Suppose you have data on a large population, a small proportion of which is treated. Let's assume there are enough treated data points that you don't need propensity scores for data reduction. There is then a choice between
- normal logistic regression with all the covariates in, including 'isTreated' as a binary covariate.
- propensity score matching to create a control group & subsequent comparison of the two groups.
Does the second option reduce omitted variable bias, because:
- individuals that are similar in terms of measured variables are also likely to be similar in terms of unmeasured variables
- it will pick up the effect of interaction terms that are not included in the logistic regression
I would have thought it would do so, but Frank Harrell writes:
I see many researchers using PS when direct covariate adjustment would be far superior, e.g., when there are 100,000 observations and 100 covariates.
I have found one paper that discusses this, but it's rather inconclusive.
Shah, B. R., A. Laupacis, J. E. Hux, and P. C. Austin. 2005. “Propensity Score Methods Gave Similar Results to Traditional Regression Modeling in Observational Studies: A Systematic Review.” Journal of Clinical Epidemiology 58 (6): 550–9.
