In clinical trials, treatment and non-treatment groups go through random allocation, in the hope that characteristics of both groups are similar at baseline. If there are any baseline differences they can be added as covariates to adjust for them, eg in ANCOVA.
When comparing treatment effect in observational studies, where two groups differ at baseline, I understand this approach is not suitable. Propensity score matching is a popular approach. My questions are:
- Why can't observational studies adjust for baseline differences by adding them as covariates?
- What are other alternatives to propensity score matching and their benefits?
- Imagine a flipped example: In an observational study of N number of people on treatment X, I want to compare response to treatment X between alcohol drinkers and non-drinkers. I hypothesise that drinkers will respond less well. I know that drinkers have worse disease at baseline, so this difference needs to be adjusted. I can pretend that drinking is the "treatment" and use propensity score to match drinkers and non-drinkers for baseline disease severity. However this analogy seems to me not completely correct, as drinkers will have been drinking long before they started treatment (c.f. in an observational study comparing treatment effect, the individual will have worse disease before they start treatment). Therefore is PSM unsuitable, and if so what are the alternatives?