The propensity score is obtained from logistic regression where the dependent variable is the exposure (e.g., treatment group). The predicted probabilities are then used for covariate adjustment. When you say "why not just do a good old fashioned logistic regression", I assume you are referring to the situation where the dependent variable is the outcome - not the exposure?

Hmm!

Keep in mind that propensity scores are most helpful under observational conditions, where randomization to an experimental condition is not possible. In a randomized experiment, a check on randomization is to test for group differences in covariates. Under observational conditions, the effect of a "treatment" on an outcome can be biased by, among other things, selection bias to the treatment. By estimating the effects of covariates on inclusion in the treatment group, you can adjust for some of these effects. Propensity scores can be used to find a "matched" control group similar to those who received the treatment, to stratify analyses by propensity to treatment, to weight model estimates by propensity for treatment, or simply as include the propensity score as an adjustment variable in the model. It's true that the propensity model makes assumptions (just as the regression model does), and can only account for observed covariates. Thus, it is very possible that propensity matching can exacerbate the bias of hidden confounders, though this should be a concern regardless of whether propensity matching is used.

I think this is a good question. I’ve not got a great answer as to the fundamenta advantage. The answer above conveys some of it - the propensity scoring allows you to create groups that are matched in risk according to the propensity model. The can be used to make comparisons between different levels of the “intervention” as if the groups were formed at random. But they aren’t formed at random n and you are spot on that there is a regression model underlying it. There is nothing magic. There is a relative benefit in the ability to make a compar between groups (as opposed to reporting the group effect as one parameternin a regression) but whether it is ultimately less prone to bias, J am unclear ( for all the reasons outlined in Preston‘s answer above). So 10/10 for question!

Good afternoon Mark,

Propensity Score Analysis assumes that all variables that had an effect on treatment assignment and outcome are controlled for when computing the propensity score. The propensity score can be calculated with logistic regression but could also be calculated with a regression tree, random forest or some other machine learning/statistical technique.

If you have a binary outcome and choose to perform a logistic regression with variables that had an effect on treatment/outcome as predictors you are assuming that the relationship between predictors and outcome is correctly captured by the logit model. In other words, before performing the logit transform, the additive/linear relationship is valid.

Of course, no matter how you calculate propensity scores you have to meet the assumptions of that method so propensity score analysis is by no means assumption free even if you have properly identified all confounders.

But if you are unsure of the precise relationship between confounders and outcome (is age linearly related to stroke or do I need to create age buckets or need to add age squared) but are confident that you understand the relationship between confounders and treatment assignment than propensity score would be the better option.

If you are confident that logit correctly models the relationship between confounders and outcome than there is no need to calculate a propensity score—though in my experience this is rare. It is even more rare when the outcome is continuous and OLS would be typically applied. The real world rarely has outcomes related to predictors in an additive/linear fashion. One reason propensity score analysis is so popular is because it does not demand that the precise relationship between confounders and outcome is understood.

Best,

Aran

Thanks to everyone for those excellent answers. They have really helped my understanding. By the way, after asking the original question I came across a couple of excellent youtube videos as follows:

https://www.youtube.com/watch?v=h0UU6trKR0E (Ben Lambert)

https://www.youtube.com/watch?v=ACVyPp1Fy6Y (Doug McKee)

Had similar questions but I think Nguyen et al have brought some clarity to the matter in this publication. I hope it helps.

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