Causal Hazard Ratio Estimation By Instrumental Variables or Principal Stratification. Todd MacKenzie, PhD
|
|
- Geoffrey Small
- 6 years ago
- Views:
Transcription
1 Causal Hazard Ratio Estimation By Instrumental Variables or Principal Stratification Todd MacKenzie, PhD
2 Collaborators A. James O Malley Tor Tosteson Therese Stukel 2
3 Overview 1. Instrumental variable (I.V.) 2. I.V.s for Hazard Ratio Estimation 3. Principal stratification (P.S.) 4. P.S. for Hazard Ratio Estimation 3
4 Observational Studies and Confounding Confounding is always a threat to observational studies Therefore we prefer when possible to conduct 4
5 Randomized Studies Randomized studies yield fair comparisons However Require greater resources Tend to be conducted in artificial settings Therefore, observational studies deserve more consideration 5
6 Current Arsenal of Statistical Methods for Overcoming Confounding 1. Adjustment (regression) models 2. Propensity score matching or stratification 3. Inverse propensity weighted marginal structural models Bias is removed only to the extent that confounders are included in the model 6
7 Confounding that cannot be removed Goes by different names Omitted covariates Unmeasured confounders Residual confounding 7
8 Instrumental Variables Estimation by I.V can yield unbiased estimates without observing all confounders 8
9 Instrumental Variables for the Linear Model Idea is accessible to any student of an introductory mathematical statistics class 9
10 Instrumental Variables for the Linear Model 1. Y = a + bx + ε such that Cov(I.V., ε)=0 2. Cov(Y,W) = Cov(a+bX+ε, I.V.) = bcov(x, I.V.) 3. Therefore b = Cov(Y, I.V.) / Cov(X, I.V.) 10
11 Assumptions 1. Nonzero association of X and the I.V. Usual rule of thumb: F-test of I.V. and X exceeds 10 11
12 Assumptions 2. The effect of the I.V. on the Y is strictly through the effect of the I.V on X: a. There is no direct effect of the I.V. on Y b. There is no intermediate variable for the effect of the I.V on Y except X: Exclusion Criteria or Absence of Indirect Effect c. There are no variables that effect both I.V. and Y: No I.V.- Outcome Confounders or Randomization 12
13 IV X Y 13
14 There are no paths between IV and Y except through X IV X Y 14
15 Faith based statistics: This second assumption cannot be empirically validated IV X Y 15
16 Other Assumptions Not Necessarily Worth Mentioning SUTVA: Stable Unit Treatment Value Assumption My treatment does not effect your outcome Monotonicity 16
17 Do instrumental variables exist? Yes, man-made instruments exist: Randomized Studies Randomization is an instrument for the effect of treatment on an endpoint The arm a subject is randomized to should have no effect on the endpoint through its effects on the treatment received 17
18 Do instrumental variables exist in the real world? Happenstance Be on the lookout for natural experiments Commonly employed instrumental variables: Geographic variables (regional rates, distances) Care provider propensity to prescribe a treatment Calendar time Before after a health policy change See regression discontinuity 18
19 Mendelian Randomization: Assessing the Effect of a Phenotype on a Dependent Variable Gene for Some Phenotype That Phenotype Endpoint 19
20 Instrumental Variables Theory Is Well Developed for Linear Models ˆ T 1 β = ( IV X ) ( IV T Y ) Equivalent to Two Stage Least Squares 1. regress X on IV and save predicted values as P 2. regress Y on P, use coefficient of P Equivalent to Control Function 1. regress X on IV and save residuals, R 2. regress Y on X and R, use coefficient of X 20
21 Our Aim To develop an estimator of the hazard ratio using an instrumental variable 21
22 Challenges Non-linear parameterization (e.g., Cox model) Right censoring 22
23 Prior Work in the Literature Some in econometrics literature Stukel et al (2007) JAMA 23
24 Original Motivation Stukel et al Analysis of Observational Studies in the Presence of Treatment Selection Bias: Effects of Invasive Cardiac Management on AMI Survival Using Propensity Score and Instrumental Variable Methods JAMA (2007) 24
25 Cox Proportional Hazards Model Suppose the effect of a treatment, X, on an individual s potential time-to-events, {T(x)} x, is to multiply the hazard by e β Pr[ T ( x) = t T ( x) t] = e βx λ Estimand of interest: β, the log hazard ratio ( t) 25
26 Non-Collapsibility of Cox s Model Like most non-linear models (e.g. logistic regression) Cox s model is not collapsible That is, if the conditional distribution of timeto-event T given Z 1 and Z 2 is a Cox model then the marginal conditional distribution of T given Z 1 (obtained by integrating over Z 2 ) is not a Cox model unless Z 1 is independent of T 26
27 A model that collapses to Cox The model for the joint effect of X and Z (e.g., an omitted covariate), collapses to (integrates out to) under certain conditions ) ( ] ) ( ) ( Pr[ t e t x T t x T βx λ = = z t e z Z t x T t x T x θ λ β + = = = ) ( ], ) ( ) ( Pr[ 27
