Table 1 Standardized differences

Baseline groups comparability for each covariate can be assessed with the standardized difference [19]. For a continuous covariates X, the standardized difference SD is:

\(\label {diff_stand} \text {SD}=\frac {100 \times \left |\bar {x}_{1}-\bar {x}_{0}\right |}{\sqrt {\frac {{s_{0}^{2}}+{s_{1}^{2}}}{2}}}, \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad (1) \)

where \(\bar {x}_{0}\) and \(\bar {x}_{1}\) are X means in control and intervention arm, respectively, and \({s^{2}_{0}}\) and \({s^{2}_{1}}\) the corresponding variance estimates. For a binary covariate, the SD is expressed as follows:

\(\label {diff_stand_bin} \text {SD}=\frac {100 \times \left |\hat {P}_{1}-\hat {P}_{0}\right |}{\sqrt {\frac {\hat {P}_{0} (1-\hat {P}_{0})+\hat {P}_{1}(1-\hat {P}_{1})}{2}}},\qquad \qquad \qquad \qquad \qquad \qquad \qquad \,\,\,(2) \)

where \(\hat {P}_{0}\) and \(\hat {P}_{1}\) are the observed rates for the covariate in control and intervention arm, respectively. The strength of SD as compared to statistical tests is that this measure does not depend on the sample size nor on the measurement scale [50]. Usually, covariates with a SD exceeding 10 % are considered to be unbalanced [41]. However, for binary covariates, a SD of 10 % can sometimes be negligible [51].