Fig. 1

a. Optimize plot. The plot is a graphical display of the balance criteria as a function of the GBM iteration. The graph demonstrates that a favorable balance was achieved with 1000 iterations and that such a balance was worse with a higher number of iterations that, thus were unnecessary. b. Overlap Assessment. The figure presents two sets of box plots of PS distributions. An overlap between the groups is desirable meaning that there are no values of the pretreatment variables that occur only in one of the treatment conditions. However, there are no specific rules for what constitutes sufficient overlap so, in doubtful cases the combination of the overlap plot and the balance table are used. In our model there is a good overlap between the two boxplots. c. Standardized Effect Size plot. It assesses the balance of pretreatment variables before and after weighting. It shows the maximum pairwise ASMDs. The ASMDs cutoff for defining unbalanced variables was 0.20. The light blue line represents pretreatment covariates for which the maximum pairwise ASMD reduced after weighting. The red lines mean the pretreatment covariates for which the maximum pairwise ASMD increased after weighting. A good balance is obtained when, after weighting in the majority of variables the ASMDs are < 0.20 and there is a prevalence of light blue lines. In our model, after weighting the pretreatment variables, the balance showed excellent results with all ASMD values being well below 0.2. d. Quantile-quantile (Q-Q) plot. This plot also assesses the balance of pretreatment variables. In the plot, the Kolmogorov-Smirnov p-value is plotted against the rank of p-value for pretreatment variables. Along a 45-degree fitting line, open symbols represent weighted covariates and solid symbols represent unweighted covariates. A good balance is obtained when open symbols lie close, below or above, the 45-degree line. After weighting, in our model, all covariates were well above the reference line