. Highly valuable in a phase II setting. 39 A completed phase II study, which would typically have a reasonable amount of MRI data but limited relapse data and no information about disability progression Increased access to individual patient data clinical trial information (EMA data transparency) Therefore, combining individual patient data with summary data in a surrogate outcome setting would provide an important area for future research.
40 References Pozzi L, Schmidli H, Ohlssen D, A Bayesian hierarchical surrogate outcome model for multiple sclerosis (Submitted to Pharmaceutical statistics) Sormani M, Bonzano L, Roccatagliata L, Mancardi G, Uccelli A, Bruzzi P. Surrogate endpoints for EDSS worsening in multiple sclerosis. Neurology 2010; 75(4): Prentice R. Surrogate endpoints in clinical trials: definition and operational criteria. Statistics in Medicine 1989; 8(4): Daniels M, Hughes M. Metaanalysis for the evaluation of potential surrogate markers. Statistics in Medicine 1997; 16(17): Gelman A. Prior distributions for variance parameters in hierarchical models. Bayesian Analysis 2006; 1(33): Spiegelhalter D, Abrams K, Myles J. Bayesian Approaches to Clinical Trials and Health Care Evaluation. Wiley: Chichester, Riley R. Multivariate metaanalysis: the effect of ignoring within study correlation. Journal of the Friede T, Schmidli H. Blinded sample size reestimation with count data: methods and applications in multiple sclerosis. Statistics in Medicine 2010;Royal Statistical Society, 40 Series A 2009; 172(4):
41 41 Backup
42 Forest plot of EDSS treatment effects 42
Methods for Metaanalysis in Medical Research
Methods for Metaanalysis in Medical Research Alex J. Sutton University of Leicester, UK Keith R. Abrams University of Leicester, UK David R. Jones University of Leicester, UK Trevor A. Sheldon University
More informationINTRODUCTORY STATISTICS
INTRODUCTORY STATISTICS FIFTH EDITION Thomas H. Wonnacott University of Western Ontario Ronald J. Wonnacott University of Western Ontario WILEY JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore
More informationPSI Pharmaceutical Statistics Journal Club Meeting David Ohlssen, Novartis. 25th November 2014
Guidance on the implementation and reporting of a drug safety Bayesian network metaanalysis PSI Pharmaceutical Statistics Journal Club Meeting David Ohlssen, Novartis 25th November 2014 1 2 Outline Overview
More informationCHAPTER 3 EXAMPLES: REGRESSION AND PATH ANALYSIS
Examples: Regression And Path Analysis CHAPTER 3 EXAMPLES: REGRESSION AND PATH ANALYSIS Regression analysis with univariate or multivariate dependent variables is a standard procedure for modeling relationships
More informationSTA 4273H: Statistical Machine Learning
STA 4273H: Statistical Machine Learning Russ Salakhutdinov Department of Statistics! rsalakhu@utstat.toronto.edu! http://www.cs.toronto.edu/~rsalakhu/ Lecture 6 Three Approaches to Classification Construct
More informationThe role of focal white matter lesions on magnetic resonance
ORIGINAL ARTICLE Treatment Effect on Brain Atrophy Correlates with Treatment Effect on Disability in Multiple Sclerosis Maria Pia Sormani, PhD, 1 Douglas L. Arnold, MD, 2 and Nicola De Stefano, MD 3 Objective:
More informationHandling attrition and nonresponse in longitudinal data
Longitudinal and Life Course Studies 2009 Volume 1 Issue 1 Pp 6372 Handling attrition and nonresponse in longitudinal data Harvey Goldstein University of Bristol Correspondence. Professor H. Goldstein
More informationStatistical Rules of Thumb
Statistical Rules of Thumb Second Edition Gerald van Belle University of Washington Department of Biostatistics and Department of Environmental and Occupational Health Sciences Seattle, WA WILEY AJOHN
More informationRegression Modeling Strategies
Frank E. Harrell, Jr. Regression Modeling Strategies With Applications to Linear Models, Logistic Regression, and Survival Analysis With 141 Figures Springer Contents Preface Typographical Conventions
More informationService courses for graduate students in degree programs other than the MS or PhD programs in Biostatistics.
