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)

Rosenbaum DOS: Chapters 7 and 8 (8.1-8.4)

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.

Lalonde NSW data (DOS sec 2.1). Subclassification/Stratification and Full matching.

pdf slides for CC1 2021 audio companion

Week 1 handout Lalonde NSW data

Rogosa R-session (using R 3.3.3) 4/1/18 redo in R 3.4.4 (sparse)

2019 lalonde Matchit: full matching, balance with cobalt love.plot and bal.tab

2019 lalonde optmatch: fullmatch with outcome analysis

MatchIt: Nonparametric Preprocessing for Parametric Casual Inference Daniel Ho, Kosuke Imai, Gary King, Elizabeth Stuart

MatchIt vignette

JSS May 2011 exposition: MatchIt: Nonparametric Preprocessing for Parametric Causal Inference

optmatch:fullmatch vignette optmatch another version another good tutorial optmatch Functions for Optimal Matching

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

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.)

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.

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)

Rosenbaum DOS: Chapter 2 (plus week1 items)

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.

Lindner data, Percutaneous Coronary Intervention with 'evidence based medicine'.

Percutaneous coronary intervention (PCI), commonly known as coronary angioplasty or simply angioplasty, is a non-surgical procedure used to treat the stenotic (narrowed) coronary arteries of the heart found in coronary heart disease.

Lindner data in package

cc2 pdf slides Lindner example 2021 audio companion

Week 2 handout Rogosa R-session

Additional R-session Lindner fullmatch in optmatch and cobalt

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

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.

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 set is

Additional exercises (checking balance) using the nuclearplants data from Mark Fredrickson here

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.

nuclearplants using Matchit (Stat209 handout) optmatch for Review Question 5

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) -

Rosenbaum DOS: Chapters 8 and 9

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)

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?

First model for observational studies (DOS, Sections 15.1 and 15.4; 3.1-3.3)

Alternative propensity score analyses. Propensity score weighting: Inverse Probability of Treatment Weighting (IPTW). Treatment effect estimation without matching.

Review paper: Moving towards best practice when using inverse probability of treatment weighting (IPTW) using the propensity score to estimate causal treatment effectsin observational studies Peter C. Austin and Elizabeth A. Stuart, Statistics in Medicine Statist. Med.2015,34 3661-36793661

A thorough R exposition using the Lalonde data A Practical Guide for Using Propensity Score Weighting in R Practical Assessment, Research & Evaluation, v20 n13 Jun 2015.

pdf slides cc4 2021 audio companion Rogosa R-session

Additional Resources:

A Guide to Using WeightIt for Estimating Balancing Weights Noah Greifer

Propensity score techniques and the assessment of measured covariate balance to test causal associations in psychological research Valerie S. Harder, M.H.S., Ph.D., Elizabeth A. Stuart, Ph.D., and James C.Anthony, Ph.D. .R file (readable code showing matchit fullmatch and IPW) for paper Also Cox Regression, comparison with full matching (Elizabeth Stuart)

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.

3. The Wilcoxon signed rank test takes as its input a fixed number, designate this number