Rescaling

When indicators have different units of scale, rescaling on a common scale is required to allow comparison and aggregation. Different methods may produce different CM [19, 35] and it is not clear which method is favorable. Following Shwartz et al., we compare the two most widely used approaches for healthcare CM, i.e., z-score standardization and min–max normalization [19]. A priori we use z-score standardization (Model 1), as it preserves the relative differences, and extreme values and outliers don’t distort the mean but are recognized as exceptional performance. The z-score standardization transforms all individual measures on a dimensionless scale with mean = 0 and standard deviation (SD) = 1. Z-scores express how many SD an individual’s outcome is above or below the average of the population and is calculated as:

where x is the observed PRO of an individuum, μ is the PRO-mean, and σ is the SD. See Appendix II for an exemplary rescaling calculation.