  In many real-world causal inference applications, the primary outcomes
(labels) are often partially missing, especially if they are expensive or
difficult to collect. If the missingness depends on covariates (i.e.,
missingness is not completely at random), analyses based on fully observed
samples alone may be biased. Incorporating surrogates, which are fully observed
post-treatment variables related to the primary outcome, can improve estimation
in this case. In this paper, we study the role of surrogates in estimating
continuous treatment effects and propose a doubly robust method to efficiently
incorporate surrogates in the analysis, which uses both labeled and unlabeled
data and does not suffer from the above selection bias problem. Importantly, we
establish the asymptotic normality of the proposed estimator and show possible
improvements on the variance compared with methods that solely use labeled
data. Extensive simulations show our methods enjoy appealing empirical
performance.
