Continuous Treatment Effects with Surrogate Outcomes
This work addresses bias in causal inference for real-world applications where outcome data is expensive or difficult to collect, offering a solution for researchers and practitioners in fields like healthcare or social sciences, though it is incremental as it builds on existing surrogate and doubly robust methods.
The paper tackles the problem of estimating continuous treatment effects when primary outcomes are partially missing due to selection bias, by proposing a doubly robust method that incorporates surrogate outcomes to improve estimation efficiency. The result includes establishing asymptotic normality and showing variance improvements compared to methods using only labeled data, with simulations confirming empirical performance.
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.