Propensity score matching and linear regression covariates

[bob mcpop]

Hello, can someone help? 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 stratification or matching or weighting (eg in tutorial by http://personalpages.manchester.ac.u...sity_guide.pdf) 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 (as some people do https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4004383/) PS is used for model reduction and the PS is added as a covariate.

Thank you

[David Radwin]

Yes, it can. Another argument for this "first match, then regress on the matched sample" approach is

Ho, D.E., Imai, K., King, G., and Stuart, E.A. (2007). Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference. Political Analysis, 15(3): 199–236.

For an argument on why this approach is preferable for complex sample survey data, see

DuGoff, E.H., Schuler, M., and Stuart, E.A. (2014). Generalizing Observational Study Results: Applying Propensity Score Methods to Complex Surveys. Health Services Research, 49(1): 284–303.

The latter reference also argues for including the propensity score in the regression model, which differs from the second reference in your post.

[bob mcpop]

Thank you so much that's great. Have you got any good references explaining benefits of PSM over adjusting for baseline as a covariates?

[David Radwin]

Sorry, Bob, I do not.