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.
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asked May 28, 2017 at 7:39
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1$\begingroup$ See Stuart, Lee, & Leacy (2013), page S85 for a brief discussion about this. In short, yes. Disease risk scores, aka "prognostic scores", can be used to assess balance after propensity score preprocessing. $\endgroup$– NoahCommented May 28, 2017 at 23:09
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2 Answers
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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.
answered May 28, 2017 at 12:21
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2$\begingroup$ I think by disease risk score, OP means "prognostic score", which is computed by fitting an outcome regression model on just the control data and generating predicted values for the whole dataset based on this model. $\endgroup$– NoahCommented May 28, 2017 at 23:08
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1$\begingroup$ I had assumed it was fitting the outcome using the whole dataset. Fitting on just the controls is worse than I described above, because any overfitting (e.g., fitting noise) will fit idiosyncrasies in the controls, making the comparison with the exposure group more biased. $\endgroup$ Commented May 29, 2017 at 12:11
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$\begingroup$ Depends how you use it. In the Stuart et al paper I posted in the comments of the question, prognostic scores were valuable even when misspecified. $\endgroup$– NoahCommented May 29, 2017 at 15:46
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$\begingroup$ Whether misspecified or not, the standard error of the exposure effect will be too low and I suspect bias in the estimate itself. $\endgroup$ Commented May 29, 2017 at 20:49
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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.
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1$\begingroup$ The appropriate approach is to pre-specify the major prognostic factors, and adjust for them as covariates in addition (if needed) to adjusting for logit propensity. $\endgroup$ Commented May 29, 2017 at 20:49