A simple to implement algorithm for natural direct and indirect effects in survival studies with a repeatedly measured mediator
|
|
- Bennett Lindsey
- 8 years ago
- Views:
Transcription
1 A simple to implement algorithm for natural direct and indirect effects in survival studies with a repeatedly measured mediator Susanne Strohmaier 1, Nicolai Rosenkranz 2, Jørn Wetterslev 2 and Theis Lange 3 1 University of Oslo, 2 Copenhagen University Hospital, 3 University of Copenhagen ISCB Utrecht, August 2015
2 Outline Background and motivation The 6S study Generalisation of natural direct and indirect effects Data structure and notation Objectives and encountered challenges Estimation General idea Proposed algorithm Application results Discussion References Additional Material
3 Background and motivation The 6S study Motivating example - The 6S trial 6S - Scandinavian Starch for Severe Sepsis/Septic Shock trial Background: Intravenous fluids are the mainstay of treatment for patients with hypovolemia due to severe sepsis to obtain fast circulatory stabilisation. Commonly applied interventions: Crystalloids including saline and dextrose (Ringer s solution) Colloids containing larger molecules such as starch or gelatine. Preferred choice in Scandinavian intensive care units (ICU) Hydtroxyethyl starch (HES) 130/0.42 (previously high molecular weight HES - reported to cause acute kidney failure and bleeding) However HES 130/0.42 is largely unstudied in patients with severe sepsis; Lack of efficacy data and concerns about safety
4 Background and motivation The 6S study 6S in brief Study population: Patients with severe sepsis admitted to an intensive care unit (ICU) who needed fluid for circulatory stabilisation Randomisation to: Hydroxyethyl starch (HES 130/0.42) Ringer s solution Primary outcome: Death or end-stage kidney failure at 90 days after randomisation Results reported in NEJM: (Perner et al. (2012)) At 90 days after randomisation, 201 of 398 assigned to HES had died as compared with 172 of 400 patients assigned to Ringer s acetate. (RR 1.17; 95% confidence interval, 1.01 to 1.36: p=0.03) Speculated mechanism Effect of HES vs. Ringer s solution is mediated through acute kidney impairment. Starch particles cause acute kidney injury.
5 A simple to implement algorithm for natural direct and indirect effects in survival studies with a repeatedly measured mediator Background and motivation The 6S study Particular data collection M 1 M 2... M τ A N 1 N 2... N τ L Figure: Assumed causal structure
6 A simple to implement algorithm for natural direct and indirect effects in survival studies with a repeatedly measured mediator Generalisation of natural direct and indirect effects Data structure and notation Assumed structure M A L N/dN/T Figure: Local independence graph C Some notation A... dichotomous treatment, values {0, 1} L... a set of baseline confounders T = min( T, U)... minimum of event- and censoring time = I ( T U)... censoring indicator M...mediator process M t... mediator measured at time t M t... mediator history up to time t N t = I (T t, = 1)... counting process the event of interest C t... censoring process
7 Generalisation of natural direct and indirect effects Objectives and encountered challenges Objectives Estimation of average natural direct and indirect effects Question we could consider What would be the effect of treatment on time-to-event if treatment had not had an effect on the mediator? Effect of treatment attributable to the treatment induced change in the mediator Simple to implement algorithm for estimation for direct parametrisation of those effects
8 Generalisation of natural direct and indirect effects Objectives and encountered challenges Effect definitions Average natural direct effect E[ T ama T a M a L] comparing the survival times (within levels of baseline covariates L) had the treatment been changed from a to a, but the mediator history had followed the path it would have naturally followed under some reference condition for the treatment A = a. Average natural indirect effect E[ T ama T ama L], which compares the effect of the mediator histories M a and M a on the outcome, when the treatment is set to A = a. Effect decompostion on the mean survial scale E[ T a T a L] = E[ T ama T a M a L] = E[ T ama T a M a L] + E[ T ama T ama L],
9 Generalisation of natural direct and indirect effects Objectives and encountered challenges Encountered Challenges Conterfactual survial times T a, mediator trajectories M a and respective nested counterfactuals T ama have only been defined for mediators measured at one single time point Considerations under which conditions generalised effects are well-defined qunatities (Zheng and van der Laan (2012)) Extend respective no-unmeasurened confounder assumptions and the sequential ignorability assumption to the process setting
10 Estimation General idea General idea Directly parameterise the natural direct and indirect effects Extension of Lange et al. (2012) A Simple unified approach for estimating natural direct and indirect effects to the current setting. For GLMs and a mediator measured at a single point in time g(e[y ama ]) = c 0 + c 1 a + c 2 a + c 3 a a Method builds on ideas of Hong (2010), but has been generalised to various types of outcomes and mediators. Estimate the effects through analysis of an expanded and reweighted data set (ratio of mediator probabilities under different treatment regimes)
11 Estimation General idea Considering survival outcomes Assuming independent censoring Cox and Aalen models for the hazard function corresponding to the counterfactual survival time, expressed as Cox natural effects model λ 0(t) exp {c 0 + c 1a + c 2a + c 3a a + c 4L} Aalen natural effects model γ 0(t) + c 1a + c 2a + c 3a a + c 4L Natural effects models for the counterfactual variable T can ama expressed in the same fashion Effect decomposition can also be done on the hazard or hazard ratio scale (VanderWeele (2011)).