28 Incorporating the I.V. Assuming that the I.V. is independent of the omitted covariate, Z, an argument using risk sets or martingales, e.g., βx E[ I. V. { dn( t) e λ( t)}] 0 can be made that results in the estimating equation on the next slide 28
29 Estimation of the Hazard Ratio Using Instrumental Variables Solve the estimating equation below for β Counting process notation In conventional notation ) ( ] ) ( ) ( [ t dn e t Y e t IV Y IV i n i n j X j n j X j j i j j = = = = τ β β ] [ 0 1 ) ( ) ( = = n i R j X R j X j i i i j i j e e IV IV β β δ 29
30 Simulations Conducted simulations to evaluate bias For the unmeasured confounder two models were assume 1. Additive effect of the confounder on the hazard 2. Multiplicative effect (Cox) of the confounder on the hazard 30
31 Simulation Results for Multiplicative Omitted Covariate 31
32 Application using data from Stukel et al (2007) JAMA National cohort of 120,000 patients on Medicare, hospitalized with acute myocardial infarction (AMI) Exposure: coronary catheterization within 30 days of hospitalization Endpoint: mortality by 4 years after hospitalization Covariates: rich set of prognostic variables 32
33 Aim of Stukel s study Estimate the effect of coronary catheterization on survival using three different approaches Regression (Cox s model) Propensity Scores (with and without matching) Instrumental variables Compare the estimates to those obtained in randomized studies 33
34 Instrumental Variables in Stukel et al (2007) Instrument: regional cardiac catheterization rate proportion of eligible patients receiving cardiac catheterization within 30 days of admission in each area 566 areas Assumption: the effect of this proportion on survival is strictly through its association with an individual s propensity to have a card. cath. Methods for linear instrument variable models applied to survival Used endpoint of survival at 1 year (4 years) Excludes subjects who were censored before that time Converted coefficient from linear model into hazard ratio 34
35 Example: Effect of coronary catheterization on survival Approach Hazard Ratio (95%CI) Cox adjusted Cox adjusted excluding.rst 31 days Prop Score matched within Stukel L.M. Instrumental Variable at 1 Yr Stukel L.M. Instrumental Variable at 4 Yrs Instrumental Variable Estimator (Overall) Based on First Year Whereas randomized studies yielded estimates of 0.80 to
36 Related Work Accelerated Failure Time model Additive Hazards Model (Jason Fine) Mitra & Small, Chan & Small Tchetgen Tchetgen 36
37 Principal Stratification
38 Randomized Trial Goal: Estimate treatment effect e.g., drug vs placebo 38
39 Compliance Not all participants comply 39
40 Common Estimators from a Randomized Trial Intention-to-treat As treated Per protocol 40
41 Intention-to-treat Analyze as randomized Unbiased estimate of treatment assignment It does not estimate the effect of treatment, were a subject to comply 41
42 As Treated Selection bias is introduced Treatment is selected as opposed to randomized 42
43 Per Protocol Excludes subjects who did not comply What is it estimating? 43
44 How to Estimate the effect of treatment? What is the effect of treatment, if someone complies with treatment Principal Stratification is a framework for defining a meaningful estimand To start with, consider the relationship of the exposure a subject receives to the arm of the study they are randomized to 44
45 Mappings from Support of the Binary Assignment to the Support of the Binary Expsosure? There are 4 mappings from the two possible values of the assignment, R, to the two possible values of the exposure, X Mapping R to X Principal Strata Name Identity 0 to 0, 1 to 1 Compliers Contant Zero Constant Unity 0 to 0, 1 to 0 Never Takers 0 to 1, 1 to 1 Always Takers Reverse 0 to 1, 1 to 0 Defiers 45
46 The Principal Strata Latent Not directly observable Names are suggestive but should not be taken at face value 46
47 No Defiers It appears reasonable to assume that there is no defiers (or at least they are very rare) Furthermore this assumption facilitates identification of some of the latent strata This assumption is called Monotonicity 47
48 Identification of Strata from the Observations Assignment Exposure Principal Strata 0 0 Complier (Co) or Never Taker (NT) 0 1 Always Taker (AT) 1 0 Never Taker (NT) 1 1 Complier (Co) or Always Taker (AT) 48
49 Calculating the Strata Probabilities Assignment Exposure Principal Strata 0 0 Pr[Co]+Pr[NT] = Pr[X=0 R=0] 0 1 Pr[AT] = Pr[X=1 R=0] 1 0 Pr[NT] = Pr[X=0 R=1] 1 1 Pr[Co]+Pr[AT] = Pr[X=1 R=1] Arithmetic shows that Pr[Co] = Pr[X=0 R=0] - Pr[X=0 R=1] or = Pr[X=1 R=1] - Pr[X=1 R=0] Thus it is possible to identify the strata probabilities 49
50 Complier Average Causal Effect for Continuous Endpoints 50
51 Extending Principal Stratification to Non-Linear Parameter Estimation The following slides show a way of arriving at estimates of the distributions of an endpoint in treated compliers and in untreated compliers These respective distributions can then be used to estimate parameters that characterize these distributions 51
