STAT266/CHPR266/HRP292-- Course Files, Readings, Examples
Week 1--Course Introduction; Matching Methods part 1 (intro and theory)
Lecture Topics Lecture 1 slide
deck (companion audio part 1) (companion audio part 2)
1. Course outline and logistics
2. A matched observational study (DOS, Chap 7)
3. Study design versus inference
4. Basic tools of multivariate matching (DOS, Secs 8.1-8.4)
Text Readings
Rosenbaum DOS: Chapters 7 and 8 (8.1-8.4)
Additional Resources
Observational Studies according to Donald B. Rubin
For objective causal inference, design trumps analysis Annals of Applied Statistics,
Volume 2, Number 3 (2008), 808-840. Rubin talk . Another Rubin overview of matching:
Matching Methods for Causal Inference Stuart, E.A. and Rubin, D.B. (2007). Best Practices in Quasi-Experimental Designs: Matching methods for causal inference. Chapter 11 (pp. 155-176) in Best Practices in Quantitative Social Science. J. Osborne (Ed.). Thousand Oaks, CA: Sage Publications.
Computing Corner: see 2019 course website for 2019 Computing Corner Week 1 pdf slides 2020 audio companion
Week 1 Review Questions
From Computing Corner
1. In Week 1 Computing Corner with the Lalonde data (effect of job training on earnings), we started out (see R-session) by showing the ubiquitous [epidemiology to economics] analysis for observational data of an analysis of covariance, aka tossing the treatment variable and all the confounders into a regression equation predicting outcome and hoping for the best (c.f 2016 Week 1 in the news analyses: mom fish consumption on child cognition). The statement made in class (technical details week 1 stat209) is that regression does not "control" for confounders; instead the coefficient of treament (putative causal effect) is obtained from a straight-line regression of outcome on the residuals from a prediction of treatment by all the other predictors in the regression. Demonstrate that equivalence using the ancova in CC1.
2. RQ1 uses the Week 1 Computing Corner Lalonde data (effect of job training on earnings) analysis of covariance: tossing the treatment variable and all the confounders into a regression equation predicting outcome and hoping for the best. Compare that ancova with an ancova the uses just the significant predictors of re78. Also compare with an ancova which uses the single available covariate/confounder having the highest correlation with outcome. Are these analyses consistent?
From Lecture
3. We will be working a lot with matching based techniques. One of the best thinkers/writers on the topic of matching is Elizabeth Stuart from Johns Hopkins. For this problem, take a look at her paper: "Matching Methods for Causal Inference: A Review and a Look Forward." In lecture 01 you were introduced to "balance tables" (a.k.a. "Table 1") which summarizes the covariate distribution of the observations. A handful of questions: (a) as concisely as possible, state why we focus on balance assessments as part of our argumentation when attempting to perform causal inference, (b) in addition to a balance table, name other tools used to report balance, (c) why do we use standardized mean differences instead of p-values to assess balance when assessing the quality of a match design?, and (d) why is it kinda weird to use a p-value of the covariates in a randomized trial to assess balance?
4. In lecture 1 we quickly outlined some of the big challenges to causal inference when using observational data (see slide 41, "There should be strong effort to show the two groups are similar..."). These challenges include: inclusion/exclusion of observations, observational units that may be completely missing (censored, survival bias), missing data, imbalances in observed data, and imbalances in unobserved data. We'll address each of these at different points in the course. But let's focus on the decision to include/exclude observations. What we're doing when matching -- i.e., removing observations that do not have adequate counterparts in the contrast group -- may seem a bit subversive. The intuition is: why "throw away" data? I think there are two reasons people worry about "throwing away data." First, it seems like limiting the kinds of observations in our study we may be losing the ability to generalize our conclusions to a wider swath of the population. The counter to that is: yes, we are trading off the ability to generalize (i.e., external validity) for the ability to make stronger claims about a candidate causal effect (i.e., internal validity). The second concern is that it seems like more data is better. Formulate a response to this concern. (Note: OMG, this question seems so nebulous. Yup. That's how this works; you're playing Big Kid academics now. We made sure to mention this argument during lecture 01, so you know it. It's a common statistical argument nowadays. If you want to read your way out of this one... here's a good paper.)
