A Novel Secondary-Outcome Approach to Estimating Primary Causal Effects with Unmeasured Confounders.

Unmeasured confounding remains a fundamental challenge permeating contemporary causal inference, substantially impeding the valid estimation of treatment effects. A rigorous identification strategy is presented for estimating average causal effects with unmeasured confounding by exploiting the information contained in primary and secondary outcomes. In contrast to existing literature, our approach is intended to construct the proxy confounder for inverse probability weighting-type estimation. Formal identification results and the asymptotic distribution theory for the proposed estimator are established. Through extensive simulation studies, it is demonstrated that the method achieves marked reduction in confounding bias and offers refinements to causal effect estimation. In practical applications, by integrating secondary outcomes that characterize cognitive aspects, we successfully supplemented information not captured by the covariates, enabling us to draw significant inferences regarding the effects of maternal delivery mode on child's test scores. This approach provides a promising methodology for data sets with multiple secondary outcomes.