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Estimating the long-term effects of treatments is of interest in many fields.A common challenge in estimating such treatment effects is that long-termoutcomes are unobserved in the time frame needed to make policy decisions. Oneapproach to overcome this missing data problem is to analyze treatments effectson an intermediate outcome, often called a statistical surrogate, if itsatisfies the condition that treatment and outcome are independent conditionalon the statistical surrogate. The validity of the surrogacy condition is oftencontroversial. Here we exploit that fact that in modern datasets, researchersoften observe a large number, possibly hundreds or thousands, of intermediateoutcomes, thought to lie on or close to the causal chain between the treatmentand the long-term outcome of interest. Even if none of the individual proxiessatisfies the statistical surrogacy criterion by itself, using multiple proxiescan be useful in causal inference. We focus primarily on a setting with twosamples, an experimental sample containing data about the treatment indicatorand the surrogates and an observational sample containing information about thesurrogates and the primary outcome. We state assumptions under which theaverage treatment effect be identified and estimated with a high-dimensionalvector of proxies that collectively satisfy the surrogacy assumption, andderive the bias from violations of the surrogacy assumption, and show that evenif the primary outcome is also observed in the experimental sample, there isstill information to be gained from using surrogates.

Estimating Treatment Effects using Multiple Surrogates: The Role of the Surrogate Score and the Surrogate Index