From Computing Corner
5. Exercise in pair matching. In DOS Sec 2.1, Rosenbaum works with the randomized experiment data from NSW. In Week 1,2 Computing Corner we used the constructed observational study version of these data. Use the observational study data to do a version of the 1:1 matching in DOS section 2.1. Compare the balance improvement achieved from nearest neighbor matching with the full matching results in Computing Corner Week 1,2.
6. For the fullmatch analysis done in the Lalonde class presentation weeks 1 and 2, the outcome comparison was carried out using lmer to average the treatment effects over the 104 subclasses. A hand-wavy analogy to the paired t-test here would be to use the mean difference within each subclass. Show that (because some of the subclasses are large) this simplified analysis doesn't well replicate the lmer results.
7. optmatch package, fullmatch, lalonde.
MatchIt uses the optmatch package fullmatch command for its "full" option, as used in the class example. Using the raw optmatch (without the matchit wrapper) allows additional specifications and controlls for the full or optimal matching.
For lalonde data try out optmatch fullmatching and compare results for subclasses and balance with the class example using optmatch through MatchIt.
Week 2-- Matching Methods Part 2 (implementation); Potential Outcomes and Study Design
Lecture Topics Lecture 2 slide
deck (companion audio)
1. Basic tools of multivariate matching (DOS, Secs 8.1-8.4)
2. Potential outcomes framework (DOS 2.2)
3. Fisher's sharp null; permutation test (DOS 2.3)
4. Various practical issues in matching (DOS, Chap 9)
Text Readings
Rosenbaum DOS: Chapter 2 (plus week1 items)
Additional Resources
From Donald B. Rubin
First section of Basic Concepts of Statistical Inference for Causal Effects in Experiments and Observational Studies Similar material Chaps 1 and 2 Causal Inference in Statistics, Social and Biomedical Sciences: An Introduction, Guido Imbens and Don Rubin linked on main page.
Computing Corner: see 2019 course website for 2019 Computing Corner Week 2 pdf slides 2020 audio companion
Week 2 Review Questions
From Computing Corner
1. The JSS vignette for PSAgraphics (linked week 2 Computing Corner) does subclassification matching for Lindner data. Repeat their subclassification analyses and try out their balance displays and tests. They have some specialized functions. Compare with our basic approach.
2. The Week 2 presentation showed an alternative propensity score analysis -- analysis of covariance with propensity score as covariate. A rough analogy is to ancova vs blocking (where blocking is our subclassification, say quintiles). Try out the basic (here logistic regression) ancova approach for the lifepres dichotomous outcome
From Lecture
3. Modify Fisher's Sharp Null to reflect the null hypothesis that the treatment adds five units to the outcome under control. Build a small simulation (e.g., 10 observations) and construct a table that summarizes the potential outcomes. Randomize using a fair coin flip to assign treatment or control for each observational unit. Use the permutation test to assess your data set using (i) Fisher's Sharp Null and (ii) the null hypothesis that the treatment adds five units to the outcome under control.
4. Building off of RQ#3 above, sort your observations so they are in ascending order based on the outcome under control. Randomize two at a time: one fair coin flip now assigns either the first or second observation to treatment (and the other to control). A second fair coin flip assigns either the third or the fourth observation to treatment (and the other to control). This continues so on and so forth. Use the appropriate permutation test to assess your data set using (i) Fisher's Sharp Null and (ii) the null hypothesis that the treatment adds five units to the outcome under control. Contrast the results here with the results from RQ#3.
From Computing Corner
5. Pair matching--nuclear plants data. See also week8,Stat209. Another (small) canonical matching example for optmatch expositions is the nuclear plants data from Cox and Snell text.
Data cleaning gives 7 "treatment" and resevoir of 19 controls. Try out 1:2 optimal pair matching using MatchIt (see also stat209 exs) and compare with pairmatch in optmatch plus balance diagnostics.