52 Mixture Distributions R X Observed Mixture of Weights Y(X) 0 0 Y(X) R=0,X=0 Y(0) PS=Co and Y(0) PS=NT (p C0, p NT ) / (p C0 + p NT ) 0 1 Y(X) R=0,X=1 Y(1) PS=AT 1 0 Y(X) R=1,X=0 Y(0) PS=NT 1 1 Y(X) R=1,X=1 Y(1) PS=Co and Y(1) PS=AT (p C0, p AT ) / (p C0 + p AT ) 52
53 Arithmetic Shows The Potential Outcomes in the Compliers Can be Identified Using the Observable Distributions Potential Outcomes in the Compliers Mixture of Weights Y(0) PS=Co Y(X) R=0,X=0 and Y(X) PS=NT (1+p NT /p C0, -p NT /p Co ) Y(1) PS=Co Y(X) R=1,X=1 and Y(X) PS=AT (1+p Co /p AT, -p AT /p Co ) 53
54 Operationalizing: Weights To estimate the distribution, or parameters related to the distribution of the potential outcomes on the compliers, use the observeable samples but weight them in proportion to the weights on the previous slide Note: Some of the weights are negative! Negative weights not readily implemented with some software (e.g. R) 54
55 Principal Stratification Weights for Hazard Ratio Estimation To estimate the hazard ratio of Cox s model we apply weights to the observed follow-up and censoring indicators to create samples from treated and untreated individuals from the complier strata 55
56 Results of Simulations 56
57 Summary It is possible to estimate the causal hazard ratio with little or no bias in the setting of allor-nothing compliance I.T.T., Per Protocol and As Treated Estimators are Biased 57
58 Future Steps Instrumental Variables Time-varying exposure e.g. compliance that varies with time Weak instruments Principal Stratification Smooth weights to remove negative values Generalization of three principal strata (NT, Co, AT) to a latent variable that is continuous variable indicating propensity for obtaining treatment 58
59 59
60 60
61 Causal Inference Syntax Exposure X: 1=treatment, 0=no treatment Potential outcomes Y(0) is outcome if there is no treatment Y(1) is outcome if there is treatment We observe only one of the potential outcomes, Y(X) The others are counterfactuals 61
62 Resemblance to maximum partial likelihood Estimating Equation with I.V. ) ( ] ) ( ) ( [ t dn e t Y e t W Y W i n i n j X j n j X j j i j j = = = = τ β β Partial Likelihood Score ) ( ] ) ( ) ( [ t dn e t Y e t Y X X i n i n j X j n j X j j i j j = = = = τ β β 62
63 Simulation Results for Additive Omitted Covariate 63
64 Principal Stratification: When treatment is not accessible to controls Two classes One sided compliance 1. Compliers: do as assigned 2. Never takers: will not do treatment regardless of assignment 64
Instrumental variables estimation in the Cox Proportional Hazard regression model
Instrumental variables estimation in the Cox Proportional Hazard regression model James O Malley, Ph.D. Department of Biomedical Data Science The Dartmouth Institute for Health Policy and Clinical Practice
More informationWORKSHOP ON PRINCIPAL STRATIFICATION STANFORD UNIVERSITY, Luke W. Miratrix (Harvard University) Lindsay C. Page (University of Pittsburgh)
WORKSHOP ON PRINCIPAL STRATIFICATION STANFORD UNIVERSITY, 2016 Luke W. Miratrix (Harvard University) Lindsay C. Page (University of Pittsburgh) Our team! 2 Avi Feller (Berkeley) Jane Furey (Abt Associates)
More informationPropensity Score Methods for Causal Inference
John Pura BIOS790 October 2, 2015 Causal inference Philosophical problem, statistical solution Important in various disciplines (e.g. Koch s postulates, Bradford Hill criteria, Granger causality) Good
More informationMarginal versus conditional effects: does it make a difference? Mireille Schnitzer, PhD Université de Montréal
Marginal versus conditional effects: does it make a difference? Mireille Schnitzer, PhD Université de Montréal Overview In observational and experimental studies, the goal may be to estimate the effect
More informationStatistical Analysis of Randomized Experiments with Nonignorable Missing Binary Outcomes
Statistical Analysis of Randomized Experiments with Nonignorable Missing Binary Outcomes Kosuke Imai Department of Politics Princeton University July 31 2007 Kosuke Imai (Princeton University) Nonignorable
More informationIntroduction to causal identification. Nidhiya Menon IGC Summer School, New Delhi, July 2015
Introduction to causal identification Nidhiya Menon IGC Summer School, New Delhi, July 2015 Outline 1. Micro-empirical methods 2. Rubin causal model 3. More on Instrumental Variables (IV) Estimating causal
More informationRank preserving Structural Nested Distribution Model (RPSNDM) for Continuous
Rank preserving Structural Nested Distribution Model (RPSNDM) for Continuous Y : X M Y a=0 = Y a a m = Y a cum (a) : Y a = Y a=0 + cum (a) an unknown parameter. = 0, Y a = Y a=0 = Y for all subjects Rank
More informationComparative effectiveness of dynamic treatment regimes
