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I am not acquainted with Pearl's approach for causal inference. From what I have seen so far, the causality is inferred from directed acyclic graphs(DAGs).

Rubin's Causal Inference Sec 7.5 proved a theorem stating that asymptotic unbiasedness of OLS estimator for superpopulation treatment effect.

By Rubin, if sample is so large that we have very small bias, the estimation of treatment effect can be done by using OLS with a few covariates. From this, under large sample assumption, I can just perform ordinary linear regression to estimate treatment effect.

If one is inferring such treatment effect, why does one need DAGs to estimate treatment effect as compared to the asymptotic unbiasedness provided by Rubin's result? It seems to me that DAGs should be a special case of Rubin's theorem.

user45765
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    The theorem in Section 7.5 starts with "Suppose we conduct a completely randomized experiment." This is very much a special case, and not a general result about OLS. This is where the identifying assumptions represented in the DAG can give you some leverage, though of course you can draw a DAG for the completely randomized case as well. – dimitriy Feb 26 '22 at 02:12
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    Applications of DAGs are especially useful to causal inference for observational designs, although they can also useful for RCTs (which also suffer from selection biases to causal inferences), including special cases like Mendelian randomized designs. – Alexis Feb 26 '22 at 04:29
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    @Alexis Nice, I had not heard the term [Mendelian randomization](https://en.wikipedia.org/wiki/Mendelian_randomization) before. – DifferentialPleiometry Feb 26 '22 at 04:43
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    If nothing else, DAGs and the backdoor criterion identify confounders. If you can't figure out what is a confounder and what isn't, you're flying blind. I view this, indeed, as one of the CHIEF benefits of the causal DAG approach. It is also non-parametric, which makes it fairly robust. It does not depend on ignorability, either - a difficult assumption to verify. – Adrian Keister Feb 26 '22 at 16:13
  • @AdrianKeister I do not think confounder is issue in completely randomized experiment. Confounder issue is mostly related to experimental design problem in my view. I am only concerned with completely randomized experiment. I do not think there is general assertion on asymptotic unbiasedness in general experimental design. I do not think you can verify ignorability as it requires reveal of unknown information which is never available in general. And I think others are missing the point that previous linear regression estimation is independent of model misspecification. – user45765 Feb 26 '22 at 16:32
  • @dimitriy I think DAG is at best semi-parametric as you need to assume some structure.(The main advantage of OLS is that it is immune to model misspecification issue.) I am aware of the assumption on completely randomized experiment which I am interested in to see how much more mileage can be obtained by OLS. For DAGs, I do not know whether it is susceptible to model misspecifiction bias and finite sample bias. If so, would it be superior to OLS? I am concerned about bias and efficiency. – user45765 Feb 26 '22 at 16:36
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    A DAG is a graph that encodes some assumptions about causality. It’s not an estimation method, so it’s not semi-parametric or efficient or biased in finite samples. It’s very strange to me to compare a DAG to OLS. – dimitriy Feb 26 '22 at 17:12
  • @dimitriy In this context, I agree. For clarity, DAG's are a type of graph that doesn't have to do with causality *per se*, but DAG's can be used to model assumptions about causality as you said. This is salient to me because I use DAG's for things outside the context of causal inference. – DifferentialPleiometry Feb 26 '22 at 17:19
  • @dimitriy Thanks. I will check how DAG works to estimate treatment effect as I am only reading Rubin's book so far and I only have seen some DAGs shown to me in the past. – user45765 Feb 26 '22 at 17:19
  • If you are coming from a PO outcome approach, the two links [here](https://stats.stackexchange.com/a/559254/7071) are useful for understanding DAGs. – dimitriy Feb 26 '22 at 17:24
  • @dimitriy Thanks a lot for reference. I will check them out. – user45765 Feb 26 '22 at 17:27
  • @Noah Thanks. I think to certain extent it answers various of expected issues in DAGs and dimitriy's references do answer the question. – user45765 Feb 26 '22 at 22:40
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    @user45765 Confounders are almost the MAIN issue with any experiment! The whole point of an experiment of any design is to remove confounders. If you don't know which variables are confounders, or if there are confounders you miss, then your experimental design is flying blind. A well-designed experiment should remove confounding bias altogether, but that is not always possible. An understanding of causal DAGs shows you some of the options for analysis, whether that's frontdoor adjustment, backdoor adjustment, instrumental variables, stratified analysis, inverse probability weighing, etc. – Adrian Keister Feb 27 '22 at 00:39
  • *I am only concerned with completely randomized experiment.* This is so important that it should be specified in your post (by editing it), not in the comments. – Richard Hardy Feb 28 '22 at 20:42
  • @AdrianKeister The "main issue" for those who ignore selection bias to the detriment of their science perhaps? – Alexis Mar 02 '22 at 21:00
  • @Alexis Well, the whole idea of an experiment is to control some variables so as to eliminate confounding bias from them. I'm using the word "issue" here to mean "a routine design concern", not "a probably fatal problem with the entire approach". – Adrian Keister Mar 02 '22 at 22:02
  • @AdrianKeister Selection bias is not in any way controlled by RCTs (in fact RCTs *introduce* certain kinds of selection bias). Given that selection bias is capable reversing, fabricating, hiding, amplifying existing and non-existing causal effects estimates, I think it is a mistake to take the position that design should only (or mostly) consider confounders, but not also selection biases. That's all. (RCTs are very good at eliminating confounders: totally agree.) – Alexis Mar 02 '22 at 22:05
  • @Alexis: I think we're fundamentally on the same page: a good experimental design should, by taking selection bias into consideration, avoid its primary pitfalls. – Adrian Keister Mar 02 '22 at 22:24

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