Standardizing Remeasurement Data into Percentile Ranks Using Baseline Reference for VBP's Patient Satisfaction Measures

Hospital performance data on 8 satisfaction measures in Value-Based Purchasing (VBP) program are standardized to percentile ranks relative to their baseline distribution. The conversion task is more challenging when two data sets are involved. We examine three ways of performing this calculation: (1) Cross Ranking – repeatedly ranking each data point within the entire baseline distribution, (2) Percentile Mapping – mapping the data to the nearest baseline percentile value for corresponding ranks, and (3) Distribution Modeling – modeling the empirical (KDE) baseline distribution with quadratic spline regression as predicted percentile ranks are discretized CDF.

We compare three methods in rank correlation (Kendall-tau), degree of agreement (RMSE and ICC), variation (SD) and computation efficiency. Distribution Modeling is nicely featured by higher correspondence with the raw data and smaller variation and run time but differs more from others in agreement. Cross Ranking is characterized more adversely by lower correspondence but larger variation and run time. Percentile Mapping is as efficient as Distribution Modeling but its statistical properties are closer to Cross Ranking.

Distribution Modeling is the most parsimonious and efficient method. Its statistical properties are also superior but it requires more advanced mathematical knowledge. Cross Ranking can be easily implemented using a simple algorithm by standard IT solution (SQL) at a cost of more computation time and less accuracy when sample size is small and too many tied values exist. Percentile Mapping is an in-between choice which is still efficient for online applications but not too difficult to understand and implement.