12 Estimation Proposed algorithm Proposed estimation algorithm (1/3) 1. Organise your data in wide format Censored or dead subjects will have missing for the mediators where they were not observed. 2. Estimate models for the mediator at each measurement time t conditional on the assigned treatment A, the mediator history and baseline confounders L by using the original data set. 3. Construct a new dataset; repeating each observation twice and including an additional auxiliary variable A, which equal A for the first replication and 1 A for the second replication. Further, add and indicator,identifying which data originate from the same subject.
13 Estimation Proposed algorithm Proposed estimation algorithm (2/3) 4. Apply the predict function twice to predict from the models in step 2, once based on A and once based on A. By dividing the predicted values the local weights at time s can be obtained W s j = P(Ms = m s j M s 1 = m s 1 j, A = a j, L = l j ) P(M s = m s j Ms 1 = m s 1 j, A = a j, L = l j ) (1) 5. Compute the cumulative weights by multiplying the local weights obtained in step 4 across the relevant rows T j W j = Wj s (2) s=1
14 Estimation Proposed algorithm Proposed estimation algorithm (3/3) 6. Fit a suitable outcome model, i.e. the Cox model including A and A, possible interactions and baseline covariates. The model should be weighted by the weights from step Confidence intervals can be obtained using bootstrap.
15 Estimation Proposed algorithm Some intuition... The resulting regression coefficient associated with A will capture the natural direct effect while the coefficient of A* will capture the natural indirect effect The derived weights are a tool to distinguish between direct and indirect effects by giving more weights to observations where the observed mediator trajectory would have been more likely to occur under a different treatment level than actually observed. For a constructive illustration see Hong (2010)
16 Application results Back to the original medical problem A quick recapitulation Patients selection: 795 patients admitted to intensive care units (396 in HES group vs. 399 Ringer solution) Mediator: KDIGO (Kidney Disease: Improving Global Outcome) score, taking values {0, 1, 2, 3} measured daily within the first 5 days of follow-up. Mediator model: Multinomial logistic regression Outcome: Time to death within 90 days after randomisation Outcome model: Cox regression
17 Application results Table: Direct, indirect effect through KDIGO and total effects and 95% confidence intervals (CI) comparing HES to Ringer solution. HR (95% CI ) Direct effect 1.16 ( ) Indirect efffect 1.05 ( ) Total effect 1.21 ( ) Both direct and indirect effect are not significant However, the magnitude of the direct effect indicates that could be another importatn pathway through which the treatment could bring about the outcome. Potential pathways Coagulapathy (bleeding disorder) Patients generally have a low immune response, additionally adding foreign bodies could cause there immune system to crash
18 Discussion Discussion Easy to implement in standard software (predict functionality, weighted modeling) Generally applicable for various mediator types, although some caution with continuous mediators (unstable weights) Can handle treatment-by-mediator interactions Effect definitions involves critical assumptions
19 References References Hong, G. (2010). Ratio od mediator probability weighting for estimating natural direct and indirect effects. Proceedings of the American Statistical Association, Biometrics Section, pages Lange, T., Vansteelandt, S., and Bekaert, M. (2012). A simple unified approach for estimating natural direct and indirect effects. American Journal of Epidemiology, 176(3): Pearl, J. (2001). Direct and indirect effects. In Proceedings of the Seventeenth Conference on Uncertainy in Artifcial Intelligence, pages Perner, A., Haase, N., Guttormsen, A., Tenhunen, J., Klemenzson, G., Åneman, A., Madsen, K., Møller, M., Elkjæ, J., Poulsen, L., Bendtsen, A., Winding, R., Steensen, M., Berezowicz, P., Søe-Jensen, P., Bestle, M., Strand, K., Wiis, J., White, J., Thornberg, K., Quist, L., Nielsen, J., Andersen, L., Holst, L., Thormar, K., Kjældgaard, A., Fabritius, M., Mondrup, F., Pott, F., Møller, T., Winkel, P., Wetterslev, J., the 6S Trial Group, and the Scandinavian Critical Care Trials Group. (2012). Hydrocyethyl starch 130/0.42 versus Ringer s acetate in severe sepsis. New England Jounral of Medicine, 367: VanderWeele, T. (2011). Causal mediation analysis with survival data. Epidemiology, 22(4): VanderWeele, T. J. and Vansteelandt, S. (2009). Conceptual issues concerning mediation, interventions and composition. Stat Interface, pages Zheng, W. and van der Laan, M. J. (2012). Causal mediation in a survival setting with time-dependent mediators. Berkeley Division of Biostatistics Working Paper Series. Working paper 295.
