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Suppose I use PSM to balance confounders for treatment effect in observational studies, and the logistic model for the PS includes age, gender, comorbidities.

And then use either stratification or matching or weighting (eg in tutorial by http://personalpages.manchester.ac.uk/staff/mark.lunt/) followed by PS matched linear regression.

Can the PS matched linear regression then have age, gender, comorbidities as covariates?

Conceptually it seems to me that you should be able to, but not if PS is used for model reduction and the PS is added as a covariate (as some people do https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4004383/).

Thank you

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Yes you certainly can! This is called the "doubly robust" approach and is recommended by many authors. You essentially run the linear regression model you would have run had you not performed the propensity score analysis, but you do so on your propensity score adjusted sample. See Stuart (2010), section 5 for an introduction to this idea.

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  • $\begingroup$ Thanks Noah that's very helpful. Have you got any good references explaining benefits of PSM over "adjusting for baseline as a covariates"? $\endgroup$
    – bobmcpop
    Commented Dec 1, 2016 at 18:45
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    $\begingroup$ Gary King has written a fair amount about this. See Ho, Imai, King & Stuart (2007) and Nielson & King (2016). $\endgroup$
    – Noah
    Commented Dec 2, 2016 at 5:02
  • $\begingroup$ +1. I would suggest that you not only can but should do this! $\endgroup$
    – usεr11852
    Commented May 9, 2017 at 20:26

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