Multiply robust estimation of causal effects using linked data

Unmeasured confounding presents a common challenge in observational studies, potentially making standard causal parameters unidentifiable without additional assumptions. Given the increasing availability of diverse data sources, exploiting data linkage offers a potential solution to mitigate unmeasured confounding within a primary study of interest. However, this approach often introduces selection bias, as data linkage is feasible only for a subset of the study population. To address such a concern, this paper explores three nonparametric identification strategies assuming that a unit's inclusion in the linked cohort is determined solely by the observed confounders, while acknowledging that the ignorability assumption may depend on some partially unobserved covariates. The existence of multiple identification strategies motivates the development of estimators that effectively capture distinct components of the observed data distribution. Appropriately combining these estimators yields triply robust estimators for the average treatment effect. These estimators remain consistent if at least one of the three distinct parts of the observed data law is correct. Moreover, they are locally efficient if all the models are correctly specified. The proposed estimators are evaluated using simulation studies and real data analysis.