  Shortcomings of randomized clinical trials are pronounced in urgent health
crises, when rapid identification of effective treatments is critical.
Leveraging short-term surrogates in real-world data (RWD) can guide
policymakers evaluating new treatments. In this paper, we develop novel
estimators for the proportion of treatment effect (PTE) on the true outcome
explained by a surrogate in RWD settings. We propose inverse probability
weighted and doubly robust (DR) estimators of an optimal transformation of the
surrogate and PTE by semi-nonparametrically modeling the relationship between
the true outcome and surrogate given baseline covariates. We show that our
estimators are consistent and asymptotically normal, and the DR estimator is
consistent when either the propensity score model or outcome regression model
is correctly specified. We compare our proposed estimators to existing
estimators and show a reduction in bias and gains in efficiency through
simulations. We illustrate the utility of our method in obtaining an
interpretable PTE by conducting a cross-trial comparison of two biologic
therapies for ulcerative colitis.
