Toward a clearer portrayal of confounding bias in instrumental variable applications

Recommendations for reporting instrumental variable analyses often include presenting the balance of covariates across levels of the proposed instrument and levels of the treatment. However, such presentation can be misleading as relatively small imbalances among covariates across levels of the instrument can result in greater bias because of bias amplification. We introduce bias plots and bias component plots as alternative tools for understanding biases in instrumental variable analyses. Using previously published data on proposed preference-based, geography-based, and distance-based instruments, we demonstrate why presenting covariate balance alone can be problematic, and how bias component plots can provide more accurate context for bias from omitting a covariate from an instrumental variable versus non-instrumental variable analysis. These plots can also provide relevant comparisons of different proposed instruments considered in the same data. Adaptable code is provided for creating the plots.