Instrumental variable methods for causal inference

Abstract

A goal of many health studies is to determine the causal effect of a treatment or intervention on health outcomes. Often, it is not ethically or practically possible to conduct a perfectly randomized experiment, and instead, an observational study must be used. A major challenge to the validity of observational studies is the possibility of unmeasured confounding (i.e., unmeasured ways in which the treatment and control groups differ before treatment administration, which also affect the outcome). Instrumental variables analysis is a method for controlling for unmeasured confounding. This type of analysis requires the measurement of a valid instrumental variable, which is a variable that (i) is independent of the unmeasured confounding; (ii) affects the treatment; and (iii) affects the outcome only indirectly through its effect on the treatment. This tutorial discusses the types of causal effects that can be estimated by instrumental variables analysis; the assumptions needed for instrumental variables analysis to provide valid estimates of causal effects and sensitivity analysis for those assumptions; methods of estimation of causal effects using instrumental variables; and sources of instrumental variables in health studies.

Keywords: comparative effectiveness; confounding; instrumental variables; observational study.

Figure 1

Directed acyclic graph for the relationship between an instrumental variable Z, a treatment D, unmeasured confounders U and an outcome Y.

Figure 2

Causal diagrams for the effect of the sickle cell trait (the IV) and malaria episodes (the treatment) on stunting (the outcome) in African children and African-American children. If the sickle cell trait is a valid IV, then the dashed lines should be absent and the sickle cell trait will have no effect on stunting among African-American children.

Figure 3

Causal diagram explaining the motivation behind the treatment-unaffected outcome test for the validity of an IV. The IV is Z, the treatment is D, the outcome of interest is Y and the treatment unaffected outcome is Y 2.

Figure 4

The two stage least squares estimate for the NICU study using an IV is a weighted average of the average causal effects for subjects who are “compliers at level z” (subjects who would go to a high level NICU if the excess travel time was at most z but otherwise go to a low level NICU), where the weighting depends on the coding of the IV. The figure shows these weights for two IVs, (i) the dichotomized IV of excess travel time ≤ 10 minutes or excess travel time > 10 minutes and (ii) the continuous IV of excess travel time.

Figure 5

Scatterplot smooth estimate of P(D = 1|Z) where D = 1 is attending a high level NICU and Z is excess travel time. The estimate was obtained using the gam function in R. The observed values of excess travel time are shown at the bottom of the plot.