Comparative effectiveness of dynamic treatment regimes An application of the parametric g- formula Miguel Hernán Departments of Epidemiology and Biostatistics Harvard School of Public Health www.hsph.harvard.edu/causal
More informationNoncompliance in Randomized Experiments
Noncompliance in Randomized Experiments Kosuke Imai Harvard University STAT186/GOV2002 CAUSAL INFERENCE Fall 2018 Kosuke Imai (Harvard) Noncompliance in Experiments Stat186/Gov2002 Fall 2018 1 / 15 Encouragement
More informationExtending causal inferences from a randomized trial to a target population
Extending causal inferences from a randomized trial to a target population Issa Dahabreh Center for Evidence Synthesis in Health, Brown University issa dahabreh@brown.edu January 16, 2019 Issa Dahabreh
More informationEcon 2148, fall 2017 Instrumental variables I, origins and binary treatment case
Econ 2148, fall 2017 Instrumental variables I, origins and binary treatment case Maximilian Kasy Department of Economics, Harvard University 1 / 40 Agenda instrumental variables part I Origins of instrumental
More informationBounds on Causal Effects in Three-Arm Trials with Non-compliance. Jing Cheng Dylan Small
Bounds on Causal Effects in Three-Arm Trials with Non-compliance Jing Cheng Dylan Small Department of Biostatistics and Department of Statistics University of Pennsylvania June 20, 2005 A Three-Arm Randomized
More informationPropensity Score Weighting with Multilevel Data
Propensity Score Weighting with Multilevel Data Fan Li Department of Statistical Science Duke University October 25, 2012 Joint work with Alan Zaslavsky and Mary Beth Landrum Introduction In comparative
More informationAGEC 661 Note Fourteen
AGEC 661 Note Fourteen Ximing Wu 1 Selection bias 1.1 Heckman s two-step model Consider the model in Heckman (1979) Y i = X iβ + ε i, D i = I {Z iγ + η i > 0}. For a random sample from the population,
More informationA Bayesian Nonparametric Approach to Causal Inference for Semi-competing risks
A Bayesian Nonparametric Approach to Causal Inference for Semi-competing risks Y. Xu, D. Scharfstein, P. Mueller, M. Daniels Johns Hopkins, Johns Hopkins, UT-Austin, UF JSM 2018, Vancouver 1 What are semi-competing
More informationAdvanced Statistical Methods for Observational Studies L E C T U R E 0 6
Advanced Statistical Methods for Observational Studies L E C T U R E 0 6 class management Problem set 1 is posted Questions? design thus far We re off to a bad start. 1 2 1 2 1 2 2 2 1 1 1 2 1 1 2 2 2
More informationIntroduction to Econometrics
Introduction to Econometrics STAT-S-301 Experiments and Quasi-Experiments (2016/2017) Lecturer: Yves Dominicy Teaching Assistant: Elise Petit 1 Why study experiments? Ideal randomized controlled experiments
More informationInstrumental Variables
Instrumental Variables Teppei Yamamoto Keio University Introduction to Causal Inference Spring 2016 Noncompliance in Randomized Experiments Often we cannot force subjects to take specific treatments Units
More informationThe problem of causality in microeconometrics.
The problem of causality in microeconometrics. Andrea Ichino University of Bologna and Cepr June 11, 2007 Contents 1 The Problem of Causality 1 1.1 A formal framework to think about causality....................................
More informationInvestigating mediation when counterfactuals are not metaphysical: Does sunlight exposure mediate the effect of eye-glasses on cataracts?
Investigating mediation when counterfactuals are not metaphysical: Does sunlight exposure mediate the effect of eye-glasses on cataracts? Brian Egleston Fox Chase Cancer Center Collaborators: Daniel Scharfstein,
More informationIntroduction to Causal Inference. Solutions to Quiz 4
Introduction to Causal Inference Solutions to Quiz 4 Teppei Yamamoto Tuesday, July 9 206 Instructions: Write your name in the space provided below before you begin. You have 20 minutes to complete the
More informationECON Introductory Econometrics. Lecture 17: Experiments
ECON4150 - Introductory Econometrics Lecture 17: Experiments Monique de Haan (moniqued@econ.uio.no) Stock and Watson Chapter 13 Lecture outline 2 Why study experiments? The potential outcome framework.
More informationSREE WORKSHOP ON PRINCIPAL STRATIFICATION MARCH Avi Feller & Lindsay C. Page
SREE WORKSHOP ON PRINCIPAL STRATIFICATION MARCH 2017 Avi Feller & Lindsay C. Page Agenda 2 Conceptual framework (45 minutes) Small group exercise (30 minutes) Break (15 minutes) Estimation & bounds (1.5
More informationRecitation Notes 6. Konrad Menzel. October 22, 2006
Recitation Notes 6 Konrad Menzel October, 006 Random Coefficient Models. Motivation In the empirical literature on education and earnings, the main object of interest is the human capital earnings function
More informationThe problem of causality in microeconometrics.
The problem of causality in microeconometrics. Andrea Ichino European University Institute April 15, 2014 Contents 1 The Problem of Causality 1 1.1 A formal framework to think about causality....................................
