STATISTICAL ANALYSIS OF SAFETY DATA IN LONG-TERM CLINICAL TRIALS
|
|
- Kristopher Cross
- 7 years ago
- Views:
Transcription
1 STATISTICAL ANALYSIS OF SAFETY DATA IN LONG-TERM CLINICAL TRIALS Tailiang Xie, Ping Zhao and Joel Waksman, Wyeth Consumer Healthcare Five Giralda Farms, Madison, NJ 794 KEY WORDS: Safety Data, Adverse Event, Statistical Analysis, Multivariate Survival Analysis, Clinical Trial. 1. Introduction In the past 4 years, approximately 15 drugs worldwide have been withdrawn from market for safety-related reasons since the withdrawal of thalidomide in A recent article claimed that serious adverse events (AEs) are now between the fourth and sixth leading cause of death in the United States. 2 In the ICH-E9, it is clearly stated that in all clinical trials, the evaluation of safety and tolerability of a drug constitutes an important element of the overall benefit/risk assessment. 3 Over the past decades, although much research has been done and many statistical methods have been utilized for analyzing efficacy data, not much has been utilized directly for the analysis of safety data. One of the reasons might be the complicity of safety data, particularly the data from long-term trials. Unlike efficacy analysis, the Type II error is usually of more concern in the safety analysis, especially for serious AEs. Therefore, more powerful statistical methods should be used. To date, most of the analyses of safety data are routine and exploratory in nature. Listing of AEs and summary of the crude rate are among the most commonly used analyses in regulatory submissions and publications. The crude rate is defined as the number of subjects with the event occurring at any time during exposure, divided by the total number of subjects exposed, regardless of duration of exposure, and it is usually analyzed via Fisher s exact test. This crude rate method may be efficient and sufficient for acute drug use in single-dose trials because the duration of drug exposure is usually short and equal among subjects 4. However, for longterm clinical trials with chronic and variable exposures and multiple incidences of AEs, the crude rate method could be invalid and misleading. There are at least three drawbacks associated with the crude rate method for long-term trials. First, because multiple incidences of an AE are counted only once for each subject during the entire trial, the crude rate method could be misleading without reference to chronic exposure of medication and multiple incidences of the same AE. Second, the crude rate method does not take into account important covariates that may have potential impacts on AE, such as demographic and baseline characteristics. Finally, the crude rate method is mostly underpowered for evaluating AE data. The purpose of this paper is to compare and discuss alternative methods for AE analysis. Methods to be discussed are the Cochran- Mantel-Haenszel (CMH) test, Poisson regression and two multivariate survival analysis models, Anderson-Gill multiplicative hazards model (AG model) 5 and proportional mean model (PM model) 6. The relative performance of these procedures in terms of power and Type I error rate will be evaluated using simulation studies. 2. Aspects of Safety Data in Long-term Trials Long-term clinical trials have a number of unique aspects important to AE assessment. Compared to single-dose trials, the drop out rate is usually higher in long-term trials, which results in variable duration of exposure time. Consider a long-term clinical trial illustrated in Figure 1, where there were 1, subjects enrolled in a one-year clinical trial. Most of the subjects remained exposed during the first three months. Approximately half of the subjects dropped out after six months and only a quarter of the subjects remained active at the end of the trial. 3824
2 Figure 1. Exposure Pattern for Subjects Followed-up Month of Exposure A third aspect of AE data in long-term trials is that a subject may experience multiple incidences of the same AE. Consider a 1-day clinical trial, in which there were a total of 85 incidences of an AE reported by 98 subjects. A useful graphical method to show multiple AE incidences within subjects is depicted in Figure 3, where each horizontal line represents the time course of a subject who was in the trial and the dots on the line represent the onset of AE incidences for the subject. Figure 3. Example Data with Multiple Incidences of AE Number of Events A second aspect is that the time pattern of an AE might be different for different drugs. Figure 2 illustrates an example in which the AE rate was approximately the same among three treatment groups. For Drug A, most of the AE incidences occurred at the beginning of the treatment and the number of AEs gradually declined until Month 6 and eventually disappeared. This may indicate a gradual buildup of tolerance to Drug A. For Drug B, most of the AE incidences were distributed evenly during Months 1-6. For Drug C, there was no AE incidence until Month 3. The AE rate then peaked around Months 6-8. This may indicate a cumulative toxicity of Drug C. Although the crude rates were the same for all three drugs, the time course when the AE occurred was completely different. 5 Figure 2. Pattern of AEs for Three Drugs Month of Exposure Drug A Drug B Drug C Subjects Study Days Finally, a fourth aspect of long-term AE data is the dependence among AEs within a subject, in the sense that a subject who had an AE is likely to have the same AE again. For instance, multiple incidences of somnolence can be induced by certain antihistamine drugs. These aspects undoubtedly bring challenges in assessing safety and tolerability of a drug for long-term use. Clearly, the conventional crude rate method is subject to bias in analysis of longterm safety data because it throws out a great deal of information. Methods capable of capturing these aspects should be used. In the next section, the crude rate method, CMH test, Poisson regression, AG model and PM model will be compared. 3. Comparison of Statistical Methods Among the methods compared, the AG model 5 6 and PM model are relatively recent advancements of multivariate survival analysis, and will be summarized briefly. 3825