20 Additional Material (Nested) counterfactual quantities Assuming no censoring Counterfactual survival time Tam the outcome one would - possibly contrary to the fact - observe had the treatment A been set to the variable a and the entire mediator history M to m Counterfactual mediator trajectory M a corresponds to the mediator history that one would - possibly contrary to the fact - observe had treatment A been set to the value a. Nested counterfactual denoting the outcome one would have observed if A had been set to A = a and had M been set to the values it would have taken if A had been set to a. TaMa
21 Additional Material Average natural direct effect E[ T ama T a M a L] comparing the survival times (within levels of baseline covariates L) had the treatment been changed from a to a, but the mediator history had followed the path it would have naturally followed under some reference condition for the treatment A = a. Average natural indirect effect E[ T ama T ama L], which compares the effect of the mediator histories M a and M a on the outcome, when the treatment is set to A = a. Effect decompostion on the mean survial scale E[ T a T a L] = E[ T ama T a M a L] = E[ T ama T a M a L] + E[ T ama T ama L],
22 A simple to implement algorithm for natural direct and indirect effects in survival studies with a repeatedly measured mediator Additional Material Assumptions... to relate the counterfactual quantities to the observed data A M 1 M 2... M τ A N 1 N 2... N τ Figure: Augemented DAG L Treatment is randomised No unmeasured confounding between treatment and the outcome process, treatment and the mediator process and the mediator and outcome process.
23 Additional Material Non-parametric structural equation models Current mediator value M t Ma t = f M (M t 1 a, A = a, L = l, ε t a), with ε t a denoting an error term. Caution: Contains an assumption that all time-dependent predictors of both the mediator and survival status are contained in the mediator process (critical discussion in Zheng and van der Laan (2012)). Counterfactual event process N t aa = f N(M t a, Nt 1 aa, A = a, L = l, γt a), with γ t a again denoting an error term. Using those equations the assumptions can be pharsed in terms of the error terms.
24 Additional Material Assumptions Consistency: As stated in the main text, consistency assumes that the counterfactual outcomes T am and M a are the observed outcomes T with probability 1 among subjects with A = a and M = m and for the mediator trajectories M a are the observed mediator trajectories m with probability 1 for subject with A = a. Positivity: Further to ensure that the equations above describe non-degenerate probability distributions, we assume that the error terms follow uniform distributions ε t a unif ([0, 1]), a = 0, 1 (3) γ t a unif ([0, 1]), a = 0, 1 (4) and that fm t and f N t are not constant for the whole range ([0, 1]) in the arguments ε t and γ t. Further the full vectors of error terms (ε 1 a,..., ε τ a ) and (γa, 1..., γa τ ) are assumed to be an independent and identically distributed sequence.
25 Additional Material Assumptions cont. No unmeasured confounders: Random treatment allocation should ensure that treatment-outcome as well as the treatment - mediator relationship will not be confounded with either measured or unmeasured confounders. This can be expressed as ε t 0 ( ) ε t 1 A γ 0 t A. (5) γ1 t For the mediator-outcome relationship we assume ( ) ( ) ε t 0γ0 t A A and ε t 1γ1 t A A
26 Additional Material Assumptions cont. Extended sequential ignorability: The sequential ignorability assumption known from the single mediator case to be required for identifying natural effects needs to be modified to accommodate the multiple measurements. In terms of the error terms it can be expressed as ( ) ε t γ t 0 a γ1 t ( ) a = 0, 1 and γa t ε t 0 ε t 1 a = 0, 1. (6)
27 Additional Material Proof Algorithm Under these assumptions E[g((T, ) ama )] can be linked to the observed data as follows, where the function g() is any measureable function (this ensures that the distributions are the same, not just a single expected value) and h() corresponds to a density with respect to a suitable measure. E[g((T, ) ama ) L = l] = E[g(T, ) A = a, A = a, L = l] Recall that τ denotes the maximal follow up time, so we have = τ g(t, δ)h(t, δ A = a, A = a, L = l), δ=0,1 t=1 further, let M denote the space of possible mediator values, then = τ g(t, δ) h(t, δ, m t A = a, A = a, L = l)d m t δ=0,1 t=1 m t M t = τ g(t, δ) δ=0,1 t=1 m t M t h(t, δ m t, A = a, A = a, L = l) h( mt A = a, A = a, L = l) h( m t A = a, A = a, L = l) h( m t A = a, A = a, L = l)d m t,
28 Additional Material Proof continued conditioning on m t in the first term allows to remove A from the conditioning set, further using that M t depends only on A gives the following equality = τ δ=0,1 t=1 g(t, δ) h(t, δ m t, A = a, L = l) h( mt A = a, L = l) m t M t h( m t A = a, L = l) h( m t A = a, L = l)d m t, applying the same independence arguments again, we have = τ g(t, δ) h(t, δ m t, A = a, A = a, L = l)h( m t A = a, A = a, L = l) δ=0,1 t=1 m t M t h( mt A = a, L = l) h( m t A = a, L = l) )d mt, what can be writen as = τ g(t, δ)w ( m t, a, a, l)h(t, δ, m t A = a, A = a, L = l)d m t. δ=0,1 t=1 m t M t
29 Additional Material Proof continued The last expression has the sample counterpart 1 #{N } where T g(t i, i )W aa (M i i, a, a, L i ), i N N = {i {1,..., n} : A i = a, L i = l}.