More informationHarvard University. A Note on the Control Function Approach with an Instrumental Variable and a Binary Outcome. Eric Tchetgen Tchetgen
Harvard University Harvard University Biostatistics Working Paper Series Year 2014 Paper 175 A Note on the Control Function Approach with an Instrumental Variable and a Binary Outcome Eric Tchetgen Tchetgen
More informationDistributed analysis in multi-center studies
Distributed analysis in multi-center studies Sharing of individual-level data across health plans or healthcare delivery systems continues to be challenging due to concerns about loss of patient privacy,
More informationPh.D. course: Regression models. Introduction. 19 April 2012
Ph.D. course: Regression models Introduction PKA & LTS Sect. 1.1, 1.2, 1.4 19 April 2012 www.biostat.ku.dk/~pka/regrmodels12 Per Kragh Andersen 1 Regression models The distribution of one outcome variable
More informationPSC 504: Instrumental Variables
PSC 504: Instrumental Variables Matthew Blackwell 3/28/2013 Instrumental Variables and Structural Equation Modeling Setup e basic idea behind instrumental variables is that we have a treatment with unmeasured
More informationCausal inference in paired two-arm experimental studies under non-compliance with application to prognosis of myocardial infarction
Causal inference in paired two-arm experimental studies under non-compliance with application to prognosis of myocardial infarction Francesco Bartolucci Alessio Farcomeni Abstract Motivated by a study
More informationExperiments and Quasi-Experiments
Experiments and Quasi-Experiments (SW Chapter 13) Outline 1. Potential Outcomes, Causal Effects, and Idealized Experiments 2. Threats to Validity of Experiments 3. Application: The Tennessee STAR Experiment
More informationPrinciples Underlying Evaluation Estimators
The Principles Underlying Evaluation Estimators James J. University of Chicago Econ 350, Winter 2019 The Basic Principles Underlying the Identification of the Main Econometric Evaluation Estimators Two
More informationPropensity Score Analysis with Hierarchical Data
Propensity Score Analysis with Hierarchical Data Fan Li Alan Zaslavsky Mary Beth Landrum Department of Health Care Policy Harvard Medical School May 19, 2008 Introduction Population-based observational
More informationCausal Effect Estimation Under Linear and Log- Linear Structural Nested Mean Models in the Presence of Unmeasured Confounding
University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations Summer 8-13-2010 Causal Effect Estimation Under Linear and Log- Linear Structural Nested Mean Models in the Presence of
More informationCombining Experimental and Non-Experimental Design in Causal Inference
Combining Experimental and Non-Experimental Design in Causal Inference Kari Lock Morgan Department of Statistics Penn State University Rao Prize Conference May 12 th, 2017 A Tribute to Don Design trumps
More informationarxiv: v1 [stat.me] 8 Jun 2016
Principal Score Methods: Assumptions and Extensions Avi Feller UC Berkeley Fabrizia Mealli Università di Firenze Luke Miratrix Harvard GSE arxiv:1606.02682v1 [stat.me] 8 Jun 2016 June 9, 2016 Abstract
More information150C Causal Inference
150C Causal Inference Instrumental Variables: Modern Perspective with Heterogeneous Treatment Effects Jonathan Mummolo May 22, 2017 Jonathan Mummolo 150C Causal Inference May 22, 2017 1 / 26 Two Views
More informationCasual Mediation Analysis
Casual Mediation Analysis Tyler J. VanderWeele, Ph.D. Upcoming Seminar: April 21-22, 2017, Philadelphia, Pennsylvania OXFORD UNIVERSITY PRESS Explanation in Causal Inference Methods for Mediation and Interaction
More informationPh.D. course: Regression models. Regression models. Explanatory variables. Example 1.1: Body mass index and vitamin D status
Ph.D. course: Regression models Introduction PKA & LTS Sect. 1.1, 1.2, 1.4 25 April 2013 www.biostat.ku.dk/~pka/regrmodels13 Per Kragh Andersen Regression models The distribution of one outcome variable
More informationBIAS OF MAXIMUM-LIKELIHOOD ESTIMATES IN LOGISTIC AND COX REGRESSION MODELS: A COMPARATIVE SIMULATION STUDY
BIAS OF MAXIMUM-LIKELIHOOD ESTIMATES IN LOGISTIC AND COX REGRESSION MODELS: A COMPARATIVE SIMULATION STUDY Ingo Langner 1, Ralf Bender 2, Rebecca Lenz-Tönjes 1, Helmut Küchenhoff 2, Maria Blettner 2 1
More informationLecture 8. Roy Model, IV with essential heterogeneity, MTE
Lecture 8. Roy Model, IV with essential heterogeneity, MTE Economics 2123 George Washington University Instructor: Prof. Ben Williams Heterogeneity When we talk about heterogeneity, usually we mean heterogeneity
More informationOptimal Treatment Regimes for Survival Endpoints from a Classification Perspective. Anastasios (Butch) Tsiatis and Xiaofei Bai
Optimal Treatment Regimes for Survival Endpoints from a Classification Perspective Anastasios (Butch) Tsiatis and Xiaofei Bai Department of Statistics North Carolina State University 1/35 Optimal Treatment
More informationIdentification Analysis for Randomized Experiments with Noncompliance and Truncation-by-Death
Identification Analysis for Randomized Experiments with Noncompliance and Truncation-by-Death Kosuke Imai First Draft: January 19, 2007 This Draft: August 24, 2007 Abstract Zhang and Rubin 2003) derives
More informationCausal inference in biomedical sciences: causal models involving genotypes. Mendelian randomization genes as Instrumental Variables
Causal inference in biomedical sciences: causal models involving genotypes Causal models for observational data Instrumental variables estimation and Mendelian randomization Krista Fischer Estonian Genome
More informationThe returns to schooling, ability bias, and regression
The returns to schooling, ability bias, and regression Jörn-Steffen Pischke LSE October 4, 2016 Pischke (LSE) Griliches 1977 October 4, 2016 1 / 44 Counterfactual outcomes Scholing for individual i is
More informationEstimating the Mean Response of Treatment Duration Regimes in an Observational Study. Anastasios A. Tsiatis.