3 Let N(t) be a counting process representing number of events occurring over the time interval [, t] (t ). Assuming that N(t) is a nonhomogeneous Poisson process and letting Λ Z (t) be the cumulative intensity function of N(t), conditional on a p-dimensional covariate process Z, then the AG model takes the form of β T Z ( t) Λ ( t) = e Λ ( t), Z where Λ is an unspecified continuous intensity function and β is a p-vector of regression parameters. By contrast, the PM model does not impose the Poisson assumption on N(t) and takes the form of β T Z ( t ) m ( t) = e m ( t), Z where m z (t)=e{ N(t) Z }, a mean function of N(t). If N(t) is a non-homogeneous Poisson process, then the mean function is the cumulative intensity function. Therefore, the PM model is an extension of the AG model. By assuming a non-homogeneous Poisson structure of N(.), the AG model essentially assumes independence among events. The naïve variance-covariance estimator (i.e. the Fisher information matrix) is used. However, the PM model allows dependence among events. The robust variance-covariance estimator (i.e. the sandwich estimator) is used. The crude rate method and CMH test are nonparametric; while the Poisson regression and AG model are parametric, in that they assume the number of events follows a Poisson distribution. The PM model is a semi-parametric method, in that it does not assume a specific distribution of N(t), however, it does assume a proportional structure of the mean functions between treatment groups. Among the compared methods, the PM model is the only method that is capable of capturing all of the mentioned aspects of safety data in long-term trials. A comparison of the methods is summarized in Table 1. Table 1. Comparison of Statistical Methods Aspect Consideration Method PA MT TE DP CE DE Crude No No No No No No CMH No Yes No No No No Poisson Yes Yes No No Yes No AG Yes Yes Yes No Yes Yes PM Yes* Yes Yes Yes Yes Yes *PM model is only semi-parametric. PA: Parametric assumption. MT: Multiplicity. TE: Time to event. DP: Dependence. CE: Covariate effect. DE: Duration of Exposure. 4. Simulation Results A number of simulation studies were conducted to assess the performance of these methods. We focused on the following aspects of performance: power, Type I error and robustness. The number of events was first simulated via a Poisson distribution for power and Type I error assessment. To assess robustness, the number of events was then simulated via a contaminated Poisson distribution. All simulations were performed using SAS Version 6.12 (SAS Institute, Cary, NC). For Poisson regression, the SAS GENMOD procedure was used. For both the AG and PM models, the SAS PHREG procedure was used with counting process data input. For the PM model, the SAS IML procedure also was used to compute the robust covariance-variance estimator. Data with Poisson Distribution In order to assess power, the AE data sets were generated, in which the number of AEs followed Poisson distributions with rates of 1 and 1.5, and the time to AE had marginal exponential distributions with medians of 1 and 1.5 days for the reference and test treatment groups, respectively. The correlation coefficients ρ among times to AE were.,.4,.6 and.9. There were 1 subjects in each treatment group. For the Type I error assessment, the AE data sets were generated in the same manner, except that the number of AEs followed Poisson distributions with rates of 1, and the time to AE had marginal exponential distributions with medians of 1 day for both of the reference and test treatment groups. 3826
4 The simulated data were then analyzed using each of the five methods. The simulation was repeated 1, times for each combination of correlation and method, and the proportion of times the null hypothesis of equal treatment AE rates was rejected at the.5 level was recorded. Table 2 has the results. Table 2. Comparison of the Simulated Power and Type I Error ρ Method Power Type I Error. Crude CMH Poisson AG PM Crude CMH Poisson AG PM Crude CMH Poisson AG PM Crude CMH Poisson AG PM Unsurprisingly, the crude rate method had the lowest power among all methods compared. All other methods had reasonably high power, especially the AG model, which took advantage of meeting all its model assumptions and utilizing almost all the information in the data. The PM model was the second most powerful method among all methods compared. For those methods that do not take into account the dependence of AEs within subject, the power was stable. For the PM model, however, as expected the power decreased as the withinsubject correlation increased. As shown in Table 2, all methods had reasonable Type I error rate, except for the AG model that had a Type I error rate in a range of To further investigate why the AG model inflates the Type I error, we performed additional simulations as shown in Table 3. Table3.TypeIerrorforAGmodel ρ N=2 N=3 N=ranpoi() N: the number of events per subject. N=ranpoi() means the number of events following a Poisson distribution. For the cases with