Instrumental Variable Estimation with a Stochastic Monotonicity Assumption

Abstract

The instrumental variables (IV) method is a method for making causal inferences about the effect of a treatment based on an observational study in which there are unmeasured confounding variables. The method requires a valid IV, a variable that is independent of the unmeasured confounding variables and is associated with the treatment but which has no effect on the outcome beyond its effect on the treatment. An additional assumption that is often made for the IV method is deterministic monotonicity, which is an assumption that for each subject, the level of the treatment that a subject would take if given a level of the IV is a monotonic increasing function of the level of the IV. Under deterministic monotonicity, the IV method identifies the average treatment effect for the compliers (those subject who would take the treatment if encouraged to do so by the IV and not take the treatment if not encouraged). However, deterministic monotonicity is sometimes not realistic. We introduce a stochastic monotonicity condition which relaxes deterministic monotonicity in that it does not require that a monotonic increasing relationship hold within subjects between the levels of the IV and the level of the treatment that the subject would take if given a level of the IV, but only that a monotonic increasing relationship hold across subjects between the IV and the treatment in a certain manner. We show that under stochastic monotonicity, the IV method identifies a weighted average of treatment effects with greater weight on subgroups of subjects on whom the IV has a stronger effect. We provide bounds on the global average treatment effect under stochastic monotonicity and a sensitivity analysis for violations of the stochastic monotonicity assumption. We apply the methods of IV inference under stochastic monotonicity that we develop to a study of the effect of premature babies being delivered in a high volume, high technology neonatal intensive care unit (NICU) vs. a lower level unit.

Noncompliance and Missing Data in Health Economic Evaluation

“…costs). Similarly, sensitivity analyses to the monotonicity assumption have been developed in the wider methodological literature (Baiocchi et al, 2014;Small et al, 2017), but they warrant careful consideration in the health economics context.…”

Instrumental variable analysis as a complementary analysis in studies of adverse effects: venous thromboembolism and second‐generation versus third‐generation oral contraceptives

“…a weighted average of the effects of type of oral contraceptive on risk of venous thromboembolism in these relevant subgroups, where the weights are the strength of the instrumental variable within these subgroups) . The interpretation of the estimate (but not the analysis or estimate itself) differs from the interpretation under a different point‐identifying assumption, such as deterministic or global monotonicity (that if physician A would prescribe a third‐generation OC to a certain patient, then all physicians with a preference for third‐generation OCs greater than or equal to the preference of physician A should also prescribe a third‐generation oral contraceptive to that patient) . For an explanation of the interpretation of the estimates under these different assumptions and for a discussion of the plausibility of these different assumptions, we refer to the literature …”

“…[15][16][17] For an explanation of the interpretation of the estimates under these different assumptions and for a discussion of the plausibility of these different assumptions, we refer to the literature. 15,16 Statistical analyses All statistical analyses were performed using Stata 10.1.…”

Instrumental variables: Don't throw the baby out with the bathwater

“…See Keele et al for an example of describing the complier population in a clinical investigation. Second, investigators can use the IV estimate to place bounds on the average treatment effect for the study patient population . When the bounds on the average treatment effect clearly show benefits from treatment, concerns about whether a specific patient is marginal are less relevant since treatment should be beneficial on average.…”