Definition and evaluation of the monotonicity condition for preference-based instruments.

Comparative effectiveness research frequently uses instrumental variable methods to estimate causal effects.1–3 Such methods require investigators to propose a variable (the “instrument”) that meets the three instrumental conditions: it is associated with treatment, it causes the outcome only through treatment, and its effect on the outcome is not confounded. Commonly proposed instruments are based on facility or physician prescribing preferences,1,2 e.g., a physician’s preference for Treatment A over Treatment B. Even if preference met the instrumental conditions, an additional condition is necessary to identify a causal effect. Most instrumental variable applications assume the additional condition of monotonicity.3,4 The monotonicity assumption implies there are no “defiers”, i.e., no patients who would be prescribed Treatment A when seen by a physician who usually prefers B and would be prescribed Treatment B when seen by a physician who usually prefers A (a rigorous and more general definition is provided below). Under this assumption, instrumental variable methods can be used to identify the average causal effect in the subset of patients who would be prescribed the treatment preferred by any treating physician, i.e., the “compliers”. Monotonicity generally cannot be verified because we cannot observe what would have happened had the same patient been treated by another physician. Monotonicity might be reasonably assumed if patient characteristics naturally collapsed into a single dimension related to treatment decisions (e.g., a propensity score), and clinicians had different cut points along this continuum for deciding when to prescribe which treatment. However, given the complexity of information physicians integrate into their prescribing decisions, preferences are unlikely to be so cleanly ordered. As a simplified example, consider a physician who generally prefers Treatment A, but prescribes Treatment B for more physically active patients (e.g., because Treatment A is associated with risk of motor-skill impairment), and another physician who generally prefers Treatment B, but makes exceptions for patients with a family history of diabetes (e.g., because a new study suggests such patients might respond better to Treatment A). Any physically active patient with a family history of diabetes who could potentially have seen either of these providers would “defy” both preferences and thus violate the monotonicity assumption, even conditional on covariates other than physical activity and family history. Despite many opportunities for monotonicity violations, the possible bias introduced from such violations in instrumental variable analyses has not been previously explored. Moreover, the meaning of monotonicity itself is unclear in realistic applications of instrumental variable analyses with preference-based instruments, something rarely discussed in the literature. Here we (1) define monotonicity and the interpretation of instrumental variable estimates in the context of preference-based instruments and a dichotomous prescribing decision (e.g., Treatment A vs. B), (2) describe a novel study design to assess deviations from monotonicity empirically by surveying physicians about their prescribing preferences and the treatment decisions they would make for a set of hypothetical patients, and (3) implement a pilot study to demonstrate the feasibility of our design to detect monotonicity violations when studying the effects of atypical versus conventional antipsychotic medication on risk of death in the elderly.