fixed number of events, the Type I error inflation may be due to the increasing of within-subject correlation in the simulated data. For the case with random number of events, the inflation may be due to not only the increasing of within-subject correlation in the simulated data, but also the violation of the proportionality property caused by the randomness of the number of events. Non-Poisson Distribution Data In this simulation study, we attempted to assess the robustness of these methods under the non- Poisson situation, especially for the Poisson regression and the AG model. The AE data sets were generated in a similar manner as above, in which the time to AEs was simulated with the same distribution. The number of AEs, however, was contaminated by a random noise added to the Poisson distribution in order to create overdispersion to the data. The simulation was run for 1, times for each combination of correlation and method. Because the results were consistent across different correlation coefficients, only the results for correlation of.6 are displayed. Table 4. Comparison of Power for Non- Poisson Data (ρ =.6) Method Simulated Power Poisson Regression.28 AG.898 PM
5 As shown in Table 4, the powers for the Poisson regression and AG model were decreased. A severe impact was observed on the Poisson regression. For the AG model, although the Poisson condition was not held, the difference between the median times to event helped to lessen the power loss. Since the PM model is distribution free, its power remained essentially unchanged. 5. Discussion and Conclusion Since failure in detecting elevated AE rates related to a study drug could result in severe consequences, the Type II error is usually of more concern than the Type I error especially for serious AEs, in the safety analysis. The usual crude rate method is severely under-powered for long-term clinical trials. Thus it should not be used routinely for confirmatory analysis, especially for analyzing serious AEs. In addition, the crude rate method cannot factor in the effects of covariates that may affect AEs. The CMH test and Poisson regression are relatively powerful. However, neither of the methods can take into account the time course of AEs and the dependence of recurrent AEs within subjects. In addition, the Poisson regression can be severely impacted by violation of its parametric assumption. fairly easy to implement it in major software, such as SAS (PHREG and IML) and S-Plus (COXPH). Thus, the PM model has the best overall performances in terms of power, Type I error rate, robustness and capacity of capturing all aspects of safety data in long-term clinical trials. References 1. Spriet-Pourra C, Auriche M. (1994). Drug withdrawal from sale. 2 nd edition. Scrip Reports. Richmond, England: PJB Publications Ltd. 2. Lazarou J, Pomeranz BH, Corey PN. (1998). Incidence of adverse drug reactions in hospitalized patients. JAMA; 279: ICH-E9. 4. O Neil RT. (1987). Statistical analysis of adverse event data from clinical trials. Special emphasis on serious events. Drug Inf. J.; 21: Anderson, P.K. and Gill, R.D. (1982). Cox s Regression Model for counting processes: a large sample study. The Annals of Statistics, 1, Lin, D.Y., Wei, L. J., Yang, I. And Ying, Z. (2). Semiparametric regression for the mean and rate functions of recurrent events. J. R. Statist. Soc. B; 62, Part 4, pp The AG model has the highest power when all conditions pertaining to its model assumption are met. However, it does not take the dependence into account. As indicated by the Table 3, it should be used with caution when the number of events was widely divergent or the time to events were clustered type data. The PM model has reasonable Type I error rate, while its power is only slightly lower than that of the AG model. It is capable of capturing all aspects of long-term safety data. In addition, it is built under a regression framework and thus able to take into account the effects of covariates such as baseline and demographic characteristics. Unlike the AG model and Poisson regression, it is robust to the violation of the underlying distribution assumption. Additionally, because it models the mean instead of intensity function as in the AG model, it is intuitive and easily interpreted. Finally, it is 3828
SAS and R calculations for cause specific hazard ratios in a competing risks analysis with time dependent covariates
SAS and R calculations for cause specific hazard ratios in a competing risks analysis with time dependent covariates Martin Wolkewitz, Ralf Peter Vonberg, Hajo Grundmann, Jan Beyersmann, Petra Gastmeier,
More informationSample Size and Power in Clinical Trials
Sample Size and Power in Clinical Trials Version 1.0 May 011 1. Power of a Test. Factors affecting Power 3. Required Sample Size RELATED ISSUES 1. Effect Size. Test Statistics 3. Variation 4. Significance
More informationChapter 1 Introduction. 1.1 Introduction
Chapter 1 Introduction 1.1 Introduction 1 1.2 What Is a Monte Carlo Study? 2 1.2.1 Simulating the Rolling of Two Dice 2 1.3 Why Is Monte Carlo Simulation Often Necessary? 4 1.4 What Are Some Typical Situations
More information1.0 Abstract. Title: Real Life Evaluation of Rheumatoid Arthritis in Canadians taking HUMIRA. Keywords. Rationale and Background:
1.0 Abstract Title: Real Life Evaluation of Rheumatoid Arthritis in Canadians taking HUMIRA Keywords Rationale and Background: This abbreviated clinical study report is based on a clinical surveillance
More informationThis clinical study synopsis is provided in line with Boehringer Ingelheim s Policy on Transparency and Publication of Clinical Study Data.
