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I am working on estimating the causal effect of a binary treatment T on a binary outcome y, from observational data. I have access to features X and W, which presumably have affected y and T, respectably.

In terms of methods, I'm looking at double machine learning (DML), or doubly robust estimation (DRE). From what I've read, both seem to be applicable to my problem, and I'm having trouble understanding which is preferable in my situation. As I understand it, both methods

  • Model the propensity (probability of treatment).
  • Model the conditional probability of y given X.
  • Provide an estimate of the average treatment effect (ATE).

Thus, the two methods seem to solve the same problem (estimating the ATE), using the same 'ingredients' (models for T and y). For example, the EconML documentation describes both methods with a short 'when should you use it?' section for each, and the sections are almost identical:

When to use DML is described as:

Suppose you have observational (or experimental from an A/B test) historical data, where some treatment(s)/intervention(s)/action(s) T were chosen and some outcome(s) Y were observed and all the variables W that could have potentially gone into the choice of T, and simultaneously could have had a direct effect on the outcome Y (aka controls or confounders) are also recorded in the dataset.

whereas DRE is described as:

Suppose you have observational (or experimental from an A/B test) historical data, where some treatment/intervention/action T from among a finite set of treatments was chosen and some outcome(s) Y was observed and all the variables W that could have potentially gone into the choice of T, and simultaneously could have had a direct effect on the outcome Y (aka controls or confounders) are also recorded in the dataset.

The only difference I can see is that DRE seems to be restricted to categorical treatments, whereas the treatment can be numerical (e.g. a price) for DML.

Am I correct in thinking both methods are applicable to my problem (binary outcome + treatment, with known confounders)? Is one method always preferable to the other? If not, are there any cases where one is generally better?

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    $\begingroup$ DRE is not restricted to categorical treatments. For the distinction, see stats.stackexchange.com/questions/482445/… $\endgroup$
    – pzivich
    Jul 7 at 11:21
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    $\begingroup$ What makes you think that they are different? $\endgroup$
    – Eike P.
    Jul 16 at 15:21
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    $\begingroup$ In econml.azurewebsites.net/spec/estimation/dr.html they are described to be different $\endgroup$
    – Scriddie
    Jul 17 at 9:27
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    $\begingroup$ @ Eike I'm assuming the documentation for econml (and others) didn't just randomly decide to use two distinct sections to describe the exact same method? $\endgroup$
    – bjarkemoensted
    Jul 17 at 16:07
  • $\begingroup$ On first glance I couldn't find such a distinction in the documentation of DoubleML which is extremely solid and seems to have quite some overlap with EconML. $\endgroup$
    – Scriddie
    Jul 18 at 9:05

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