Tips 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 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 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 & One-way
More informationAn Application of the G-formula to Asbestos and Lung Cancer. Stephen R. Cole. Epidemiology, UNC Chapel Hill. Slides: www.unc.
An Application of the G-formula 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 informationMany research questions in epidemiology are concerned. Estimation of Direct Causal Effects ORIGINAL ARTICLE
ORIGINAL ARTICLE Maya L. Petersen, Sandra E. Sinisi, and Mark J. van der Laan Abstract: Many common problems in epidemiologic and clinical research involve estimating the effect of an exposure on an outcome
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 informationBig data size isn t enough! Irene Petersen, PhD Primary Care & Population Health
Big data size isn t enough! Irene Petersen, PhD Primary Care & Population Health Introduction Reader (Statistics and Epidemiology) Research team epidemiologists/statisticians/phd students Primary care
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 informationPersonalized Predictive Medicine and Genomic Clinical Trials
Personalized Predictive Medicine and Genomic Clinical Trials Richard Simon, D.Sc. Chief, Biometric Research Branch National Cancer Institute http://brb.nci.nih.gov brb.nci.nih.gov Powerpoint presentations
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 informationWith Big Data Comes Big Responsibility
With Big Data Comes Big Responsibility Using health care data to emulate randomized trials when randomized trials are not available Miguel A. Hernán Departments of Epidemiology and Biostatistics Harvard
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 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 informationUnit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.)
Unit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.) Logistic regression generalizes methods for 2-way tables Adds capability studying several predictors, but Limited to
More informationA LONGITUDINAL AND SURVIVAL MODEL WITH HEALTH CARE USAGE FOR INSURED ELDERLY. Workshop
A LONGITUDINAL AND SURVIVAL MODEL WITH HEALTH CARE USAGE FOR INSURED ELDERLY Ramon Alemany Montserrat Guillén Xavier Piulachs Lozada Riskcenter - IREA Universitat de Barcelona http://www.ub.edu/riskcenter
More informationDepartment/Academic Unit: Public Health Sciences Degree Program: Biostatistics Collaborative Program
Department/Academic Unit: Public Health Sciences Degree Program: Biostatistics Collaborative Program Department of Mathematics and Statistics Degree Level Expectations, Learning Outcomes, Indicators of
More informationMissing data and net survival analysis Bernard Rachet
Workshop on Flexible Models for Longitudinal and Survival Data with Applications in Biostatistics Warwick, 27-29 July 2015 Missing data and net survival analysis Bernard Rachet General context Population-based,
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 informationModule 223 Major A: Concepts, methods and design in Epidemiology
Module 223 Major A: Concepts, methods and design in Epidemiology Module : 223 UE coordinator Concepts, methods and design in Epidemiology Dates December 15 th to 19 th, 2014 Credits/ECTS UE description
More informationExplaining Causal Findings Without Bias: Detecting and Assessing Direct Effects *
Explaining Causal Findings Without Bias: Detecting and Assessing Direct Effects * Avidit Acharya, Matthew Blackwell, and Maya Sen April 9, 2015 Abstract Scholars trying to establish causal relationships
More informationEvaluation of Treatment Pathways in Oncology: Modeling Approaches. Feng Pan, PhD United BioSource Corporation Bethesda, MD
Evaluation of Treatment Pathways in Oncology: Modeling Approaches Feng Pan, PhD United BioSource Corporation Bethesda, MD 1 Objectives Rationale for modeling treatment pathways Treatment pathway simulation
More informationExample: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not.
