Robust Inference of Individualized Treatment Effect in Mendelian Randomization
Mendelian randomization (MR), leveraging genetic variants as instrumental variables (IVs), is widely used to draw causal conclusions in the presence of unmeasured confounding, but most MR analyses focus on average treatment effects and rely on strong assumptions. For precision medicine, the primary target is instead the individualized treatment effect (ITE); yet in MR, such effects are not point-identified under core IV assumptions, and valid inference for identifiable bounds of the ITEs is particularly challenging. In this work, we propose a robust partial identification inference framework for the identifiable bounds of the ITEs under MR allowing multiple IVs. Under minimal causal assumptions, we derive a sharp inference procedure for the bounds of ITE by adopting a multiplier bootstrap procedure with data-adaptive bootstrap distribution shifting and heterogeneous variance adjustment. In theory, we prove that the proposed method achieves nominal coverage and asymptotic sharpness. Further, we extend the procedure to tolerate possible invalid IVs under a minimal proportion rule assumption by aggregating over plausible IV subsets while preserving coverage. Simulation studies demonstrate that the proposed methods attain nominal coverage and substantially shorter intervals than existing procedures. We illustrate the framework using data from the Alzheimers Disease Neuroimaging Initiative to assess heterogeneous causal effects of TREM2 expression on Alzheimers disease risk across education-defined subgroups.