Week 3-- Full matching, Inclusion and Exclusion, and Defining Treatment Effects
Lecture Topics Lecture 3 slide
deck (companion audio)
optmatch example from lecture
1. Finish up: Basic tools of multivariate matching (DOS, Secs 8.1-8.4)
2. Various practical issues in matching (DOS, Chap 9)
3. Inverse probability weighting ( Robins & Hernan, Chap 2.4) -
Text Readings
Rosenbaum DOS: Chapters 8 and 9
Additional Resources
Smoking study (Prochaska et al 2016)
Dealing with limited overlap in estimation of average treatment effects (Crump et al 2009) (or see http://public.econ.duke.edu/~vjh3/working_papers/overlap.pdf )
Defining the Study Population for an Observational Study to Ensure Sufficient Overlap: A Tree Approach (Traskin & Small 2011)
CONSORT Statement (randomized trials)
STROBE Statement (observational studies)
Computing Corner resumes Week 4 with IPW methods
Week 3 Review Questions:
From Lecture
1. In this class we've shown you a couple of tools to assess the adequacy of a matched set - for example: Love plots, balance tables, standardized mean differences, and histogram plots of fitted propensity scores (or covariates). Why haven't we shown you a statistical test? That's weird, right? A ton of researchers fall for this, failing to see why assessing balance using a hypothesis test in an observational study is problematic. There are a couple of valid critiques; try articulating at least one such critique. (Hint: think about how we calculate the SMD vs a standard error.) Once you've given it a go, check out Section 6.6 of this paper (great paper!) for a couple of solutions to this question.
2. In section 6.7 of that same paper, the authors say their preferred tool for assessing balance is an empirical QQ plot. What's a QQ plot? Compare and contrast the use of QQ plots and a balance table. Neither of these tools in dominate, so what are the benefits and drawbacks to each?
Week 4-- Models for Observational Studies
Lecture Topics Lecture 4 slide
deck (companion audio)
1. First model for observational studies (DOS, Sections 3.1-3.3)
Computing Corner: see 2019 course website for 2019 Computing Corner Week 4 pdf slides 2020 audio companion
Week 4 Review Questions
From Computing Corner
1. Try out the ATE IPTW analysis (done in week4 computing corner) for the dichotomous outcome lifepres in the Lindner data. Compare with full matching results shown in class.
2. Try an ATT IPTW analysis for log(cardbill) outcome in the Lindner data.
From Lecture
3. The Wilcoxon signed rank test takes as its input a fixed number, designate this number I, of matched pairs. The Wilcoxon signed rank test is a permutation test with a specific test statistic. Let's explore the behavior of its statistic compared to the behavior of the average of the within-pair differences. You can use the sample code provided to simulate (i.e., simulation 1 here). Consider playing around with the sd in the data generating functions to see the impact in the histograms.
Question: what happens when we introduce one really 'weird' data point in our matched sets? Compare what happens to the distributions for mean(y_t - y_c |matched pairs) vs the Wilcoxon rank sign test. The solution is in the comments in simulation 3 in the link above.
Week 5-- Randomized Experiments, Design Sensitivity, and Augmenting the Primary Study
Lecture Topics Lecture 5 slide deck (companion audio)
1. The naive model - DOS chptr 3.4-3.8
2. Design sensitivity - DOS chpr 14
3. Prognostic scores - Hansen (2008), Leacy & Stuart (2014)
4. Design devices (multiple controls, coherence, and known effects) - DOS 5.2.2 through 5.2.4
References:
Hansen BB. The prognostic analogue of the propensity score. Biometrika. 2008 Jun 1;95(2):481-8.
Leacy FP, Stuart EA. On the joint use of propensity and prognostic scores in estimation of the average treatment effect on the treated: a simulation study. Statistics in medicine. 2014 Sep 10;33(20):3488-508.
Computing Corner: see 2019 course website for 2019 Computing Corner Week 5 pdf slides 2020 audio companion
Week 5 Review Questions
From Computing Corner
1. Try out, using the Lalonde data (Week 1), the boosted regression approach to computing propensity scores using Ridgeway's (via Friedman) gbm package. Are the balance and overlap results improved compared to the logistic regression estimation shown in Week 1?