Statistical Learning: Chapter 4 Classification 4.1 Introduction Supervised learning with a categorical (Qualitative) response Notation: - Feature vector X, - qualitative response Y, taking values in C
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 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 two-armed trial comparing
More informationElements of statistics (MATH0487-1)
Elements of statistics (MATH0487-1) Prof. Dr. Dr. K. Van Steen University of Liège, Belgium December 10, 2012 Introduction to Statistics Basic Probability Revisited Sampling Exploratory Data Analysis -
More informationData Analysis, Research Study Design and the IRB
Minding the p-values p and Quartiles: Data Analysis, Research Study Design and the IRB Don Allensworth-Davies, MSc Research Manager, Data Coordinating Center Boston University School of Public Health IRB
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 informationProblem of Missing Data
VASA Mission of VA Statisticians Association (VASA) Promote & disseminate statistical methodological research relevant to VA studies; Facilitate communication & collaboration among VA-affiliated statisticians;
More informationCS&SS / STAT 566 CAUSAL MODELING
CS&SS / STAT 566 CAUSAL MODELING Instructor: Thomas Richardson E-mail: thomasr@u.washington.edu Lecture: MWF 2:30-3:20 SIG 227; WINTER 2016 Office hour: W 3.30-4.20 in Padelford (PDL) B-313 (or by appointment)
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 informationLecture 15 Introduction to Survival Analysis
Lecture 15 Introduction to Survival Analysis BIOST 515 February 26, 2004 BIOST 515, Lecture 15 Background In logistic regression, we were interested in studying how risk factors were associated with presence
More informationUniversity of Maryland School of Medicine Master of Public Health Program. Evaluation of Public Health Competencies
Semester/Year of Graduation University of Maryland School of Medicine Master of Public Health Program Evaluation of Public Health Competencies Students graduating with an MPH degree, and planning to work
More informationVignette for survrm2 package: Comparing two survival curves using the restricted mean survival time
Vignette for survrm2 package: Comparing two survival curves using the restricted mean survival time Hajime Uno Dana-Farber Cancer Institute March 16, 2015 1 Introduction In a comparative, longitudinal
More informationCross Validation techniques in R: A brief overview of some methods, packages, and functions for assessing prediction models.
Cross Validation techniques in R: A brief overview of some methods, packages, and functions for assessing prediction models. Dr. Jon Starkweather, Research and Statistical Support consultant This month
More informationCOMMON METHODOLOGICAL ISSUES FOR CER IN BIG DATA
COMMON METHODOLOGICAL ISSUES FOR CER IN BIG DATA Harvard Medical School and Harvard School of Public Health sharon@hcp.med.harvard.edu December 2013 1 / 16 OUTLINE UNCERTAINTY AND SELECTIVE INFERENCE 1
More informationSchool of Public Health and Health Services Department of Epidemiology and Biostatistics
School of Public Health and Health Services Department of Epidemiology and Biostatistics Master of Public Health and Graduate Certificate Biostatistics 0-04 Note: All curriculum revisions will be updated
More informationX X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1)
CORRELATION AND REGRESSION / 47 CHAPTER EIGHT CORRELATION AND REGRESSION Correlation and regression are statistical methods that are commonly used in the medical literature to compare two or more variables.
More informationCorrelational Research
Correlational Research Chapter Fifteen Correlational Research Chapter Fifteen Bring folder of readings The Nature of Correlational Research Correlational Research is also known as Associational Research.
More informationOverview Classes. 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7)
Overview Classes 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7) 2-4 Loglinear models (8) 5-4 15-17 hrs; 5B02 Building and
More informationThe Harvard MPH in Epidemiology Online/On-Campus/In the Field. Two-Year, Part-Time Program. Sample Curriculum Guide 2016-2018
The Harvard MPH in Epidemiology Online/On-Campus/In the Field Two-Year, Part-Time Program Sample Curriculum Guide 2016-2018 For more information about the program, please visit: http://www.hsph.harvard.edu/admissions/degree-programs/online-mph-inepidemiology.
