Doubly robust machine learning-based estimation methods for instrumental variables with an application to surgical care for cholecystitis

Comparative effectiveness research frequently employs the instrumental variable design since randomized trials can be infeasible. In this study, we investigate treatments for emergency cholecystitis-inflammation of the gallbladder. A standard treatment for cholecystitis is surgical removal of the gallbladder, while alternative non-surgical treatments include managed care and pharmaceutical options. We use an instrument for operative care: the surgeon's tendency to operate. Standard instrumental variable estimation methods, however, often rely on parametric models that are prone to bias from model misspecification. Thus, we outline instrumental variable methods based on the doubly robust machine learning framework. These methods enable us to employ machine learning techniques, delivering consistent estimates, and permitting valid inference on various estimands. We use these methods to estimate the primary target estimand in an instrumental variable design. Additionally, we expand these methods to develop new estimators for heterogeneous causal effects, profiling principal strata, and sensitivity analyses for a key instrumental variable assumption. We conduct a simulation to identify scenarios where more flexible estimation methods outperform standard methods. Our findings indicate that operative care is generally more effective for cholecystitis patients, although the benefits of surgery can be less pronounced for key patient subgroups.