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The Average Treatment Effect (ATE) and the Average Treatment Effect on Treated (ATT) are commonly defined across the different groups of individuals. In addition, ATE and ATT are often different because they might measure outcomes ($Y$) that are not affected from the treatment $D$ in the same manner. First, some additional notation: $Y^0$: population-...


35

It's true that there are not only other ways of performing matching but also ways of adjusting for confounding using just the treatment and potential confounders (e.g., weighting, with or without propensity scores). Here I'll just mention the documented problems with propensity score (PS) matching. Matching, in general, can be a problematic method because it ...


22

Propensity score methods are one type of method used to adjust for confounding. There are several other methods that rely on different assumptions. Some of the most popular include difference-in-differences, which relies on an assumption about stability over time, and instrumental variable analysis, which relies on an assumption about randomization of some ...


18

As some of the information you provided states, the two are not the same. I like better the terminology of conditional (on covariates) and unconditional (marginal) estimates. There is a very subtle language problem that clouds the issue greatly. Analysts who tend to love "population average effects" have a dangerous tendency to try to estimate such ...


14

I'll try to give you an intuitive understanding with minimal emphasis on the mathematics. The main problem with observational data and analyses that stem from it is confounding. Confounding occurs when a variable affects not only the treatment assigned but also the outcomes. When a randomized experiment is performed, subjects are randomized to ...


14

The easiest way I've found is to use NearestNeighbors from sklearn: from sklearn.preprocessing import StandardScaler from sklearn.neighbors import NearestNeighbors def get_matching_pairs(treated_df, non_treated_df, scaler=True): treated_x = treated_df.values non_treated_x = non_treated_df.values if scaler == True: scaler = ...


13

There are two approaches for modeling propensity scores. One is to try to approximate the treatment assignment process as closely as possible, and the other is to obtain propensity scores that yield covariate balance. The first approach relies on the finding that balancing on a well-formed propensity score balances all pre-treatment covariates fully (i.e., ...


12

I am not an expert on either R nor propensity matching, but I ran into the same problem while working on a project. I think what matchit does is randomly pick one of the control subjects that falls within the caliper interval around the treated subject. If you set your seed to the same number every time you run your match.out line, you will get the same ...


12

The procedure you described is not propensity score matching but rather propensity score subclassification. In propensity score matching, pairs of units are selected based on the difference between their propensity scores, and unpaired units are dropped. Both methods are popular ways of using propensity scores to reduce imbalance that causes confounding bias ...


11

You don't need the survey package or anything complicated. Wooldridge (2010, p. 920 onwards) "Econometric Analysis of Cross Section and Panel Data" has a simple procedure from which you can obtain the standard errors in order to construct the confidence intervals. Under the assumption that you have correctly specified the propensity score which we denote as ...


11

Let's step back and think more broadly about how you could match given some data X. Exact or Cell Matching This is hard to do with continuous Xs. You could try rounding/discretizing each variable, but that introduces some measurement error. If you choose to proceed anyway, then you interact these new variables to define cells. Here you run into the curse of ...


11

You need to distinguish between uses of propensity scores for matching of cases versus for more general adjustments. The discussion on this page suggests that there isn't much of a use case for propensity score matching. Among other problems, there is seldom much to be gained by throwing away information. Yet that is what matching cases does, with additional ...


10

One important detail that may not be clear from the answer above is that the default form of matching in the matchit package (and in much of the scholarly literature in any field) is to use a propensity score that estimates, for each observation, the probability of assignment to treatment given some set of pre-treatment covariates using logistic regression. ...


10

The propensity score $p(x_i)$ calculated is the probability of subject $i$ to receive a treatment given the information in $X$. The IPTW procedure tries to make counter-factual inference more prominent using the propensity scores. Having a high-probability to receive treatment and then to actually receive treatment is expected, no counterfactual information ...