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 informationElectronic Health Records in an Integrated Delivery System: Effects on Diabetes Care Quality
Electronic Health Records in an Integrated Delivery System: Effects on Diabetes Care Quality Mary Reed, DrPH 1 Jie Huang, PhD 1 Ilana Graetz 1 Richard Brand, PhD 2 Marc Jaffe, MD 3 Bruce Fireman, MA 1
More informationBiostat Methods STAT 5820/6910 Handout #6: Intro. to Clinical Trials (Matthews text)
Biostat Methods STAT 5820/6910 Handout #6: Intro. to Clinical Trials (Matthews text) Key features of RCT (randomized controlled trial) One group (treatment) receives its treatment at the same time another
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 informationSurvival Analysis of Left Truncated Income Protection Insurance Data. [March 29, 2012]
Survival Analysis of Left Truncated Income Protection Insurance Data [March 29, 2012] 1 Qing Liu 2 David Pitt 3 Yan Wang 4 Xueyuan Wu Abstract One of the main characteristics of Income Protection Insurance
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 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 information13. Poisson Regression Analysis
136 Poisson Regression Analysis 13. Poisson Regression Analysis We have so far considered situations where the outcome variable is numeric and Normally distributed, or binary. In clinical work one often
More informationUMEÅ INTERNATIONAL SCHOOL
UMEÅ INTERNATIONAL SCHOOL OF PUBLIC HEALTH Master Programme in Public Health - Programme and Courses Academic year 2015-2016 Public Health and Clinical Medicine Umeå International School of Public Health
More informationThe Landmark Approach: An Introduction and Application to Dynamic Prediction in Competing Risks
Landmarking and landmarking Landmarking and competing risks Discussion The Landmark Approach: An Introduction and Application to Dynamic Prediction in Competing Risks Department of Medical Statistics and
More informationSurvival Analysis of Dental Implants. Abstracts
Survival Analysis of Dental Implants Andrew Kai-Ming Kwan 1,4, Dr. Fu Lee Wang 2, and Dr. Tak-Kun Chow 3 1 Census and Statistics Department, Hong Kong, China 2 Caritas Institute of Higher Education, Hong
More informationImputing Values to Missing Data
Imputing Values to Missing Data In federated data, between 30%-70% of the data points will have at least one missing attribute - data wastage if we ignore all records with a missing value Remaining data
More informationSafety & Effectiveness of Drug Therapies for Type 2 Diabetes: Are pharmacoepi studies part of the problem, or part of the solution?
Safety & Effectiveness of Drug Therapies for Type 2 Diabetes: Are pharmacoepi studies part of the problem, or part of the solution? IDEG Training Workshop Melbourne, Australia November 29, 2013 Jeffrey
More informationAuxiliary Variables in Mixture Modeling: 3-Step Approaches Using Mplus
Auxiliary Variables in Mixture Modeling: 3-Step 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 informationTargeted Learning with Big Data
Targeted Learning with Big Data Mark van der Laan UC Berkeley Center for Philosophy and History of Science Revisiting the Foundations of Statistics in the Era of Big Data: Scaling Up to Meet the Challenge
More informationAlemtuzumab for treating relapsing-remitting multiple sclerosis
Alemtuzumab for treating relapsing-remitting multiple Issued: May 2014 guidance.nice.org.uk/ta NICE has accredited the process used by the Centre for Health Technology Evaluation at NICE to produce technology
More informationREGULATIONS FOR THE POSTGRADUATE DIPLOMA IN CLINICAL RESEARCH METHODOLOGY (PDipClinResMethodology)
452 REGULATIONS FOR THE POSTGRADUATE DIPLOMA IN CLINICAL RESEARCH METHODOLOGY (PDipClinResMethodology) (See also General Regulations) M.57 Admission requirements To be eligible for admission to the courses
More informationHow To Model The Fate Of An Animal
Models Where the Fate of Every Individual is Known This class of models is important because they provide a theory for estimation of survival probability and other parameters from radio-tagged animals.
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 informationThe Harvard MPH in Epidemiology Online/On-Campus/In the Field. Two-Year, Part-Time Program. Sample Curriculum Guide 2016-2018
The Harvard MPH in Epidemiology Online/On-Campus/In the Field Two-Year, Part-Time Program Sample Curriculum Guide 2016-2018 For more information about the program, please visit: http://www.hsph.harvard.edu/admissions/degree-programs/online-mph-inepidemiology.