abcd Clinical Study for Public Disclosure This clinical study synopsis is provided in line with s Policy on Transparency and Publication of Clinical Study Data. The synopsis which is part of the clinical
More informationIntroduction to Fixed Effects Methods
Introduction to Fixed Effects Methods 1 1.1 The Promise of Fixed Effects for Nonexperimental Research... 1 1.2 The Paired-Comparisons t-test as a Fixed Effects Method... 2 1.3 Costs and Benefits of Fixed
More informationTips for surviving the analysis of survival data. Philip Twumasi-Ankrah, PhD
Tips for surviving the analysis of survival data Philip Twumasi-Ankrah, PhD Big picture In medical research and many other areas of research, we often confront continuous, ordinal or dichotomous outcomes
More informationMISSING DATA TECHNIQUES WITH SAS. IDRE Statistical Consulting Group
MISSING DATA TECHNIQUES WITH SAS IDRE Statistical Consulting Group ROAD MAP FOR TODAY To discuss: 1. Commonly used techniques for handling missing data, focusing on multiple imputation 2. Issues that could
More informationAssociation Between Variables
Contents 11 Association Between Variables 767 11.1 Introduction............................ 767 11.1.1 Measure of Association................. 768 11.1.2 Chapter Summary.................... 769 11.2 Chi
More informationIntroduction to Event History Analysis DUSTIN BROWN POPULATION RESEARCH CENTER
Introduction to Event History Analysis DUSTIN BROWN POPULATION RESEARCH CENTER Objectives Introduce event history analysis Describe some common survival (hazard) distributions Introduce some useful Stata
More informationNon Parametric Inference
Maura Department of Economics and Finance Università Tor Vergata Outline 1 2 3 Inverse distribution function Theorem: Let U be a uniform random variable on (0, 1). Let X be a continuous random variable
More informationIntroduction. Survival Analysis. Censoring. Plan of Talk
Survival Analysis Mark Lunt Arthritis Research UK Centre for Excellence in Epidemiology University of Manchester 01/12/2015 Survival Analysis is concerned with the length of time before an event occurs.
More informationMultiple logistic regression analysis of cigarette use among high school students
Multiple logistic regression analysis of cigarette use among high school students ABSTRACT Joseph Adwere-Boamah Alliant International University A binary logistic regression analysis was performed to predict
More informationECON 142 SKETCH OF SOLUTIONS FOR APPLIED EXERCISE #2
University of California, Berkeley Prof. Ken Chay Department of Economics Fall Semester, 005 ECON 14 SKETCH OF SOLUTIONS FOR APPLIED EXERCISE # Question 1: a. Below are the scatter plots of hourly wages
More informationPlacement Stability and Number of Children in a Foster Home. Mark F. Testa. Martin Nieto. Tamara L. Fuller
Placement Stability and Number of Children in a Foster Home Mark F. Testa Martin Nieto Tamara L. Fuller Children and Family Research Center School of Social Work University of Illinois at Urbana-Champaign
More informationWHAT IS A JOURNAL CLUB?
WHAT IS A JOURNAL CLUB? With its September 2002 issue, the American Journal of Critical Care debuts a new feature, the AJCC Journal Club. Each issue of the journal will now feature an AJCC Journal Club
More informationStatistics Graduate Courses
Statistics Graduate Courses STAT 7002--Topics in Statistics-Biological/Physical/Mathematics (cr.arr.).organized study of selected topics. Subjects and earnable credit may vary from semester to semester.
More informationAntipsychotic drugs are the cornerstone of treatment
Article Effectiveness of Olanzapine, Quetiapine, Risperidone, and Ziprasidone in Patients With Chronic Schizophrenia Following Discontinuation of a Previous Atypical Antipsychotic T. Scott Stroup, M.D.,
More informationPROPERTIES OF THE SAMPLE CORRELATION OF THE BIVARIATE LOGNORMAL DISTRIBUTION
PROPERTIES OF THE SAMPLE CORRELATION OF THE BIVARIATE LOGNORMAL DISTRIBUTION Chin-Diew Lai, Department of Statistics, Massey University, New Zealand John C W Rayner, School of Mathematics and Applied Statistics,
More informationModule 5: Multiple Regression Analysis
Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College
More informationFairfield Public Schools
Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity
More informationApplications of Structural Equation Modeling in Social Sciences Research
American International Journal of Contemporary Research Vol. 4 No. 1; January 2014 Applications of Structural Equation Modeling in Social Sciences Research Jackson de Carvalho, PhD Assistant Professor
More informationModelling spousal mortality dependence: evidence of heterogeneities and implications
1/23 Modelling spousal mortality dependence: evidence of heterogeneities and implications Yang Lu Scor and Aix-Marseille School of Economics Lyon, September 2015 2/23 INTRODUCTION 3/23 Motivation It has
More informationCome scegliere un test statistico
Come scegliere un test statistico Estratto dal Capitolo 37 of Intuitive Biostatistics (ISBN 0-19-508607-4) by Harvey Motulsky. Copyright 1995 by Oxfd University Press Inc. (disponibile in Iinternet) Table
More informationSUMAN DUVVURU STAT 567 PROJECT REPORT
SUMAN DUVVURU STAT 567 PROJECT REPORT SURVIVAL ANALYSIS OF HEROIN ADDICTS Background and introduction: Current illicit drug use among teens is continuing to increase in many countries around the world.