Estimating the Mean Response of Treatment Duration Regimes in an Observational Study Anastasios A. Tsiatis http://www.stat.ncsu.edu/ tsiatis/ Introduction to Dynamic Treatment Regimes 1 Outline Description
More informationLecture Discussion. Confounding, Non-Collapsibility, Precision, and Power Statistics Statistical Methods II. Presented February 27, 2018
, Non-, Precision, and Power Statistics 211 - Statistical Methods II Presented February 27, 2018 Dan Gillen Department of Statistics University of California, Irvine Discussion.1 Various definitions of
More informationPotential Outcomes and Causal Inference I
Potential Outcomes and Causal Inference I Jonathan Wand Polisci 350C Stanford University May 3, 2006 Example A: Get-out-the-Vote (GOTV) Question: Is it possible to increase the likelihood of an individuals
More informationEstimating Causal Effects of Organ Transplantation Treatment Regimes
Estimating Causal Effects of Organ Transplantation Treatment Regimes David M. Vock, Jeffrey A. Verdoliva Boatman Division of Biostatistics University of Minnesota July 31, 2018 1 / 27 Hot off the Press
More informationEconometric Analysis of Cross Section and Panel Data
Econometric Analysis of Cross Section and Panel Data Jeffrey M. Wooldridge / The MIT Press Cambridge, Massachusetts London, England Contents Preface Acknowledgments xvii xxiii I INTRODUCTION AND BACKGROUND
More informationComparison of Three Approaches to Causal Mediation Analysis. Donna L. Coffman David P. MacKinnon Yeying Zhu Debashis Ghosh
Comparison of Three Approaches to Causal Mediation Analysis Donna L. Coffman David P. MacKinnon Yeying Zhu Debashis Ghosh Introduction Mediation defined using the potential outcomes framework natural effects
More informationCausal Modeling in Environmental Epidemiology. Joel Schwartz Harvard University
Causal Modeling in Environmental Epidemiology Joel Schwartz Harvard University When I was Young What do I mean by Causal Modeling? What would have happened if the population had been exposed to a instead
More informationA Bayesian Nonparametric Approach to Monotone Missing Data in Longitudinal Studies with Informative Missingness
A Bayesian Nonparametric Approach to Monotone Missing Data in Longitudinal Studies with Informative Missingness A. Linero and M. Daniels UF, UT-Austin SRC 2014, Galveston, TX 1 Background 2 Working model
More informationOUTCOME REGRESSION AND PROPENSITY SCORES (CHAPTER 15) BIOS Outcome regressions and propensity scores
OUTCOME REGRESSION AND PROPENSITY SCORES (CHAPTER 15) BIOS 776 1 15 Outcome regressions and propensity scores Outcome Regression and Propensity Scores ( 15) Outline 15.1 Outcome regression 15.2 Propensity
More informationIgnoring the matching variables in cohort studies - when is it valid, and why?
Ignoring the matching variables in cohort studies - when is it valid, and why? Arvid Sjölander Abstract In observational studies of the effect of an exposure on an outcome, the exposure-outcome association
More informationAn Alternative Assumption to Identify LATE in Regression Discontinuity Design
An Alternative Assumption to Identify LATE in Regression Discontinuity Design Yingying Dong University of California Irvine May 2014 Abstract One key assumption Imbens and Angrist (1994) use to identify
More informationMultistate models and recurrent event models
Multistate models Multistate models and recurrent event models Patrick Breheny December 10 Patrick Breheny Survival Data Analysis (BIOS 7210) 1/22 Introduction Multistate models In this final lecture,
More informationCausal Inference Basics
Causal Inference Basics Sam Lendle October 09, 2013 Observed data, question, counterfactuals Observed data: n i.i.d copies of baseline covariates W, treatment A {0, 1}, and outcome Y. O i = (W i, A i,
More informationEstimating direct effects in cohort and case-control studies
Estimating direct effects in cohort and case-control studies, Ghent University Direct effects Introduction Motivation The problem of standard approaches Controlled direct effect models In many research
More informationCausal Inference with Big Data Sets
Causal Inference with Big Data Sets Marcelo Coca Perraillon University of Colorado AMC November 2016 1 / 1 Outlone Outline Big data Causal inference in economics and statistics Regression discontinuity
More informationTHE DERIVATION OF A LATENT THRESHOLD INSTRUMENTAL VARIABLES MODEL
Statistica Sinica 10(2000), 517-544 THE DERIVATION OF A LATENT THRESHOLD INSTRUMENTAL VARIABLES MODEL Mark E. Glickman and Sharon-Lise T. Normand Boston University and Harvard Medical School Abstract:
More informationBalancing Covariates via Propensity Score Weighting
Balancing Covariates via Propensity Score Weighting Kari Lock Morgan Department of Statistics Penn State University klm47@psu.edu Stochastic Modeling and Computational Statistics Seminar October 17, 2014
More informationCombining multiple observational data sources to estimate causal eects
Department of Statistics, North Carolina State University Combining multiple observational data sources to estimate causal eects Shu Yang* syang24@ncsuedu Joint work with Peng Ding UC Berkeley May 23,
More informationAn Introduction to Causal Analysis on Observational Data using Propensity Scores
An Introduction to Causal Analysis on Observational Data using Propensity Scores Margie Rosenberg*, PhD, FSA Brian Hartman**, PhD, ASA Shannon Lane* *University of Wisconsin Madison **University of Connecticut
More informationBalancing Covariates via Propensity Score Weighting: The Overlap Weights
Balancing Covariates via Propensity Score Weighting: The Overlap Weights Kari Lock Morgan Department of Statistics Penn State University klm47@psu.edu PSU Methodology Center Brown Bag April 6th, 2017 Joint
More informationEMERGING MARKETS - Lecture 2: Methodology refresher
EMERGING MARKETS - Lecture 2: Methodology refresher Maria Perrotta April 4, 2013 SITE http://www.hhs.se/site/pages/default.aspx My contact: maria.perrotta@hhs.se Aim of this class There are many different
More informationECO Class 6 Nonparametric Econometrics
ECO 523 - Class 6 Nonparametric Econometrics Carolina Caetano Contents 1 Nonparametric instrumental variable regression 1 2 Nonparametric Estimation of Average Treatment Effects 3 2.1 Asymptotic results................................