More informationPrediction for Multilevel Models
Prediction for Multilevel Models Sophia Rabe-Hesketh Graduate School of Education & Graduate Group in Biostatistics University of California, Berkeley Institute of Education, University of London Joint
More informationEpidemiologists typically seek to answer causal questions using statistical data:
c16.qxd 2/8/06 12:43 AM Page 387 Y CHAPTER SIXTEEN USING CAUSAL DIAGRAMS TO UNDERSTAND COMMON PROBLEMS IN SOCIAL EPIDEMIOLOGY M. Maria Glymour Epidemiologists typically seek to answer causal questions
More informationProgramme du parcours Clinical Epidemiology 2014-2015. UMR 1. Methods in therapeutic evaluation A Dechartres/A Flahault
Programme du parcours Clinical Epidemiology 2014-2015 UR 1. ethods in therapeutic evaluation A /A Date cours Horaires 15/10/2014 14-17h General principal of therapeutic evaluation (1) 22/10/2014 14-17h
More informationImpact of Critical Care Nursing on 30-day Mortality of Mechanically Ventilated Older Adults
Impact of Critical Care Nursing on 30-day Mortality of Mechanically Ventilated Older Adults Deena M. Kelly PhD RN Post-doctoral Fellow Department of Critical Care University of Pittsburgh School of Medicine
More informationLecture 2 ESTIMATING THE SURVIVAL FUNCTION. One-sample nonparametric methods
Lecture 2 ESTIMATING THE SURVIVAL FUNCTION One-sample nonparametric methods There are commonly three methods for estimating a survivorship function S(t) = P (T > t) without resorting to parametric models:
More informationGuide to Biostatistics
MedPage Tools Guide to Biostatistics Study Designs Here is a compilation of important epidemiologic and common biostatistical terms used in medical research. You can use it as a reference guide when reading
More informationPackage dsmodellingclient
Package dsmodellingclient Maintainer Author Version 4.1.0 License GPL-3 August 20, 2015 Title DataSHIELD client site functions for statistical modelling DataSHIELD
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 informationAverage Redistributional Effects. IFAI/IZA Conference on Labor Market Policy Evaluation
Average Redistributional Effects IFAI/IZA Conference on Labor Market Policy Evaluation Geert Ridder, Department of Economics, University of Southern California. October 10, 2006 1 Motivation Most papers
More informationMEU. INSTITUTE OF HEALTH SCIENCES COURSE SYLLABUS. Biostatistics
MEU. INSTITUTE OF HEALTH SCIENCES COURSE SYLLABUS title- course code: Program name: Contingency Tables and Log Linear Models Level Biostatistics Hours/week Ther. Recite. Lab. Others Total Master of Sci.
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 informationSupplementary PROCESS Documentation
Supplementary PROCESS Documentation This document is an addendum to Appendix A of Introduction to Mediation, Moderation, and Conditional Process Analysis that describes options and output added to PROCESS
More informationSurvival analysis methods in Insurance Applications in car insurance contracts
Survival analysis methods in Insurance Applications in car insurance contracts Abder OULIDI 1-2 Jean-Marie MARION 1 Hérvé GANACHAUD 3 1 Institut de Mathématiques Appliquées (IMA) Angers France 2 Institut
More informationApplying Survival Analysis Techniques to Loan Terminations for HUD s Reverse Mortgage Insurance Program - HECM
Applying Survival Analysis Techniques to Loan Terminations for HUD s Reverse Mortgage Insurance Program - HECM Ming H. Chow, Edward J. Szymanoski, Theresa R. DiVenti 1 I. Introduction "Survival Analysis"
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 informationIdentification and Sensitivity Analysis for Multiple Causal Mechanisms: Revisiting Evidence from Framing Experiments
Advance Access publication January 12, 2013 Political Analysis (2013) 21:141 171 doi:10.1093/pan/mps040 Identification and Sensitivity Analysis for Multiple Causal Mechanisms: Revisiting Evidence from
More informationU.S. Food and Drug Administration
U.S. Food and Drug Administration Notice: Archived Document The content in this document is provided on the FDA s website for reference purposes only. It was current when produced, but is no longer maintained
More informationREGULATIONS FOR THE POSTGRADUATE CERTIFICATE IN PUBLIC HEALTH (PCPH) (Subject to approval)
512 REGULATIONS FOR THE POSTGRADUATE CERTIFICATE IN PUBLIC HEALTH (PCPH) (Subject to approval) (See also General Regulations) M.113 Admission requirements To be eligible for admission to the programme
More informationApixaban Plus Mono vs. Dual Antiplatelet Therapy in Acute Coronary Syndromes: Insights from the APPRAISE-2 Trial
Apixaban Plus Mono vs. Dual Antiplatelet Therapy in Acute Coronary Syndromes: Insights from the APPRAISE-2 Trial Connie N. Hess, MD, MHS, Stefan James, MD, PhD, Renato D. Lopes, MD, PhD, Daniel M. Wojdyla,
More informationCompetency 1 Describe the role of epidemiology in public health
The Northwest Center for Public Health Practice (NWCPHP) has developed competency-based epidemiology training materials for public health professionals in practice. Epidemiology is broadly accepted as
More informationEvaluation of Treatment Pathways in Oncology: An Example in mcrpc