More informationTUTORIAL on ICH E9 and Other Statistical Regulatory Guidance. Session 1: ICH E9 and E10. PSI Conference, May 2011
TUTORIAL on ICH E9 and Other Statistical Regulatory Guidance Session 1: PSI Conference, May 2011 Kerry Gordon, Quintiles 1 E9, and how to locate it 2 ICH E9 Statistical Principles for Clinical Trials (Issued
More informationClinical Study Synopsis for Public Disclosure
abcd Clinical Study for Public Disclosure This clinical study synopsis is provided in line with s Policy on Transparency and Publication of Clinical Study Data. The synopsis - which is part of the clinical
More informationResearch Methods & Experimental Design
Research Methods & Experimental Design 16.422 Human Supervisory Control April 2004 Research Methods Qualitative vs. quantitative Understanding the relationship between objectives (research question) and
More informationSAMPLE SIZE TABLES FOR LOGISTIC REGRESSION
STATISTICS IN MEDICINE, VOL. 8, 795-802 (1989) SAMPLE SIZE TABLES FOR LOGISTIC REGRESSION F. Y. HSIEH* Department of Epidemiology and Social Medicine, Albert Einstein College of Medicine, Bronx, N Y 10461,
More informationChecking proportionality for Cox s regression model
Checking proportionality for Cox s regression model by Hui Hong Zhang Thesis for the degree of Master of Science (Master i Modellering og dataanalyse) Department of Mathematics Faculty of Mathematics and
More informationDescriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
More informationTests for Two Survival Curves Using Cox s Proportional Hazards Model
Chapter 730 Tests for Two Survival Curves Using Cox s Proportional Hazards Model Introduction A clinical trial is often employed to test the equality of survival distributions of two treatment groups.
More informationDEALING WITH THE DATA An important assumption underlying statistical quality control is that their interpretation is based on normal distribution of t
APPLICATION OF UNIVARIATE AND MULTIVARIATE PROCESS CONTROL PROCEDURES IN INDUSTRY Mali Abdollahian * H. Abachi + and S. Nahavandi ++ * Department of Statistics and Operations Research RMIT University,
More informationSENSITIVITY ANALYSIS AND INFERENCE. Lecture 12
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. Your use of this material constitutes acceptance of that license and the conditions of use of materials on this
More informationII. DISTRIBUTIONS distribution normal distribution. standard scores
Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,
More information2. Incidence, prevalence and duration of breastfeeding
2. Incidence, prevalence and duration of breastfeeding Key Findings Mothers in the UK are breastfeeding their babies for longer with one in three mothers still breastfeeding at six months in 2010 compared
More informationApplied Statistics. J. Blanchet and J. Wadsworth. Institute of Mathematics, Analysis, and Applications EPF Lausanne
Applied Statistics J. Blanchet and J. Wadsworth Institute of Mathematics, Analysis, and Applications EPF Lausanne An MSc Course for Applied Mathematicians, Fall 2012 Outline 1 Model Comparison 2 Model
More informationStudy Design and Statistical Analysis
Study Design and Statistical Analysis Anny H Xiang, PhD Department of Preventive Medicine University of Southern California Outline Designing Clinical Research Studies Statistical Data Analysis Designing
More informationA Mixed Model Approach for Intent-to-Treat Analysis in Longitudinal Clinical Trials with Missing Values
Methods Report A Mixed Model Approach for Intent-to-Treat Analysis in Longitudinal Clinical Trials with Missing Values Hrishikesh Chakraborty and Hong Gu March 9 RTI Press About the Author Hrishikesh Chakraborty,
More informationChi-square test Fisher s Exact test
Lesson 1 Chi-square test Fisher s Exact test McNemar s Test Lesson 1 Overview Lesson 11 covered two inference methods for categorical data from groups Confidence Intervals for the difference of two proportions
More informationCOMPARING DATA ANALYSIS TECHNIQUES FOR EVALUATION DESIGNS WITH NON -NORMAL POFULP_TIOKS Elaine S. Jeffers, University of Maryland, Eastern Shore*
COMPARING DATA ANALYSIS TECHNIQUES FOR EVALUATION DESIGNS WITH NON -NORMAL POFULP_TIOKS Elaine S. Jeffers, University of Maryland, Eastern Shore* The data collection phases for evaluation designs may involve
More informationLOGISTIC REGRESSION ANALYSIS
LOGISTIC REGRESSION ANALYSIS C. Mitchell Dayton Department of Measurement, Statistics & Evaluation Room 1230D Benjamin Building University of Maryland September 1992 1. Introduction and Model Logistic
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 informationBasic research methods. Basic research methods. Question: BRM.2. Question: BRM.1