More informationEconometrics with Observational Data. Introduction and Identification Todd Wagner February 1, 2017
Econometrics with Observational Data Introduction and Identification Todd Wagner February 1, 2017 Goals for Course To enable researchers to conduct careful quantitative analyses with existing VA (and non-va)
More informationHarvard University. Harvard University Biostatistics Working Paper Series
Harvard University Harvard University Biostatistics Working Paper Series Year 2010 Paper 117 Estimating Causal Effects in Trials Involving Multi-treatment Arms Subject to Non-compliance: A Bayesian Frame-work
More informationSTAT 5500/6500 Conditional Logistic Regression for Matched Pairs
STAT 5500/6500 Conditional Logistic Regression for Matched Pairs Motivating Example: The data we will be using comes from a subset of data taken from the Los Angeles Study of the Endometrial Cancer Data
More informationIsoLATEing: Identifying Heterogeneous Effects of Multiple Treatments
IsoLATEing: Identifying Heterogeneous Effects of Multiple Treatments Peter Hull December 2014 PRELIMINARY: Please do not cite or distribute without permission. Please see www.mit.edu/~hull/research.html
More informationarxiv: v1 [stat.me] 3 Feb 2016
Principal stratification analysis using principal scores Peng Ding and Jiannan Lu arxiv:602.096v [stat.me] 3 Feb 206 Abstract Practitioners are interested in not only the average causal effect of the treatment
More informationMultistate models and recurrent event models
and recurrent event models Patrick Breheny December 6 Patrick Breheny University of Iowa Survival Data Analysis (BIOS:7210) 1 / 22 Introduction In this final lecture, we will briefly look at two other
More informationUsing Instrumental Variables to Find Causal Effects in Public Health
1 Using Instrumental Variables to Find Causal Effects in Public Health Antonio Trujillo, PhD John Hopkins Bloomberg School of Public Health Department of International Health Health Systems Program October
More informationA Decision Theoretic Approach to Causality
A Decision Theoretic Approach to Causality Vanessa Didelez School of Mathematics University of Bristol (based on joint work with Philip Dawid) Bordeaux, June 2011 Based on: Dawid & Didelez (2010). Identifying
More informationSurvival Analysis for Case-Cohort Studies
Survival Analysis for ase-ohort Studies Petr Klášterecký Dept. of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, harles University, Prague, zech Republic e-mail: petr.klasterecky@matfyz.cz
More informationSharp Bounds on Causal Effects under Sample Selection*
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 77, 1 (2015) 0305 9049 doi: 10.1111/obes.12056 Sharp Bounds on Causal Effects under Sample Selection* Martin Huber and Giovanni Mellace Department of Economics,
More informationPackage noncompliance
Type Package Package noncompliance February 15, 2016 Title Causal Inference in the Presence of Treatment Noncompliance Under the Binary Instrumental Variable Model Version 0.2.2 Date 2016-02-11 A finite-population
More informationAdvanced Statistical Methods for Observational Studies L E C T U R E 0 1
Advanced Statistical Methods for Observational Studies L E C T U R E 0 1 introduction this class Website Expectations Questions observational studies The world of observational studies is kind of hard
More informationA Comparison of Methods for Estimating the Causal Effect of a Treatment in Randomized. Clinical Trials Subject to Noncompliance.