Evaluation of Treatment Pathways in Oncology: An Example in mcrpc Sonja Sorensen, MPH United BioSource Corporation Bethesda, MD 1 Objectives Illustrate selection of modeling approach for evaluating pathways
More informationGamma Distribution Fitting
Chapter 552 Gamma Distribution Fitting Introduction This module fits the gamma probability distributions to a complete or censored set of individual or grouped data values. It outputs various statistics
More informationRisk Factors for Alcoholism among Taiwanese Aborigines
Risk Factors for Alcoholism among Taiwanese Aborigines Introduction Like most mental disorders, Alcoholism is a complex disease involving naturenurture interplay (1). The influence from the bio-psycho-social
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 informationSign up for IWH s free e-alert/newsletter
Sign up for IWH s free e-alert/newsletter Please fill out the Sign-up Form (available up front), go to www.iwh.on.ca/e-alerts and sign up online Every three months, you will receive an e-mail message directing
More informationGruppo di lavoro: Malattie Tromboemboliche
Gruppo di lavoro: Malattie Tromboemboliche 2381 Soluble Recombinant Thrombomodulin Ameliorates Hematological Malignancy-Induced Disseminated Intravascular Coagulation More Promptly Than Conventional Anticoagulant
More informationModeration. Moderation
Stats - Moderation Moderation A moderator is a variable that specifies conditions under which a given predictor is related to an outcome. The moderator explains when a DV and IV are related. Moderation
More informationIntroduction to Longitudinal Data Analysis
Introduction to Longitudinal Data Analysis Longitudinal Data Analysis Workshop Section 1 University of Georgia: Institute for Interdisciplinary Research in Education and Human Development Section 1: Introduction
More informationWhen to Use a Particular Statistical Test
When to Use a Particular Statistical Test Central Tendency Univariate Descriptive Mode the most commonly occurring value 6 people with ages 21, 22, 21, 23, 19, 21 - mode = 21 Median the center value the
More informationPreparation course Msc Business & Econonomics
Preparation course Msc Business & Econonomics The simple Keynesian model Tom-Reiel Heggedal BI August 2014 TRH (BI) Keynes model August 2014 1 / 19 Assumptions Keynes model Outline for this lecture: Go
More informationMortality Assessment Technology: A New Tool for Life Insurance Underwriting
Mortality Assessment Technology: A New Tool for Life Insurance Underwriting Guizhou Hu, MD, PhD BioSignia, Inc, Durham, North Carolina Abstract The ability to more accurately predict chronic disease morbidity
More informationUsing Repeated Measures Techniques To Analyze Cluster-correlated Survey Responses
Using Repeated Measures Techniques To Analyze Cluster-correlated Survey Responses G. Gordon Brown, Celia R. Eicheldinger, and James R. Chromy RTI International, Research Triangle Park, NC 27709 Abstract
More informationMultivariable survival analysis S10. Michael Hauptmann Netherlands Cancer Institute Amsterdam, The Netherlands
Multivariable survival analysis S10 Michael Hauptmann Netherlands Cancer Institute Amsterdam, The Netherlands m.hauptmann@nki.nl 1 Confounding A variable correlated with the variable of interest and with
More informationGordon S. Linoff Founder Data Miners, Inc. gordon@data-miners.com
Survival Data Mining Gordon S. Linoff Founder Data Miners, Inc. gordon@data-miners.com What to Expect from this Talk Background on survival analysis from a data miner s perspective Introduction to key
More informationSection 14 Simple Linear Regression: Introduction to Least Squares Regression
Slide 1 Section 14 Simple Linear Regression: Introduction to Least Squares Regression There are several different measures of statistical association used for understanding the quantitative relationship
More informationCURRICULUM: Evaluation & Management
CURRICULUM: Evaluation & Management The Coding Metrix SM Evaluation and Management Curriculum is a comprehensive training program designed to prepare users to accurately assign procedure codes for evaluation
More informationAnalysis of Bayesian Dynamic Linear Models
Analysis of Bayesian Dynamic Linear Models Emily M. Casleton December 17, 2010 1 Introduction The main purpose of this project is to explore the Bayesian analysis of Dynamic Linear Models (DLMs). The main
More informationChapter 1 Acceleration, due to occupational exposure, of time to onset of a disease
Chapter 1 Acceleration, due to occupational exposure, of time to onset of a disease A. Chambaz, D. Choudat, C. Huber Abstract Occupational exposure to pollution may accelerate or even induce the onset
More informationPSA Testing 101. Stanley H. Weiss, MD. Professor, UMDNJ-New Jersey Medical School. Director & PI, Essex County Cancer Coalition. weiss@umdnj.
PSA Testing 101 Stanley H. Weiss, MD Professor, UMDNJ-New Jersey Medical School Director & PI, Essex County Cancer Coalition weiss@umdnj.edu September 23, 2010 Screening: 3 tests for PCa A good screening
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 information