  In biomedical studies, estimating drug effects on chronic diseases requires a
long follow-up period, which is difficult to meet in randomized clinical trials
(RCTs). The use of a short-term surrogate to replace the long-term outcome for
assessing the drug effect relies on stringent assumptions that empirical
studies often fail to satisfy. Motivated by a kidney disease study, we
investigate the drug effects on long-term outcomes by combining an RCT without
observation of long-term outcome and an observational study in which the
long-term outcome is observed but unmeasured confounding may exist. Under a
mean exchangeability assumption weaker than the previous literature, we
identify the average treatment effects in the RCT and derive the associated
efficient influence function and semiparametric efficiency bound. Furthermore,
we propose a locally efficient doubly robust estimator and an inverse
probability weighted (IPW) estimator. The former attains the semiparametric
efficiency bound if all the working models are correctly specified. The latter
has a simpler form and requires much fewer model specifications. The IPW
estimator using estimated propensity scores is more efficient than that using
true propensity scores and achieves the semiparametric efficient bound in the
case of discrete covariates and surrogates with finite support. Both estimators
are shown to be consistent and asymptotically normally distributed. Extensive
simulations are conducted to evaluate the finite-sample performance of the
proposed estimators. We apply the proposed methods to estimate the efficacy of
oral hydroxychloroquine on renal failure in a real-world data analysis.
