Effects of adjusting for instrumental variables on bias and precision of effect estimates

Abstract

Recent theoretical studies have shown that conditioning on an instrumental variable (IV), a variable that is associated with exposure but not associated with outcome except through exposure, can increase both bias and variance of exposure effect estimates. Although these findings have obvious implications in cases of known IVs, their meaning remains unclear in the more common scenario where investigators are uncertain whether a measured covariate meets the criteria for an IV or rather a confounder. The authors present results from two simulation studies designed to provide insight into the problem of conditioning on potential IVs in routine epidemiologic practice. The simulations explored the effects of conditioning on IVs, near-IVs (predictors of exposure that are weakly associated with outcome), and confounders on the bias and variance of a binary exposure effect estimate. The results indicate that effect estimates which are conditional on a perfect IV or near-IV may have larger bias and variance than the unconditional estimate. However, in most scenarios considered, the increases in error due to conditioning were small compared with the total estimation error. In these cases, minimizing unmeasured confounding should be the priority when selecting variables for adjustment, even at the risk of conditioning on IVs.

Figure 1.

Causal diagram showing an unmeasured confounder, U, and an instrumental variable, Z, of the exposure-outcome pair (X, Y).

Figure 2.

Estimated hazard ratios (HRs) for mortality (top) and hip fracture (bottom) in initiators of statin medication versus initiators of glaucoma medication (details in Appendix 2). The adjustment factors used for each estimate, including the potential instrumental variable (IV) glaucoma diagnosis, are shown on the left. The x-axis is presented on the log scale with tick marks unlogged. The approximate expected effects for mortality and hip fracture were hazard ratios of 0.85 and 1.01, respectively (25). Horizontal bars, 95% confidence interval.

Figure 3.

Causal diagram showing the structure of the simulation studies. Depending on parameter values, the measured covariate Z may act as a confounder or as an instrumental variable for the exposure-outcome pair (X, Y).

Figure 4.

Bias (left panels) and standard error (right panels) of risk difference (RD) estimators with and without conditioning on Z. Each point represents one simulation scenario in the additive simulations with γ₁ = 0 (upper sections), γ₁ = 0.06 (middle sections), or γ₁ = 0.24 (lower sections). The symbols identify values of α₂ (○, zero; ▵, 0.06; +, 0.18; ×, 0.33). The solid diagonal line marks equality. Dashed lines mark the threshold for a 10% increase or decrease, and dotted lines mark a 20% increase or decrease.

Figure 5.

Standard error of exposure effect estimators obtained with and without conditioning on Z under a range of study sizes.

Figure 6.

Bias (left panels) and standard error (right panels) of risk ratio (RR) estimators with and without conditioning on Z. Each point represents one simulation scenario in the multiplicative simulations with γ₁ = 1 (upper sections), γ₁ = 1.2 (middle sections), or γ₁ = 1.8 (lower sections). The symbols identify values of α₂ (○, 1.0; ▵, 1.1); +, 1.3; ×, 1.8). The solid diagonal line marks equality. Dashed lines mark the threshold for a 10% increase or decrease, and dotted lines mark a 20% increase or decrease.