Is it reasonable to use simultaneously the disease risk score and the propensity score? I wonder whether the disease risk score and the propensity score can be simultaneously used and whether they have been ever been used together in the past.
 A: By your use of the term disease risk score I assume you have carefully fitted a regression model on the same dataset you computed the propensity score on.  As has been documented in the literature, the use of a disease risk score, pretending that its internal coefficients are constants and weren't estimated, results in overly confident analyses, i.e., underestimation of standard errors.  If you want to adjust for covariates, adjust for individual covariates.
But adjusting for the logit of propensity score as an additional covariate, which in my view is an excellent approach if you have already accounted for the overlap region, also requires adjustment for at least the key outcome predictors.  This adjustment is not made using disease risk scores but using individual pre-specified predictors thought by experts to be the most important ones.
Keep in mind that propensity scores are only necessary if the total number of covariates is too large to fit them reliably against the outcome using standard regression models.
A semi-detailed propensity score analysis strategy is in Chapter 17 of BBR.
A: Yes, in Leacy and Stuart's (2014) paper, "On the joint use of propensity and prognostic scores in estimation of the Average Treatment Effect on the Treated: A simulation study"
The authors recommend combining prognostic scores and propensity scores in effect estimation.