2. Try out using the Lindner data shown in the PSAgraphics vignette (JSS linked week 2), the regression tree classification (use rpart) approach for propensity score estimation. Examine resulting propensity scores, balance for matching in six suclassifications, and outcome analysis for cardbill measure.
Week 6--Thick Description, Bradford Hill Criteria, and Reasoning about Data
Lecture Topics Lecture 6 slide deck (companion audio)
1. Thick description
2. Bradford Hill Criteria
3. A principled prediction-problem ontology
Reading:
The causal impact of bail on case outcomes for indigent defendants in New York City
Computing Corner: see 2019 course website for 2019 Computing Corner Week 6 pdf slides 2020 audio companion
Week 6 Review Questions
From Week 6 Computing Corner
1. Mercury example (2 controls) from section 3 and 6 of Rosenbaum vignette (linked in CC_6)
Fish often contains mercury. Does eating large quantities of fish increase levels of mercury in
the blood? Data set mercury in the sensitivitymw package is from the 2009-2010 National
Health and Nutrition Examination Survey (NHANES) and is the example in Rosenbaum
(2014). There are 397 rows or matched triples and three columns, one treated with two
controls. The values are methylmercury levels in blood. Column 1, Treated,
describes an individual who had at least 15 servings of fish or shellfish in the previous
month. Column 2, Zero, describes an individual who had 0 servings of fish or shellfish
in the previous month. Column 3, One, describes an individual who had 1 serving of
fish or shellfish in the previous month. In the comparison here, Zero and One are not
distinguished; both are controls. Sets were matched for gender, age, education, household
income, black race, Hispanic, and cigarette consumption.
a. describe the apparent effect of fish consumption and try out sensitivity analyses (for both tests and CI) for the apparent effect of fish. c.f Rosenbaum vignette sec 3.2
b. look at the effects of weighting (method w in the sensitivitymw manual) as theory and simulations suggest that a sensitivity analysis will be more powerful
if matched sets with little variability are given little weight. c.f Rosenbaum vignette sec 6.3.
2. Demonstration--see solution. Mechanics of setting up a matched data set for the sensitivity functions. Easiest to create the data set for the most common 1:1 matching situation (merge works without needing thought); steps for 1:1 matching setting below
Week 7-- Alternative Designs: Discontinuity Designs and Case-Noncase Studies
Lecture Topics Lecture 7 slide
deck (companion audio)
Regression discontinuity - Lee and Lemieux 2011
Case-noncase study - Breslow 1998
Isolation in the construction of natural experiments - Zubizarreta, Small, and Rosenbaum 2014
Computing Corner: see 2019 course website for 2019 Computing Corner Week 7 pdf slides 2020 audio companion
Week 7 Review Questions
From Week 7 Computing Corner
1. Dose-Response functions. IPW (aka importance sampling) can't hit the curve? Can't hit anything??
In week 7 Computing Corner we showed results for ADRF (average dose-response function) estimates using Imbens very clever artificial data example from the linked causaldrf vignette (see also CC_7 slides).
IPW results (see Weeks 3 and 4 Computing Corner for examples for binary treatements) were notable in apparant bad bad performance (all other estimates did pretty well). Keep in mind this artificial data test is not even a "phase 2" hurdle, as we are given the selection variables (X_1, X_2) that are responsible for individuals selecting dose (here denoted by T) other than randomness.
As IPW is dominant in applications like long-term occupation exposures (to bad stuff), the dose-reponse setting is quite relevant. The artificial data ADRF has an important feature of a non-monotonic dip, reminiscent of alcohol or even salt (a bit above 0 is better than zero) for health outcomes. So for another look at IPW, I tried to make a much easier example, with basically a straight-line ADRF (just with a little wiggle) by limiting dose
(T) to > .5.
So try out the comparison of the hi_estimate (shown in class) and the iptw_estimate both from the causaldrf package with the true ADRF from the artificial data construction using values T > .5 (about half the data).