Course Catalog In order to be assured that all prerequisites are met, students must acquire a permission number from the education coordinator prior to enrolling in any Biostatistics course. Courses are
More informationSummary of Probability
Summary of Probability Mathematical Physics I Rules of Probability The probability of an event is called P(A), which is a positive number less than or equal to 1. The total probability for all possible
More informationCombined MRI lesions and relapses as a surrogate for disability in multiple sclerosis
Combined MRI lesions and relapses as a surrogate for disability in multiple sclerosis M.P. Sormani, PhD D.K. Li, MD P. Bruzzi, MD B. Stubinski, MD P. Cornelisse, MSc S. Rocak, PhD N. De Stefano, MD Address
More informationPooling and Metaanalysis. Tony O Hagan
Pooling and Metaanalysis Tony O Hagan Pooling Synthesising prior information from several experts 2 Multiple experts The case of multiple experts is important When elicitation is used to provide expert
More informationStatistical modelling with missing data using multiple imputation. Session 4: Sensitivity Analysis after Multiple Imputation
Statistical modelling with missing data using multiple imputation Session 4: Sensitivity Analysis after Multiple Imputation James Carpenter London School of Hygiene & Tropical Medicine Email: james.carpenter@lshtm.ac.uk
More informationBayesian Phylogeny and Measures of Branch Support
Bayesian Phylogeny and Measures of Branch Support Bayesian Statistics Imagine we have a bag containing 100 dice of which we know that 90 are fair and 10 are biased. The
More informationSupplementary appendix
Supplementary appendix This appendix formed part of the original submission and has been peer reviewed. We post it as supplied by the authors. Supplement to: Gold R, Giovannoni G, Selmaj K, et al, for
More informationAdequacy of Biomath. Models. Empirical Modeling Tools. Bayesian Modeling. Model Uncertainty / Selection
Directions in Statistical Methodology for Multivariable Predictive Modeling Frank E Harrell Jr University of Virginia Seattle WA 19May98 Overview of Modeling Process Model selection Regression shape Diagnostics
More informationApplications of R Software in Bayesian Data Analysis
Article International Journal of Information Science and System, 2012, 1(1): 723 International Journal of Information Science and System Journal homepage: www.modernscientificpress.com/journals/ijinfosci.aspx
More informationPS 271B: Quantitative Methods II. Lecture Notes
PS 271B: Quantitative Methods II Lecture Notes Langche Zeng zeng@ucsd.edu The Empirical Research Process; Fundamental Methodological Issues 2 Theory; Data; Models/model selection; Estimation; Inference.
More informationBayesian Statistical Analysis in Medical Research
Bayesian Statistical Analysis in Medical Research David Draper Department of Applied Mathematics and Statistics University of California, Santa Cruz draper@ams.ucsc.edu www.ams.ucsc.edu/ draper ROLE Steering
More informationMeasurement Issues in Short Term Clinical Trials. Brian Healy, PhD
Measurement Issues in Short Term Clinical Trials Brian Healy, PhD Overview n In order to iden>fy treatment effects or predictors of disease course, measurement of disease course is required n Although
More informationA Basic Introduction to Missing Data
John Fox Sociology 740 Winter 2014 Outline Why Missing Data Arise Why Missing Data Arise Global or unit nonresponse. In a survey, certain respondents may be unreachable or may refuse to participate. Item
More informationAn Application of the Gformula to Asbestos and Lung Cancer. Stephen R. Cole. Epidemiology, UNC Chapel Hill. Slides: www.unc.
An Application of the Gformula to Asbestos and Lung Cancer Stephen R. Cole Epidemiology, UNC Chapel Hill Slides: www.unc.edu/~colesr/ 1 Acknowledgements Collaboration with David B. Richardson, Haitao
More informationStatistics Graduate Courses
Statistics Graduate Courses STAT 7002Topics in StatisticsBiological/Physical/Mathematics (cr.arr.).organized study of selected topics. Subjects and earnable credit may vary from semester to semester.
