Assess the Application of the E-Value in the Unmeasured Confounder Evaluation of Observational Pharmaceutical Studies

Public health is very important in big cities, and data analysis on public health studies is always a demanding issue that determines the study effectiveness. E-value was proposed as a standard sensitivity analysis tool to assess unmeasured confounders in observational studies, but its value is doubted. To evaluate the usefulness of E-value, in this paper, we collected 368 observational studies on drug effectiveness evaluation published from 1998 to September 2019 (out of 3426 searched studies) and evaluated the features of E-value. We selected the effects of primary outcomes or the largest effects in terms of hazard ratio, risk ratio, or odds ratio. Effects were transformed into estimated effect sizes following a standard E-value computation. In all 368 studies, the disease with the highest percentage was infections and infestations, at 21.7% (80/368). Our results showed that the median relative effect size was 1.89 (Q1-Q3: 1.41–2.95), and the corresponding median E-value was 3.19 with 95% confidence interval lower bound 1.77. Smaller studies yielded larger E-values for the effect size estimate and the relationship was considerably attenuated when considering the E-value for the lower bound of 95% confidence interval on the effect size. Notably, E-values have a monotonic, almost linear relationship with effect estimates. We found that E-value may cause misimpressions on the unmeasured confounder, and the same E-value does not reflect the varying nature of the unmeasured confounders in different studies, and there lacks a guidance on how E-value can be deemed as small or large, all of which limits the capability of E-value as a standard sensitivity analysis tool in real applications.