Draft June 6, 006 A Comparison of Methods for Estimating the Causal Effect of a Treatment in Randomized Clinical Trials Subject to Noncompliance Roderick Little 1, Qi Long and Xihong Lin 3 Abstract We
More informationIntroduction to Statistical Inference
Introduction to Statistical Inference Kosuke Imai Princeton University January 31, 2010 Kosuke Imai (Princeton) Introduction to Statistical Inference January 31, 2010 1 / 21 What is Statistics? Statistics
More informationPropensity Score Methods, Models and Adjustment
Propensity Score Methods, Models and Adjustment Dr David A. Stephens Department of Mathematics & Statistics McGill University Montreal, QC, Canada. d.stephens@math.mcgill.ca www.math.mcgill.ca/dstephens/siscr2016/
More informationApplication of Time-to-Event Methods in the Assessment of Safety in Clinical Trials
Application of Time-to-Event Methods in the Assessment of Safety in Clinical Trials Progress, Updates, Problems William Jen Hoe Koh May 9, 2013 Overview Marginal vs Conditional What is TMLE? Key Estimation
More informationTargeted Maximum Likelihood Estimation in Safety Analysis
Targeted Maximum Likelihood Estimation in Safety Analysis Sam Lendle 1 Bruce Fireman 2 Mark van der Laan 1 1 UC Berkeley 2 Kaiser Permanente ISPE Advanced Topics Session, Barcelona, August 2012 1 / 35
More informationUsing Post Outcome Measurement Information in Censoring by Death Problems
Using Post Outcome Measurement Information in Censoring by Death Problems Fan Yang University of Chicago, Chicago, USA. Dylan S. Small University of Pennsylvania, Philadelphia, USA. Summary. Many clinical
More informationMediation analyses. Advanced Psychometrics Methods in Cognitive Aging Research Workshop. June 6, 2016
Mediation analyses Advanced Psychometrics Methods in Cognitive Aging Research Workshop June 6, 2016 1 / 40 1 2 3 4 5 2 / 40 Goals for today Motivate mediation analysis Survey rapidly developing field in
More informationWooldridge, Introductory Econometrics, 4th ed. Chapter 15: Instrumental variables and two stage least squares
Wooldridge, Introductory Econometrics, 4th ed. Chapter 15: Instrumental variables and two stage least squares Many economic models involve endogeneity: that is, a theoretical relationship does not fit
More informationMichael Lechner Causal Analysis RDD 2014 page 1. Lecture 7. The Regression Discontinuity Design. RDD fuzzy and sharp
page 1 Lecture 7 The Regression Discontinuity Design fuzzy and sharp page 2 Regression Discontinuity Design () Introduction (1) The design is a quasi-experimental design with the defining characteristic
More informationModeling Log Data from an Intelligent Tutor Experiment
Modeling Log Data from an Intelligent Tutor Experiment Adam Sales 1 joint work with John Pane & Asa Wilks College of Education University of Texas, Austin RAND Corporation Pittsburgh, PA & Santa Monica,
More informationSurvival Analysis. Lu Tian and Richard Olshen Stanford University
1 Survival Analysis Lu Tian and Richard Olshen Stanford University 2 Survival Time/ Failure Time/Event Time We will introduce various statistical methods for analyzing survival outcomes What is the survival
More informatione author and the promoter give permission to consult this master dissertation and to copy it or parts of it for personal use. Each other use falls
e author and the promoter give permission to consult this master dissertation and to copy it or parts of it for personal use. Each other use falls under the restrictions of the copyright, in particular
More informationCausal Inference for Complex Longitudinal Data: The Continuous Time g-computation Formula
Causal Inference for Complex Longitudinal Data: The Continuous Time g-computation Formula Richard D. Gill Mathematical Institute, University of Utrecht, Netherlands EURANDOM, Eindhoven, Netherlands November
More informationMethods to Estimate Causal Effects Theory and Applications. Prof. Dr. Sascha O. Becker U Stirling, Ifo, CESifo and IZA
Methods to Estimate Causal Effects Theory and Applications Prof. Dr. Sascha O. Becker U Stirling, Ifo, CESifo and IZA last update: 21 August 2009 Preliminaries Address Prof. Dr. Sascha O. Becker Stirling
More informationRandomization-Based Inference With Complex Data Need Not Be Complex!
Randomization-Based Inference With Complex Data Need Not Be Complex! JITAIs JITAIs Susan Murphy 07.18.17 HeartSteps JITAI JITAIs Sequential Decision Making Use data to inform science and construct decision
More informationGrowth Mixture Modeling and Causal Inference. Booil Jo Stanford University
Growth Mixture Modeling and Causal Inference Booil Jo Stanford University booil@stanford.edu Conference on Advances in Longitudinal Methods inthe Socialand and Behavioral Sciences June 17 18, 2010 Center
More informationCausal Inference. Miguel A. Hernán, James M. Robins. May 19, 2017
Causal Inference Miguel A. Hernán, James M. Robins May 19, 2017 ii Causal Inference Part III Causal inference from complex longitudinal data Chapter 19 TIME-VARYING TREATMENTS So far this book has dealt
More informationSubgroup analysis using regression modeling multiple regression. Aeilko H Zwinderman
Subgroup analysis using regression modeling multiple regression Aeilko H Zwinderman who has unusual large response? Is such occurrence associated with subgroups of patients? such question is hypothesis-generating:
More informationEstimating causal effects in trials involving multitreatment arms subject to non-compliance: a Bayesian framework
Appl. Statist. (2010) 59, Part 3, pp. 513 531 Estimating causal effects in trials involving multitreatment arms subject to non-compliance: a Bayesian framework Qi Long, Emory University, Atlanta, USA Roderick
More informationPropensity Score Matching
Methods James H. Steiger Department of Psychology and Human Development Vanderbilt University Regression Modeling, 2009 Methods 1 Introduction 2 3 4 Introduction Why Match? 5 Definition Methods and In
More informationOn the Use of Linear Fixed Effects Regression Models for Causal Inference
On the Use of Linear Fixed Effects Regression Models for ausal Inference Kosuke Imai Department of Politics Princeton University Joint work with In Song Kim Atlantic ausal Inference onference Johns Hopkins
More information