BRM.1 The proportion of individuals with a particular disease who die from that condition is called... BRM.2 This study design examines factors that may contribute to a condition by comparing subjects
More informationAnalysis of Changes in Indemnity Claim Frequency
WCIRB California Research and Analysis January 7, 2016 Analysis of Changes in Indemnity Claim Frequency January 2016 Update Report Executive Summary Historically, indemnity claim frequency has generally
More informationMISSING DATA: THE POINT OF VIEW OF ETHICAL COMMITTEES
I CONGRESSO NAZIONALE BIAS 2009 29/30 APRILE 2009 ELI LILLY SESTO FIORENTINO (FI) MISSING DATA: THE POINT OF VIEW OF ETHICAL COMMITTEES Anna Chiara Frigo Department of Environmental Medicine and Public
More information12.5: CHI-SQUARE GOODNESS OF FIT TESTS
125: Chi-Square Goodness of Fit Tests CD12-1 125: CHI-SQUARE GOODNESS OF FIT TESTS In this section, the χ 2 distribution is used for testing the goodness of fit of a set of data to a specific probability
More informationInterpreting Market Responses to Economic Data
Interpreting Market Responses to Economic Data Patrick D Arcy and Emily Poole* This article discusses how bond, equity and foreign exchange markets have responded to the surprise component of Australian
More informationChapter G08 Nonparametric Statistics
G08 Nonparametric Statistics Chapter G08 Nonparametric Statistics Contents 1 Scope of the Chapter 2 2 Background to the Problems 2 2.1 Parametric and Nonparametric Hypothesis Testing......................
More informationSTATISTICAL MODELING OF LONGITUDINAL SURVEY DATA WITH BINARY OUTCOMES
STATISTICAL MODELING OF LONGITUDINAL SURVEY DATA WITH BINARY OUTCOMES A Thesis Submitted to the College of Graduate Studies and Research in Partial Fulfillment of the Requirements for the Degree of Doctor
More informationAdditional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm
Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm
More informationUNDERSTANDING THE TWO-WAY ANOVA
UNDERSTANDING THE e have seen how the one-way ANOVA can be used to compare two or more sample means in studies involving a single independent variable. This can be extended to two independent variables
More information200609 - ATV - Lifetime Data Analysis
Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2015 200 - FME - School of Mathematics and Statistics 715 - EIO - Department of Statistics and Operations Research 1004 - UB - (ENG)Universitat
More informationTraining/Internship Brochure Advanced Clinical SAS Programming Full Time 6 months Program
Training/Internship Brochure Advanced Clinical SAS Programming Full Time 6 months Program Domain Clinical Data Sciences Private Limited 8-2-611/1/2, Road No 11, Banjara Hills, Hyderabad Andhra Pradesh
More informationMethods for Meta-analysis in Medical Research
Methods for Meta-analysis 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 informationModeling Customer Lifetime Value Using Survival Analysis An Application in the Telecommunications Industry
Paper 12028 Modeling Customer Lifetime Value Using Survival Analysis An Application in the Telecommunications Industry Junxiang Lu, Ph.D. Overland Park, Kansas ABSTRACT Increasingly, companies are viewing
More informationDesign and Analysis of Phase III Clinical Trials
Cancer Biostatistics Center, Biostatistics Shared Resource, Vanderbilt University School of Medicine June 19, 2008 Outline 1 Phases of Clinical Trials 2 3 4 5 6 Phase I Trials: Safety, Dosage Range, and
More informationMoving averages. Rob J Hyndman. November 8, 2009
Moving averages Rob J Hyndman November 8, 009 A moving average is a time series constructed by taking averages of several sequential values of another time series. It is a type of mathematical convolution.
More informationTwo-Sample T-Tests Allowing Unequal Variance (Enter Difference)
Chapter 45 Two-Sample T-Tests Allowing Unequal Variance (Enter Difference) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when no assumption
More information7.1 The Hazard and Survival Functions
Chapter 7 Survival Models Our final chapter concerns models for the analysis of data which have three main characteristics: (1) the dependent variable or response is the waiting time until the occurrence
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 informationT-test & factor analysis
Parametric tests T-test & factor analysis Better than non parametric tests Stringent assumptions More strings attached Assumes population distribution of sample is normal Major problem Alternatives Continue
More informationSTATISTICA Formula Guide: Logistic Regression. Table of Contents
: Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 Sigma-Restricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary
More informationThis clinical study synopsis is provided in line with Boehringer Ingelheim s Policy on Transparency and Publication of Clinical Study Data.
