  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.
