Assessment of the E-value in the presence of bias amplification: a simulation study

The E-value, a measure that has received recent attention in the comparative effectiveness literature, reports the minimum strength of association between an unmeasured confounder and the treatment and outcome that would explain away the estimated treatment effect. This study contributes to the literature on the applications and interpretations of E-values by examining how the E-value is impacted by data with varying levels of association of unobserved covariates with the treatment and outcome measure when covariate adjustment is applied. We calculate the E-value after using regression and propensity score methods (PSMs) to adjust for differences in observed covariates. Propensity score methods are a common observational research method used to balance observed covariates between treatment groups. In practice, researchers may assume propensity score methods that balance treatment groups across observed characteristics will extend to balance of unobserved characteristics. However, that assumption is not testable and has been shown to not hold in realistic data settings. We assess the E-value when covariate adjustment affects the imbalance in unobserved covariates.

Our study uses Monte Carlo simulations to evaluate the impact of unobserved confounders on the treatment effect estimates and to evaluate the performance of the E-Value sensitivity test with the application of regression and propensity score methods under varying levels of unobserved confounding. Specifically, we compare observed and unobserved confounder balance, odds ratios of treatment vs. control, and E-Value sensitivity test statistics from generalized linear model (GLM) regression models, inverse-probability weighted models, and propensity score matching models, over correlations of increasing strength between observed and unobserved confounders.

We confirm previous findings that propensity score methods - matching or weighting - may increase the imbalance in unobserved confounders. The magnitude of the effect depends on the strength of correlation between the confounder, treatment, and outcomes. We find that E-values calculated after applying propensity score methods tend to be larger when unobserved confounders result in more biased treatment effect estimates.

The E-Value may misrepresent the size of the unobserved effect needed to change the magnitude of the association between treatment and outcome when propensity score methods are used. Thus, caution is warranted when interpreting the E-Value in the context of propensity score methods.