More informationFixedEffect Versus RandomEffects Models
CHAPTER 13 FixedEffect Versus RandomEffects Models Introduction Definition of a summary effect Estimating the summary effect Extreme effect size in a large study or a small study Confidence interval
More informationBasic Statistics and Data Analysis for Health Researchers from Foreign Countries
Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma siersma@sund.ku.dk The Research Unit for General Practice in Copenhagen Dias 1 Content Quantifying association
More informationEffect estimation versus hypothesis testing
Department of Epidemiology and Public Health Unit of Biostatistics and Computational Sciences Effect estimation versus hypothesis testing PD Dr. C. Schindler Swiss Tropical and Public Health Institute
More informationProgramme du parcours Clinical Epidemiology 20142015. UMR 1. Methods in therapeutic evaluation A Dechartres/A Flahault
Programme du parcours Clinical Epidemiology 20142015 UR 1. ethods in therapeutic evaluation A /A Date cours Horaires 15/10/2014 1417h General principal of therapeutic evaluation (1) 22/10/2014 1417h
More informationUsing Criteria to Appraise a Metaanalyses
Using Criteria to Appraise a Metaanalyses Paul Cronin B.A., M.B. B.Ch. B.A.O., M.S., M.R.C.P.I.,.F.R.C.R. Department of Radiology, Division of Cardiothoracic Radiology, University of Michigan, Ann Arbor,
More informationSENSITIVITY ANALYSIS AND INFERENCE. Lecture 12
This work is licensed under a Creative Commons AttributionNonCommercialShareAlike License. Your use of this material constitutes acceptance of that license and the conditions of use of materials on this
More informationSAS Software to Fit the Generalized Linear Model
SAS Software to Fit the Generalized Linear Model Gordon Johnston, SAS Institute Inc., Cary, NC Abstract In recent years, the class of generalized linear models has gained popularity as a statistical modeling
More informationEconometric Analysis of Cross Section and Panel Data Second Edition. Jeffrey M. Wooldridge. The MIT Press Cambridge, Massachusetts London, England
Econometric Analysis of Cross Section and Panel Data Second Edition Jeffrey M. Wooldridge The MIT Press Cambridge, Massachusetts London, England Preface Acknowledgments xxi xxix I INTRODUCTION AND BACKGROUND
More informationSupplementary webappendix
Supplementary webappendix This webappendix formed part of the original submission and has been peer reviewed. We post it as supplied by the authors. Supplement to: Giovannoni G, Gold R, Selmaj K, et al,
More informationMissing Data Sensitivity Analysis of a Continuous Endpoint An Example from a Recent Submission
Missing Data Sensitivity Analysis of a Continuous Endpoint An Example from a Recent Submission Arno Fritsch Clinical Statistics Europe, Bayer November 21, 2014 ASA NJ Chapter / Bayer Workshop, Whippany
More informationA COMPARISON OF STATISTICAL METHODS FOR COSTEFFECTIVENESS ANALYSES THAT USE DATA FROM CLUSTER RANDOMIZED TRIALS
A COMPARISON OF STATISTICAL METHODS FOR COSTEFFECTIVENESS ANALYS THAT U DATA FROM CLUSTER RANDOMIZED TRIALS M Gomes, E Ng, R Grieve, R Nixon, J Carpenter and S Thompson Health Economists Study Group meeting
More informationEconomic Evaluation of Natalizumab (Tysabri) for the treatment of relapsing remitting multiple sclerosis that is rapidly evolving and severe or
Economic Evaluation of Natalizumab (Tysabri) for the treatment of relapsing remitting multiple sclerosis that is rapidly evolving and severe or suboptimally treated Summary In January 2007 Biogen Idec
More informationAPPLIED MISSING DATA ANALYSIS
APPLIED MISSING DATA ANALYSIS Craig K. Enders Series Editor's Note by Todd D. little THE GUILFORD PRESS New York London Contents 1 An Introduction to Missing Data 1 1.1 Introduction 1 1.2 Chapter Overview
More informationHow to evaluate medications in Multiple Sclerosis when placebo controlled RCTs are not feasible
University of Florence Dept. of Neurosciences Careggi University Hospital Dept of Neurosciences How to evaluate medications in Multiple Sclerosis when placebo controlled RCTs are not feasible Luca Massacesi,
More informationModeling and Analysis of Call Center Arrival Data: A Bayesian Approach
Modeling and Analysis of Call Center Arrival Data: A Bayesian Approach Refik Soyer * Department of Management Science The George Washington University M. Murat Tarimcilar Department of Management Science
More informationSystematic Reviews and Metaanalyses
Systematic Reviews and Metaanalyses Introduction A systematic review (also called an overview) attempts to summarize the scientific evidence related to treatment, causation, diagnosis, or prognosis of
More informationWhen Does it Make Sense to Perform a MetaAnalysis?