10

Mahalanobis distance matching (MDM) and propensity score matching (PSM) are methods of doing the same thing, which is to find a subset of control units similar to treated units to arrive at a balanced sample (i.e., where the distribution of covariates is the same in both groups). MDM works by pairing units that are close based on a distance called the ...


10

Propensity score (PS) analysis has many problems in general, and matching is especially problematic. I prefer covariate adjustment for a spline function of the logit of PS if you need propensity scores, and you must also include pre-specified individual strong covariates to absorb outcome heterogeneity. If the sample size is large in relationship to the ...


9

I've personally been asking this question for at least 5 years since for me it's the "big" practical question for using propensity score matching on observational data to estimate causal effects. This is a superb question and there's a subtle disagreement that runs deep in the statistics versus computer science communities. From my experience statisticians ...


9

As Alexis pointed out, propensity score matching (PSM) is one of many tools we have in causal inference. Another one is Inverse Probability Weighted Estimator (IPWE). You can also use causal discovery to infer a causal diagram and use do-calculus to estimate the causal effect. Or make use of instrumental variables estimation. I'm just throwing a lot of names ...


8

In a strict sense, propensity score adjustment has no more to do with causal inference than regression modeling does. The only real difference with propensity scores is that they make it easier to adjust for more observed potential confounders than that sample size may allow regression models to incorporate. Propensity score adjustment (best done through ...


8

Following up on Dimitriy's comment, which I agree with. There are (at least) three sources of uncertainty when performing a propensity score matching analysis: 1) the estimation of the PS, 2) the matching, and 3) sampling variability. I have been writing a review of uncertainty estimation after matching so I'll briefly share those findings here. The way ...


8

This is a great question and one for which there is no single answer, so I won't attempt to give one to be comprehensive. I'll mention a few topics that might satisfy some of your curiosity and point you to some interesting studies seeking to address the question you asked. The method you described of training a random forest and then producing predictions ...


7

First of all,the equation you are looking for is not possible for random forest. This is because the nature of random forest algorithm inherently leads to destruction of any simple mathematical representation. Random forest works by building decision trees & then aggregating them & hence the Beta values have no counterpart in random forest. Though ...


7

In the absence of subject matter knowledge, overinclusion of variables is generally better than underinclusion, and there is little reason to do model selection to build a PS. What is more important is to build a flexible model. My default approach is to spline every continuous variable and to not look at $P$-values for variables in the PS, i.e., I use a ...


7

You can use twang with more than 2 treatment levels -- I use it all the time to obtain propensity scores for multiple (i.e. >2) treatments and it's one of my all time favorite R packages because there is no need to guess the functional relationships between your treatments and covariates. Since twang uses gradient boosted regression, it can fit nonlinear ...


7

Based on the comments and the availability of such a large control group, I would probably advise to do in a step first exact matching on age groups and sex, and perhaps common disease groups. Hereby, you built different strata. In a second step, you can apply propensity score matching to ensure that treatment and control group are as balanced as possible ...


7

Removing good data from an analysis is scientifically suspect in my humble opinion, and naive matching methods are inefficient. It may be very easy to adjust for patient characteristics using ordinary regression models, paying attention to linearity assumptions etc. Of course it is a good idea to look at overlap in covariate distributions across treatment ...


7

1) If your goal is to make a causal inference, balance is paramount. Although you may have improved balance, if it is not good then your causal inference may still be invalid (/your estimate will still be biased). If you have untreated units that fall outside the range of your treated units, your causal inferences will not be valid for them unless you can ...


7

Matching without replacement can yield very bad matches if the number of comparison observations comparable to the treated observations is small. It keeps variance low at the cost of potential bias. Matching with replacement keeps bias low at the cost of a larger variance since you are using the same info over and over. So there's no free lunch (as long as ...


7

The definition of a confounder is somewhat complicated, but VanderWeele & Shpitser (2013) decided A pre-exposure covariate C is a confounder for the effect of A on Y if it is a member of some minimally sufficient adjustment set. A sufficient adjustment set is a set of variables conditioning on which is sufficient to remove confounding. Using the ...


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