Biased Encouragements and Heterogeneous Effects in an Instrumental Variable Study of Emergency General Surgical Outcomes

We investigate the efficacy of surgical versus nonsurgical management for two gastrointestinal conditions, colitis and diverticulitis, using observational data. We deploy an instrumental variable design with surgeons' tendencies to operate as an instrument. Assuming instrument validity, we find that nonsurgical alternatives can reduce both hospital length of stay and the risk of complications, with estimated effects larger for septic patients than for nonseptic patients. The validity of our instrument is plausible but not ironclad, necessitating a sensitivity analysis. Existing sensitivity analyses for IV designs assume effect homogeneity, unlikely to hold here because of patient-specific physiology. We develop a new sensitivity analysis that accommodates arbitrary effect heterogeneity and exploits components explainable by observed features. We find that the results for nonseptic patients prove more robust to hidden bias despite having smaller estimated effects. For nonseptic patients, two individuals with identical observed characteristics would have to differ in their odds of assignment to a high tendency to operate surgeon by a factor of 2.34 to overturn our finding of a benefit for nonsurgical management in reducing length of stay. For septic patients, this value is only 1.64. Simulations illustrate that this phenomenon may be explained by differences in within-group heterogeneity. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.