CHAPTER 40 When Does it Make Sense to Perform a MetaAnalysis? Introduction Are the studies similar enough to combine? Can I combine studies with different designs? How many studies are enough to carry
More informationGraduate Programs in Statistics
Graduate Programs in Statistics Course Titles STAT 100 CALCULUS AND MATR IX ALGEBRA FOR STATISTICS. Differential and integral calculus; infinite series; matrix algebra STAT 195 INTRODUCTION TO MATHEMATICAL
More informationProblem of Missing Data
VASA Mission of VA Statisticians Association (VASA) Promote & disseminate statistical methodological research relevant to VA studies; Facilitate communication & collaboration among VAaffiliated statisticians;
More informationMore details on the inputs, functionality, and output can be found below.
Overview: The SMEEACT (Software for More Efficient, Ethical, and Affordable Clinical Trials) web interface (http://research.mdacc.tmc.edu/smeeactweb) implements a single analysis of a twoarmed trial comparing
More informationMultivariate Logistic Regression
1 Multivariate Logistic Regression As in univariate logistic regression, let π(x) represent the probability of an event that depends on p covariates or independent variables. Then, using an inv.logit formulation
More informationC: LEVEL 800 {MASTERS OF ECONOMICS( ECONOMETRICS)}
C: LEVEL 800 {MASTERS OF ECONOMICS( ECONOMETRICS)} 1. EES 800: Econometrics I Simple linear regression and correlation analysis. Specification and estimation of a regression model. Interpretation of regression
More informationClinical Study Synopsis
Clinical Study Synopsis This file is posted on the Bayer HealthCare Clinical Trials Registry and Results website. It is provided for patients and healthcare professionals to increase the transparency of
More information1. Comparative effectiveness of alemtuzumab
Costeffectiveness of alemtuzumab (Lemtrada ) for the treatment of adult patients with relapsing remitting multiple sclerosis with active disease defined by clinical or imaging features The NCPE has issued
More informationLab 8: Introduction to WinBUGS
40.656 Lab 8 008 Lab 8: Introduction to WinBUGS Goals:. Introduce the concepts of Bayesian data analysis.. Learn the basic syntax of WinBUGS. 3. Learn the basics of using WinBUGS in a simple example. Next
More informationThe PCORI Methodology Report. Appendix A: Methodology Standards
The Appendix A: Methodology Standards November 2013 4 INTRODUCTION This page intentionally left blank. APPENDIX A A1 APPENDIX A: PCORI METHODOLOGY STANDARDS CrossCutting Standards for PCOR 1: Standards
More informationModelbased Synthesis. Tony O Hagan
Modelbased Synthesis Tony O Hagan Stochastic models Synthesising evidence through a statistical model 2 Evidence Synthesis (Session 3), Helsinki, 28/10/11 Graphical modelling The kinds of models that
More informationLeast Squares Estimation
Least Squares Estimation SARA A VAN DE GEER Volume 2, pp 1041 1045 in Encyclopedia of Statistics in Behavioral Science ISBN13: 9780470860809 ISBN10: 0470860804 Editors Brian S Everitt & David
More informationIssues Regarding Use of Placebo in MS Drug Trials. Peter Scott Chin, MD Novartis Pharmaceuticals Corporation
Issues Regarding Use of Placebo in MS Drug Trials Peter Scott Chin, MD Novartis Pharmaceuticals Corporation Context of the Guidance The draft EMA Guidance mentions placebo as a comparator for superiority
More informationSTATISTICA Formula Guide: Logistic Regression. Table of Contents
: Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 SigmaRestricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary
More informationCHAPTER 9 EXAMPLES: MULTILEVEL MODELING WITH COMPLEX SURVEY DATA
Examples: Multilevel Modeling With Complex Survey Data CHAPTER 9 EXAMPLES: MULTILEVEL MODELING WITH COMPLEX SURVEY DATA Complex survey data refers to data obtained by stratification, cluster sampling and/or
More informationTeriflunomide for treating relapsing remitting multiple sclerosis
Teriflunomide for treating relapsing remitting multiple Issued: January 2014 last modified: June 2014 guidance.nice.org.uk/ta NICE has accredited the process used by the Centre for Health Technology Evaluation
More informationTraining Program in MetaAnalysis
