Inferring the Long-Term Causal Effects of Long-Term Treatments from Short-Term Experiments

We study inference on the long-term causal effect of a continual exposure to a novel intervention, which we term a long-term treatment, based on an experiment involving only short-term observations. Key examples include the long-term health effects of regularly-taken medicine or of environmental hazards and the long-term effects on users of changes to an online platform. This stands in contrast to short-term treatments or "shocks," whose long-term effect can reasonably be mediated by short-term observations, enabling the use of surrogate methods. Long-term treatments by definition have direct effects on long-term outcomes via continual exposure so surrogacy cannot reasonably hold. Our approach instead learns long-term temporal dynamics directly from short-term experimental data, assuming that the initial dynamics observed persist but avoiding the need for both surrogacy assumptions and auxiliary data with long-term observations. We connect the problem with offline reinforcement learning, leveraging doubly-robust estimators to estimate long-term causal effects for long-term treatments and construct confidence intervals. Finally, we demonstrate the method in simulated experiments.