The Surrogate Index: Combining Short-Term Proxies to Estimate Long-Term Treatment Effects More Rapidly and Precisely

A common challenge in estimating the impact of interventions (e.g., job training programs) is that many outcomes of interest (e.g., lifetime earnings) are observed with a long delay. In biomedical settings this is often addressed by using short-term outcomes as so-called “surrogates” for the outcome of interest, e.g., tumor size as a surrogate for mortality in cancer studies. We build on this literature by combining multiple, possibly qualitatively distinct, short-term outcomes (e.g., short-run earnings and employment indicators) systematically into a “surrogate index” that captures the relative importance of the various surrogates. Under the Prentice surrogacy assumption, which requires that the primary outcome is independent of the treatment conditional on the surrogates, we show that the average treatment effect on the surrogate index equals the treatment effect on the long-term outcome. We also relate this to more structural, causal, assumptions. We then characterize the bias that arises from violations of the critical assumptions, and we provide simple methods to validate key assumptions using additional outcomes. We apply our method to analyze the long-term (nine year) impacts of a multi-site job training experiment in California. Rather than waiting a full nine years to directly observe the long-term impact, we show that it is possible to use short-term (the first six quarters) outcomes as surrogates. One could have estimated the program’s long-term impacts on mean employment rates using the employment rates observed in the first six quarters, with a 35% reduction in standard errors.