Training Program in MetaAnalysis June 2325, 2015 The University of Arizona College of Pharmacy Tucson, Arizona A 3day, handson training program for personnel in healthcare decisionmaking, industry
More informationPCORI Methodology Standards Published December 14, 2012
PCORI Methodology Standards Published December 14, 2012 PCORI s Board of Governors endorsed comprehensive standards for conducting patientcentered outcomes research on Nov. 19, 2012, as required by PCORI
More informationMODELLING AND ANALYSIS OF
MODELLING AND ANALYSIS OF FOREST FIRE IN PORTUGAL  PART I Giovani L. Silva CEAUL & DMIST  Universidade Técnica de Lisboa gsilva@math.ist.utl.pt Maria Inês Dias & Manuela Oliveira CIMA & DM  Universidade
More informationAn Introduction to Using WinBUGS for CostEffectiveness Analyses in Health Economics
Slide 1 An Introduction to Using WinBUGS for CostEffectiveness Analyses in Health Economics Dr. Christian Asseburg Centre for Health Economics Part 1 Slide 2 Talk overview Foundations of Bayesian statistics
More informationNICE DSU TECHNICAL SUPPORT DOCUMENT 2: A GENERALISED LINEAR MODELLING FRAMEWORK FOR PAIRWISE AND NETWORK METAANALYSIS OF RANDOMISED CONTROLLED TRIALS
NICE DSU TECHNICAL SUPPORT DOCUMENT 2: A GENERALISED LINEAR MODELLING FRAMEWORK FOR PAIRWISE AND NETWORK METAANALYSIS OF RANDOMISED CONTROLLED TRIALS REPORT BY THE DECISION SUPPORT UNIT August 2011 (last
More informationExperimental Designs leading to multiple regression analysis
Experimental Designs leading to multiple regression analysis 1. (Randomized) designed experiments. 2. Randomized block experiments. 3. Observational studies: probability based sample surveys 4. Observational
More informationAuxiliary Variables in Mixture Modeling: 3Step Approaches Using Mplus
Auxiliary Variables in Mixture Modeling: 3Step Approaches Using Mplus Tihomir Asparouhov and Bengt Muthén Mplus Web Notes: No. 15 Version 8, August 5, 2014 1 Abstract This paper discusses alternatives
More informationRandomized trials versus observational studies
Randomized trials versus observational studies The case of postmenopausal hormone therapy and heart disease Miguel Hernán Harvard School of Public Health www.hsph.harvard.edu/causal Joint work with James
More informationDimethyl fumarate for treating relapsing remitting multiple sclerosis
NATIONAL INSTITUTE FOR HEALTH AND CARE EXCELLENCE Final appraisal determination Dimethyl fumarate for treating relapsing remitting multiple sclerosis This guidance was developed using the single technology
More informationOverview Classes. 123 Logistic regression (5) 193 Building and applying logistic regression (6) 263 Generalizations of logistic regression (7)
Overview Classes 123 Logistic regression (5) 193 Building and applying logistic regression (6) 263 Generalizations of logistic regression (7) 24 Loglinear models (8) 54 1517 hrs; 5B02 Building and
More informationMissing Data: Part 1 What to Do? Carol B. Thompson Johns Hopkins Biostatistics Center SON Brown Bag 3/20/13
Missing Data: Part 1 What to Do? Carol B. Thompson Johns Hopkins Biostatistics Center SON Brown Bag 3/20/13 Overview Missingness and impact on statistical analysis Missing data assumptions/mechanisms Conventional
More informationWhat s New in Econometrics? Lecture 8 Cluster and Stratified Sampling
What s New in Econometrics? Lecture 8 Cluster and Stratified Sampling Jeff Wooldridge NBER Summer Institute, 2007 1. The Linear Model with Cluster Effects 2. Estimation with a Small Number of Groups and
More informationHandling missing data in Stata a whirlwind tour
Handling missing data in Stata a whirlwind tour 2012 Italian Stata Users Group Meeting Jonathan Bartlett www.missingdata.org.uk 20th September 2012 1/55 Outline The problem of missing data and a principled
More informationExponential Random Graph Models for Social Network Analysis. Danny Wyatt 590AI March 6, 2009
Exponential Random Graph Models for Social Network Analysis Danny Wyatt 590AI March 6, 2009 Traditional Social Network Analysis Covered by Eytan Traditional SNA uses descriptive statistics Path lengths
More informationSPSS Multivariable Linear Models and Logistic Regression
1 SPSS Multivariable Linear Models and Logistic Regression Multivariable Models Single continuous outcome (dependent variable), one main exposure (independent) variable, and one or more potential confounders
