Hi NadaN, I believe you can calculate a propensity score / PS (prob of being in a particular group based on covariates) and then either adjust for it (eg in a logistic regression) or choose to compare only a fraction of your individuals that have similar PS values.

There are a number of good reviews eg Benedetto (Statistical primer: propensity score matching and its alternatives) has a good abstract that seems to answer your point re why might want to use propensity scores rather than adjust via a multvariable model

"Propensity score (PS) methods offer certain advantages over more traditional regression methods to control for confounding by indication

in observational studies. Although multivariable regression models adjust for confounders by modelling the relationship between covariates

and outcome, the PS methods estimate the treatment effect by modelling the relationship between confounders and treatment assignment.

Therefore, methods based on the PS are not limited by the number of events, and their use may be warranted when the number

of confounders is large, or the number of outcomes is small. The PS is the probability for a subject to receive a treatment conditional on a

set of baseline characteristics (confounders). The PS is commonly estimated using logistic regression, and it is used to match patients with

similar distribution of confounders so that difference in outcomes gives unbiased estimate of treatment effect"