Are we any happier with the value of IPW (importance sampling)? Solution indicates to me: "no", YMMV.
Lecture 7 addendum: Case-control studies
Case-control overview (shown in class) from Encyclopedia of Public Health
Breslow NE. Statistics in epidemiology: the case-control study.J Am Stat Assoc. 1996 Mar;91(433):14-28
Carbonated Soft Drink Consumption and Risk of Esophageal Adenocarcinoma JNCI: Journal of the National Cancer Institute, Volume 98, Issue 1, 4 January 2006, Pages 72-75,
Smoking and Lung Cancer in Chap 18 of HSAUR3 (Handbook of Statistical Analysis Using R). Also driving and backpain data in Chap 7 HSAUR2
Some R-packages and resources: SensitivityCaseControl: Sensitivity Analysis for Case-Control Studies; multipleNCC: Inverse Probability Weighting of Nested Case-Control Data; Two-phase designs in epidemiology
(Thomas Lumley) ; Exact McNemar's Test and Matching Confidence Intervals
2. Case-Control Study. Matched case-control study.
From epiDisplay v3.5.0.1 by Virasakdi Chongsuvivatwong Datasets on a matched case-control study of esophageal cancer
See also matched case-control study in the epiDisplay package manual. data(VC1to1)
Data from a matched case-control study testing whether smoking,
drinking alcohol and working in the rubber industry (all dichotomous) are risk factors for oesophageal
cancer. Each case was matched with his/her neighbours of the same sex and age
group. The matching ratio in VC1to1 is 1:1 pair matching. The data are in long form (as you would get from MatchIt) with variable matset indicating subclass and case indicating cancer or not.
Discussion and analysis is found in Chap 16 of the Epicalc Book
Publication: Chongsuvivatwong, V. 1990 A case-control study of esophageal cancer in Southern Thailand. J Gastro Hep 5:391-394.
Week 8-- RCT Designs with Instrumental Variables
Lecture Topics Lecture 8 slide
deck (companion audio)
Encouragement design (Holland 1988 )
Instrumental variable methods for causal inference ( Baiocchi, Cheng and Small 2014)
Computing Corner: see 2019 course website for 2019 Computing Corner Week 8 pdf slides 2020 audio companion
Regression Discontinuity Resources
Stat209, Regression Discontinuity intro handout
William Trochim's Knowledge Base
Trochim W.M. & Cappelleri J.C. (1992). "Cutoff assignment strategies for enhancing randomized clinical trials." Controlled Clinical Trials, 13, 190-212. pubmed link
Journal of Econometrics (special issue) Volume 142, Issue 2, February 2008, The regression discontinuity design: Theory and applications Regression discontinuity designs: A guide to practice, Guido W. Imbens, Thomas Lemieux
Also from Journal of Econometrics (special issue) Volume 142, Issue 2, February 2008, Waiting for Life to Arrive: A history of the regression-discontinuity design in Psychology, Statistics and Economics, Thomas D Cook
the original paper: Thistlewaite, D., and D. Campbell (1960): "Regression-Discontinuity Analysis: An Alternative
to the Ex Post Facto Experiment," Journal of Educational Psychology, 51, 309-317.
Capitalizing on Nonrandom Assignment to Treatments: A Regression-Discontinuity Evaluation of a Crime-Control Program Richard A. Berk; David Rauma Journal of the American Statistical Association, Vol. 78, No. 381. (Mar., 1983), pp. 21-27. Jstor
Berk, R.A. & de Leeuw, J. (1999). "An evaluation of California's inmate classification system using a generalized regression discontinuity design." Journal of the American Statistical Association, 94(448), 1045-1052. Jstor
To come: Instrumental Variable Methods: packages AER(ivreg), ivpack, ivmodel
Week 8 Review Questions
Computing Exercises
1. Regression Discontinuity, classic "Sharp" design. Replicate the package rdd toy example: cutpoint = 0, sharp design, with treatment effect of 3 units (instead of 10). Try out the analysis of covariance (Rubin 1977) estimate and compare with rdd output and plot. Pick off the observations used in the Half-BW estimate and verify using t-test or wilcoxon.