More informationVersion History. Previous Versions. for secondary progressive MS (SPMS) Policy Title. Drugs for MS.Drug facts box Interferon beta 1b
Version History Policy Title Drugs for MS.Drug facts box Interferon beta 1b for secondary progressive MS (SPMS) Version 1.0 Author West Midlands Commissioning Support Unit Publication Date Jan 2013 Review
More informationSPSS TRAINING SESSION 3 ADVANCED TOPICS (PASW STATISTICS 17.0) Sun Li Centre for Academic Computing lsun@smu.edu.sg
SPSS TRAINING SESSION 3 ADVANCED TOPICS (PASW STATISTICS 17.0) Sun Li Centre for Academic Computing lsun@smu.edu.sg IN SPSS SESSION 2, WE HAVE LEARNT: Elementary Data Analysis Group Comparison & Oneway
More informationThe HB. How Bayesian methods have changed the face of marketing research. Summer 2004
The HB How Bayesian methods have changed the face of marketing research. 20 Summer 2004 Reprinted with permission from Marketing Research, Summer 2004, published by the American Marketing Association.
More informationMarketing Mix Modelling and Big Data P. M Cain
1) Introduction Marketing Mix Modelling and Big Data P. M Cain Big data is generally defined in terms of the volume and variety of structured and unstructured information. Whereas structured data is stored
More informationDATA ANALYTICS USING R
DATA ANALYTICS USING R Duration: 90 Hours Intended audience and scope: The course is targeted at fresh engineers, practicing engineers and scientists who are interested in learning and understanding data
More informationLinear Classification. Volker Tresp Summer 2015
Linear Classification Volker Tresp Summer 2015 1 Classification Classification is the central task of pattern recognition Sensors supply information about an object: to which class do the object belong
More informationOrganizing Your Approach to a Data Analysis
Biost/Stat 578 B: Data Analysis Emerson, September 29, 2003 Handout #1 Organizing Your Approach to a Data Analysis The general theme should be to maximize thinking about the data analysis and to minimize
More informationAnalyzing Clinical Trial Data via the Bayesian Multiple Logistic Random Effects Model
Analyzing Clinical Trial Data via the Bayesian Multiple Logistic Random Effects Model Bartolucci, A.A 1, Singh, K.P 2 and Bae, S.J 2 1 Dept. of Biostatistics, University of Alabama at Birmingham, Birmingham,
More informationMaster s Theory Exam Spring 2006
Spring 2006 This exam contains 7 questions. You should attempt them all. Each question is divided into parts to help lead you through the material. You should attempt to complete as much of each problem
More informationRevised (2009) Association of British Neurologists guidelines for prescribing in multiple sclerosis
Revised (2009) guidelines for prescribing in multiple sclerosis INTRODUCTION In January 2001, the (ABN) first published guidelines for the use of licensed disease modifying treatments (ßinterferon and
More informationInterpretation of Somers D under four simple models
Interpretation of Somers D under four simple models Roger B. Newson 03 September, 04 Introduction Somers D is an ordinal measure of association introduced by Somers (96)[9]. It can be defined in terms
More informationBayesian Statistics in One Hour. Patrick Lam
Bayesian Statistics in One Hour Patrick Lam Outline Introduction Bayesian Models Applications Missing Data Hierarchical Models Outline Introduction Bayesian Models Applications Missing Data Hierarchical
More information, then the form of the model is given by: which comprises a deterministic component involving the three regression coefficients (
Multiple regression Introduction Multiple regression is a logical extension of the principles of simple linear regression to situations in which there are several predictor variables. For instance if we
More informationStatistics in Retail Finance. Chapter 6: Behavioural models
Statistics in Retail Finance 1 Overview > So far we have focussed mainly on application scorecards. In this chapter we shall look at behavioural models. We shall cover the following topics: Behavioural
More informationMultiple Sclerosis (MS) Aprile Royal, Novartis Pharma Canada Inc. September 21, 2011 Toronto, ON