abcd Clinical Study for Public Disclosure This clinical study synopsis is provided in line with s Policy on Transparency and Publication of Clinical Study Data. The synopsis which is part of the clinical
More informationGuidelines for AJO-DO submissions: Randomized Clinical Trials June 2015
Guidelines for AJO-DO submissions: Randomized Clinical Trials June 2015 Complete and transparent reporting allows for accurate assessment of the quality of trial and correct interpretation of the trial
More informationAn introduction to Value-at-Risk Learning Curve September 2003
An introduction to Value-at-Risk Learning Curve September 2003 Value-at-Risk The introduction of Value-at-Risk (VaR) as an accepted methodology for quantifying market risk is part of the evolution of risk
More informationStudy Guide for the Final Exam
Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make
More informationTitle: Proton Pump Inhibitors and the risk of pneumonia: a comparison of cohort and self-controlled case series designs
Author's response to reviews Authors: Emmae Ramsay (emmae.ramsay@adelaide.edu.au) Nicole Pratt (nicole.pratt@unisa.edu.au) Philip Ryan (philip.ryan@adelaide.edu.au) Elizabeth Roughead (libby.roughead@unisa.edu.au)
More informationSeptember 19, 1984 FOOD PRODUCTION AND DIRECTION GÉNÉRALE, SECTION INSPECTION BRANCH PRODUCTION ET INSPECTION PESTICIDES DES ALIMENTS TRADE MEMORANDUM
Agriculture Canada September 19, 1984 T-1-245 FOOD PRODUCTION AND DIRECTION GÉNÉRALE, SECTION INSPECTION BRANCH PRODUCTION ET INSPECTION PESTICIDES DES ALIMENTS TRADE MEMORANDUM RE: Guidelines for Developing
More informationProbability Calculator
Chapter 95 Introduction Most statisticians have a set of probability tables that they refer to in doing their statistical wor. This procedure provides you with a set of electronic statistical tables that
More informationGuideline on missing data in confirmatory clinical trials
2 July 2010 EMA/CPMP/EWP/1776/99 Rev. 1 Committee for Medicinal Products for Human Use (CHMP) Guideline on missing data in confirmatory clinical trials Discussion in the Efficacy Working Party June 1999/
More informationUNIVERSITY OF NAIROBI
UNIVERSITY OF NAIROBI MASTERS IN PROJECT PLANNING AND MANAGEMENT NAME: SARU CAROLYNN ELIZABETH REGISTRATION NO: L50/61646/2013 COURSE CODE: LDP 603 COURSE TITLE: RESEARCH METHODS LECTURER: GAKUU CHRISTOPHER
More informationStudy Design. Date: March 11, 2003 Reviewer: Jawahar Tiwari, Ph.D. Ellis Unger, M.D. Ghanshyam Gupta, Ph.D. Chief, Therapeutics Evaluation Branch
BLA: STN 103471 Betaseron (Interferon β-1b) for the treatment of secondary progressive multiple sclerosis. Submission dated June 29, 1998. Chiron Corp. Date: March 11, 2003 Reviewer: Jawahar Tiwari, Ph.D.
More informationPermutation Tests for Comparing Two Populations
Permutation Tests for Comparing Two Populations Ferry Butar Butar, Ph.D. Jae-Wan Park Abstract Permutation tests for comparing two populations could be widely used in practice because of flexibility of
More informationSample Size Planning, Calculation, and Justification
Sample Size Planning, Calculation, and Justification Theresa A Scott, MS Vanderbilt University Department of Biostatistics theresa.scott@vanderbilt.edu http://biostat.mc.vanderbilt.edu/theresascott Theresa
More informationBusiness Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.
Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing
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 informationDo Commodity Price Spikes Cause Long-Term Inflation?
No. 11-1 Do Commodity Price Spikes Cause Long-Term Inflation? Geoffrey M.B. Tootell Abstract: This public policy brief examines the relationship between trend inflation and commodity price increases and
More informationIntroduction to Quantitative Methods
Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................
More informationComparison of resampling method applied to censored data
International Journal of Advanced Statistics and Probability, 2 (2) (2014) 48-55 c Science Publishing Corporation www.sciencepubco.com/index.php/ijasp doi: 10.14419/ijasp.v2i2.2291 Research Paper Comparison
More informationSTUDY PROGRESS AND SAFETY MONITORING PLAN TEMPLATE
STUDY PROGRESS AND SAFETY MONITORING PLAN TEMPLATE (Intended primarily for use in monitoring of Phase III/IV trials) Final December 20, 2006 20 DEC 06; Version 2.0 1 of 15 No.: DWD-POL-SR-01.00A2 TABLE
More informationUsing Proxy Measures of the Survey Variables in Post-Survey Adjustments in a Transportation Survey
Using Proxy Measures of the Survey Variables in Post-Survey Adjustments in a Transportation Survey Ting Yan 1, Trivellore Raghunathan 2 1 NORC, 1155 East 60th Street, Chicago, IL, 60634 2 Institute for
More informationCan I have FAITH in this Review?