Extra: try out also the rdrobust package for this sharp design.
2. Systematic Assignment, "fuzzy design". Probabilistic assignment on the basis of the covariate.
i. Create artificial data with the following specification. 10,000 observations; premeasure (Y_uc in my session) gaussian mean 10 variance 1. Effect of intervention (rho) if in the treatment group is 2 (or close to 2) and
uncorrelated with Y_uc. Probability of being in the treatment group depends on Y_uc but is not a deterministic step-function ("sharp design"): Pr(treatment|Y_uc) = pnorm(Y_uc, 10,1) . Plot that function.
ii. Try out analysis of covariance with Y_uc as covariate. Obtain a confidence interval for the effect of the treatment.
iii. Try out the fancy econometric estimators (using finite support) as in the rdd package. See if you find that they work poorly in this very basic fuzzy design example.
Extra: try out also the rdrobust package for this fuzzy design.
Week 9 - Observational Studies with Instrumental Variables
Lecture Topics Lecture 9 slide
deck (companion audio)
Instrumental variable methods for causal inference ( Baiocchi, Cheng and Small 2014)
Near-far matching. Package nearfar
Vignette: " Near-Far Matching in R: The nearfar Package." Journal of Statistical Software (2018).
Computing Corner: see 2019 course website for 2019 Computing Corner Week 9 pdf slides 2020 audio companion
Week 9 Review Questions
Computing Exercises
1. Broken RCT: Compliance, measured or binary
Compliance as a measured variable.
In Stat209 week 7 we also examine compliance adjustments; both those based on a dichotomous compliance variable and the much much more common measured compliance (often unwisely dichotomized to match Rubin formulation).
The Efron-Feldman study ( handout description) used a continuous compliance measure. An artificial data set a data frame containing Compliance, Group, and Outcome for Stat209 HW7 is constructed so that ITT for cholesterol reduction is about 20 (compliance .6) and effect of cholestyramine for perfect compliance is about 35. Try out some IV estimators for CACE. Obtain ITT estimate of group (treatment) effect with a confidence interval. Try using G as an instrument for the Y ~ comp regression. What does that produce? Alternatively use the Rubin formulation with a dichotomous compliance indicator defined as TRUE for compliance > .8 in these data. What is your CACE estimate. What assumptions did you make? Compare with ITT estimate. In this problem the ivreg function from AER package is used for IV estimation.
More problem 1 1. Compliance data, IV analysis, imitating Efron-Feldman cholestyramine trial. Solution showed you the widely used ivreg function from package AER package. Redo the ivreg analyses using functions from the ivmodel package.
2. Observational study: Use the Card data, described in the ivmodel vignette, to carry out some basic IV analyses. Compare ivreg with some analyses using the ivmodel package.
3. RCT, Encouragement Design. Sesamee Street. The CC example and Rogosa session, used postlet (letter recognition) as the outcome. The data also contains pretest measures (before encouragement), so an alternative outcome is improvement, post - pre, for letter recognition. Repeat the IV encouragement design analysis for the outcome improvement in letter recognition. Time1-Time2 data week4 of Stat222 (longitudinal research), and week9 Stat209.
Week 10 - Mendelian Randomization and Synthetic Control Studies
Lecture Topics Lecture 10 slide
deck (companion audio)
Mendelian Randomization (Lawlor et al 2008)
Synthetic Controls (Abadie, Diamond, and Hainmueller 2012)
Computing Corner
Mendelian Randomization Resources
1. Package mr.raps Title Two Sample Mendelian Randomization using Robust Adjusted Profile.
2. The GLIDE package: Global and Individual Tests for Direct Effects in Mendelian randomization studies
3. Package iva Title Instrumental Variable Analysis in Case-Control Association. Conducting Mendelian Randomization Analysis
4. MendelianRandomization v0.3.0: an R package for performing Mendelian randomization analyses using summarized data
5. MR studies in R How to use genetics for identifying modifiable risk factors