Multiple Sclerosis (MS) Aprile Royal, Novartis Pharma Canada Inc. September 21, 2011 Toronto, ON Firstline DMTs Reduce Relapse Frequency by ~30% vs. Placebo Frequency of relapse with various DMTs, based
More informationChapter 10. Summary & Future perspectives
Summary & Future perspectives 123 Multiple sclerosis is a chronic disorder of the central nervous system, characterized by inflammation and axonal degeneration. All current therapies modulate the peripheral
More informationHANDLING DROPOUT AND WITHDRAWAL IN LONGITUDINAL CLINICAL TRIALS
HANDLING DROPOUT AND WITHDRAWAL IN LONGITUDINAL CLINICAL TRIALS Mike Kenward London School of Hygiene and Tropical Medicine Acknowledgements to James Carpenter (LSHTM) Geert Molenberghs (Universities of
More informationReview of the Methods for Handling Missing Data in. Longitudinal Data Analysis
Int. Journal of Math. Analysis, Vol. 5, 2011, no. 1, 113 Review of the Methods for Handling Missing Data in Longitudinal Data Analysis Michikazu Nakai and Weiming Ke Department of Mathematics and Statistics
More informationI L L I N O I S UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
Beckman HLM Reading Group: Questions, Answers and Examples Carolyn J. Anderson Department of Educational Psychology I L L I N O I S UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN Linear Algebra Slide 1 of
More informationLearning outcomes. Knowledge and understanding. Competence and skills
Syllabus Master s Programme in Statistics and Data Mining 120 ECTS Credits Aim The rapid growth of databases provides scientists and business people with vast new resources. This programme meets the challenges
More informationAN ACCESSIBLE TREATMENT OF MONTE CARLO METHODS, TECHNIQUES, AND APPLICATIONS IN THE FIELD OF FINANCE AND ECONOMICS
Brochure More information from http://www.researchandmarkets.com/reports/2638617/ Handbook in Monte Carlo Simulation. Applications in Financial Engineering, Risk Management, and Economics. Wiley Handbooks
More informationBayesX  Software for Bayesian Inference in Structured Additive Regression
BayesX  Software for Bayesian Inference in Structured Additive Regression Thomas Kneib Faculty of Mathematics and Economics, University of Ulm Department of Statistics, LudwigMaximiliansUniversity Munich
More informationVersion History. Previous Versions. Drugs for MS.Drug facts box fingolimod Version 1.0 Author
Version History Policy Title Drugs for MS.Drug facts box fingolimod Version 1.0 Author West Midlands Commissioning Support Unit Publication Date Jan 2013 Review Date Supersedes/New (Further fields as required
More informationAssessment of Rescue Medication Effect in Psychiatric Clinical Trials
Society for Clinical Trials 36 th Annual Meeting Assessment of Rescue Medication Effect in Psychiatric Clinical Trials Zhibao Mi, John H. Krystal, Karen M. Jones, Robert A. Rosenheck, Joseph F. Collins
More informationMetaRegression CHAPTER 20
CHAPTER 20 MetaRegression Introduction Fixedeffect model Fixed or random effects for unexplained heterogeneity Randomeffects model INTRODUCTION In primary studies we use regression, or multiple regression,
More informationTutorial on Markov Chain Monte Carlo
Tutorial on Markov Chain Monte Carlo Kenneth M. Hanson Los Alamos National Laboratory Presented at the 29 th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Technology,
More informationTransferability of Economic Evaluations in Clinical Trials
Transferability of Economic Evaluations in Clinical Trials Henry Glick Institutt for helseledelse og helseøkonomi November 25, 2008 The Problem Multicenter and multinational studies are the norm for the
More informationHandling missing data in large data sets. Agostino Di Ciaccio Dept. of Statistics University of Rome La Sapienza
Handling missing data in large data sets Agostino Di Ciaccio Dept. of Statistics University of Rome La Sapienza The problem Often in official statistics we have large data sets with many variables and
More informationIf several different trials are mentioned in one publication, the data of each should be extracted in a separate data extraction form.
General Remarks This template of a data extraction form is intended to help you to start developing your own data extraction form, it certainly has to be adapted to your specific question. Delete unnecessary
More information