Can I have FAITH in this Review? Find Appraise Include Total Heterogeneity Paul Glasziou Centre for Research in Evidence Based Practice Bond University What do you do? For an acutely ill patient, you do
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 informationTwo-Sample T-Tests Assuming Equal Variance (Enter Means)
Chapter 4 Two-Sample T-Tests Assuming Equal Variance (Enter Means) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when the variances of
More informationSpatial Statistics Chapter 3 Basics of areal data and areal data modeling
Spatial Statistics Chapter 3 Basics of areal data and areal data modeling Recall areal data also known as lattice data are data Y (s), s D where D is a discrete index set. This usually corresponds to data
More informationNonparametric Statistics
Nonparametric Statistics J. Lozano University of Goettingen Department of Genetic Epidemiology Interdisciplinary PhD Program in Applied Statistics & Empirical Methods Graduate Seminar in Applied Statistics
More informationSponsor. Novartis Generic Drug Name. Vildagliptin. Therapeutic Area of Trial. Type 2 diabetes. Approved Indication. Investigational.
Clinical Trial Results Database Page 1 Sponsor Novartis Generic Drug Name Vildagliptin Therapeutic Area of Trial Type 2 diabetes Approved Indication Investigational Study Number CLAF237A2386 Title A single-center,
More informationFrom the help desk: Bootstrapped standard errors
The Stata Journal (2003) 3, Number 1, pp. 71 80 From the help desk: Bootstrapped standard errors Weihua Guan Stata Corporation Abstract. Bootstrapping is a nonparametric approach for evaluating the distribution
More informationProspects, Problems of Marketing Research and Data Mining in Turkey
Prospects, Problems of Marketing Research and Data Mining in Turkey Sema Kurtulu, and Kemal Kurtulu Abstract The objective of this paper is to review and assess the methodological issues and problems in
More informationAssay Development and Method Validation Essentials
Assay Development and Method Validation Essentials Thomas A. Little Ph.D. 10/13/2012 President Thomas A. Little Consulting 12401 N Wildflower Lane Highland, UT 84003 1-925-285-1847 drlittle@dr-tom.com
More informationNegative Binomials Regression Model in Analysis of Wait Time at Hospital Emergency Department
Negative Binomials Regression Model in Analysis of Wait Time at Hospital Emergency Department Bill Cai 1, Iris Shimizu 1 1 National Center for Health Statistic, 3311 Toledo Road, Hyattsville, MD 20782
More information1 Overview and background
In Neil Salkind (Ed.), Encyclopedia of Research Design. Thousand Oaks, CA: Sage. 010 The Greenhouse-Geisser Correction Hervé Abdi 1 Overview and background When performing an analysis of variance with
More informationINTERNATIONAL CONFERENCE ON HARMONISATION OF TECHNICAL REQUIREMENTS FOR REGISTRATION OF PHARMACEUTICALS FOR HUMAN USE. Current Step 4 version
INTERNATIONAL CONFERENCE ON HARMONISATION OF TECHNICAL REQUIREMENTS FOR REGISTRATION OF PHARMACEUTICALS FOR HUMAN USE ICH HARMONISED TRIPARTITE GUIDELINE THE EXTENT OF POPULATION EXPOSURE TO ASSESS CLINICAL
More informationNAG C Library Chapter Introduction. g08 Nonparametric Statistics
g08 Nonparametric Statistics Introduction g08 NAG C Library Chapter Introduction g08 Nonparametric Statistics Contents 1 Scope of the Chapter... 2 2 Background to the Problems... 2 2.1 Parametric and Nonparametric
More informationModel Fitting in PROC GENMOD Jean G. Orelien, Analytical Sciences, Inc.
Paper 264-26 Model Fitting in PROC GENMOD Jean G. Orelien, Analytical Sciences, Inc. Abstract: There are several procedures in the SAS System for statistical modeling. Most statisticians who use the SAS
More information200627 - AC - Clinical Trials
Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2014 200 - FME - School of Mathematics and Statistics 715 - EIO - Department of Statistics and Operations Research MASTER'S DEGREE
More informationHumulin (LY041001) Page 1 of 1
(LY041001) These clinical study results are supplied for informational purposes only in the interests of scientific disclosure. They are not intended to substitute for the FDA-approved package insert or
More informationOverview. Longitudinal Data Variation and Correlation Different Approaches. Linear Mixed Models Generalized Linear Mixed Models
Overview 1 Introduction Longitudinal Data Variation and Correlation Different Approaches 2 Mixed Models Linear Mixed Models Generalized Linear Mixed Models 3 Marginal Models Linear Models Generalized Linear
More informationPredicting Customer Churn in the Telecommunications Industry An Application of Survival Analysis Modeling Using SAS
Paper 114-27 Predicting Customer in the Telecommunications Industry An Application of Survival Analysis Modeling Using SAS Junxiang Lu, Ph.D. Sprint Communications Company Overland Park, Kansas ABSTRACT
More information