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Quoting David Hajage and Finbarr Leacy, respectively:

"Introduced by Hansen in 2008, the prognostic score (PGS) has been presented as ‘the prognostic analogue of the propensity score’ (PPS). PPS‐based methods are intended to estimate marginal effects. Most previous studies evaluated the performance of existing PGS‐based methods (adjustment, stratification and matching using the PGS) in situations in which the theoretical conditional and marginal effects are equal (i.e., collapsible situations)."

"This type of experimental control, Hansen notes, seeks to standardize the outcome generation process, inducing comparability between the observed covariate distributions of trial participants with differing potential outcomes by minimizing or eliminating associations between the covariates and trial outcomes."

My questions are:

  1. How can PGS be calculated in R in the context of a binomial outcome and a treatment that is: (a) continuous, (b) multinomial, and (c) binary?

  2. How could the estimated treatment effect for each of these types of treatment be interpreted?

  3. What are the tools available in R to perform the estimation and balance diagnostic of the estimated PGS for each case?
  4. Would it be conceivable to use the PGS to generate IPW (like IPTW based on PPS)?

Thank you in advance.

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Check out my R package, cobalt, which allows users to assess balance on matched, weighted, or stratified groups for binary, multi-category, and continuous treatments. In the main vignette for the package, there are instructions for how to estimate and assess balance on the PGS for binary treatments. Typically, PGS balance assessment is used when the estimand is the ATT.

For binary treatments, subset the control group data, fit (i.e., train) a model for the outcome conditional on the covariates (using, e.g., glm()), then generate predictions using the model for the whole sample (using predict()). Then balance can be assessed on the PGS as if it were any other covariate. Small standardized mean differences are desirable.

The use of the PGS for balance assessment has not been described for multi-category and continuous treatments. Conceivably for multi-category treatments, you could choose one group as above and use it to train a model that is used to compute the PGS for the whole sample.

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