Quantitative verification of instrumental variables assumption using balance measures

Background: Instrumental variable (IV) analysis appears to be an attractive method to adjust for confounding in non-randomized studies. One of the underlying assumptions is that the IV is independent of confounders. If this assumption is violated, the IV estimate can be severely biased. Methods:We conducted Monte Carlo simulations to assess the performance of balance measures commonly used in propensity score methods (in particular, the standardized difference) to verify this assumption quantitatively.We simulated cohorts of varying sample sizes, binary IV and exposure, continuous outcome, and several confounders. Different associations among IV, exposure, and confounders were considered and 10,000 replications were used in each scenario. Data were analyzed using the two-stage least square method. The balance of confounders across IV levels was assessed using the standardized difference. Values of the standardized difference that are close to zero indicate a balance of confounders across IV groups. We also estimated the correlation between the standardized difference and bias of the IV estimates. Results: Bias of IV estimates increased with weaker IVs (i.e., weak association between IV and exposure) and increasing values of the standardized difference (i.e. decreasing balance of confounders across IV categories). IV estimates were more biased than those of classical regression estimates with increasing values of the standardized difference, and a weak IV amplified this bias. Conclusions: Balance measures that are commonly used in propensity score methods can be useful tools to quantitatively verify one of the assumptions underlying IV analysis, i.e., that the IV should be independent of confounders. However, these balance measures only quantify the balance of observed confounders and not of unobserved confounders.