Research Article

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

Table 2

Effect size estimates, precision, and E-values in observational pharmaceutical studies.

DiseaseStatisticsMedian (Q1, Q3)Logged: median (Q1, Q3)

All (N = 368)Relative effect size1.89 (1.41, 2.95)0.64 (0.35, 1.08)
Standard error0.63 (0.22, 2.28)0.27 (0.13, 0.49)
E-value3.19 (2.18, 5.35)1.16 (0.78, 1.68)
E-value for the 95% CI lower bound1.77 (1.31, 2.71)0.57 (0.27, 1.00)

Infections and infestations (N = 80)Relative effect size2.18 (1.64, 2.88)0.78 (0.50, 1.06)
Standard error1.31 (0.44, 3.86)0.38 (0.21, 0.61)
E-value3.78 (2.67, 5.20)1.33 (0.98, 1.65)
E-value for the 95% CI lower bound1.69 (1.28, 2.68)0.52 (0.25, 0.98)

Cardiac disorders (N = 51)Relative effect size1.54 (1.30, 1.93)0.43 (0.27, 0.66)
Standard error0.31 (0.14, 0.59)0.15 (0.10, 0.26)
E-value2.45 (1.93, 3.27)0.90 (0.66, 1.18)
E-value for the 95% CI lower bound1.54 (1.22, 2.08)0.43 (0.20, 0.73)

Neoplasms benign, malignant and unspecified (incl cysts and polyps) (N = 26)Relative effect size1.85 (1.58, 2.59)0.61 (0.46, 0.95)
Standard error0.59 (0.30, 2.19)0.29 (0.15, 0.49)
E-value3.10 (2.54, 4.63)1.13 (0.93, 1.53)
E-value for the 95% CI lower bound2.06 (1.56, 3.25)0.72 (0.45, 1.17)

CI, confidence interval on the effect size. Note that, for consistency, we inverted effect size was necessary so that all effects were greater than 1. Here, for logged standard error (LSE), we use the equation LSE = (Ln(UB)-Ln(LB))/3.92, where UB and LB are upper and lower bounds of 95% CI.