We investigate the efficacy of surgical versus non-surgical 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 non-surgical alternatives can reduce both hospital length of stay and the risk of complications, with estimated effects larger for septic patients than for non-septic 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 non-septic patients prove more robust to hidden bias despite having smaller estimated effects. For non-septic 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 non-surgical 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.
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