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Given a large dataset, one cannot possibly check every model. In particular, it does not seem clear to me that one can check confounding or mediation in either cases.

How does one check confounding/mediation in large data context? I am no epidemiologist. Does the question even make sense in tons spurious relationship due to large data? If there are 5 variables, there might be hope. I could not see hope in data with 100 variables.

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The size of the dataset only helps a little. The only way I know to check confounding is to convene a large number of experts in the subject matter area and in operations and procedures related to subject matter and to have them list all of the factors they feel may be used in the decision making process related to the exposure or treatment you are interested in. Then see if those factors (or ones highly correlated with them) happen to be collected in your dataset and are measured accurately enough without too many missing values.

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  • $\begingroup$ Should I expect population level covariance matrix of variables sparse here and a lot of their correlations to the outcome turns out to be spurious? Or is it unreasonable to assume correlations between variables and correlation between variables and outcome is sparse? $\endgroup$
    – user45765
    May 15 at 21:59
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    $\begingroup$ You are ignoring the most important issues: the study design, how the data came about, and what influences choices such as treatment choices. Without understanding the potential for unmeasured confounders there is not a lot the data can do. $\endgroup$ May 15 at 22:14
  • $\begingroup$ I agree on the importance of study design. For studies controls confounder by blocking or randomization, I have no trouble at all. I have most of trouble for observational study where confounding cannot be ruled out by design. $\endgroup$
    – user45765
    May 15 at 22:35

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