Using Break Point Regression to Signal Non-Random Variation in Quality Improvement Control Charts

Introduction: Control charts are used for tracking performance in quality improvement (QI). Variation over time is typically analyzed with subjective rules signaling non-random variation in the QI process (Institute of Healthcare Improvement (IHI)). Segmented regression analysis (SRA) is a statistical technique used to detect breakpoints in time series and may offer a more objective approach than the IHI rules to detect non-random cause variation in QI.


Methods: We used control charts with monthly recordings from 31,924 cases in 7 U.S. PICUs participating in a QI collaboration led by VPS, LLC. Jan-22 to Dec-23 was used as the collaborative baseline and Jan-24 to Dec-24 as the intervention period. The intervention involved regional QI bundles practiced by the PICUs. According to U.S. Census, 4 PICUs were located in the South; 2 in the Midwest; 1 in the West. Control charts for: mean (M) and median (Md) medical length of stay (MLOS), mean (M) and median (Md) physical length of stay (PLOS), and their mean (M) and median (Md) differences, called discharge delay (DD), were analyzed via SRA to identify breakpoints in the control charts for geographic regions across the U.S.


Results: Among regions, the shortest baseline M and Md MLOS(days) was 3.3(SD=10.2) and 1.1(IQR=0.7-2.4) for MidWest; the shortest M and Md PLOS(days): 3.8(10.2) and 1.6(0.9-3.5) for MidWest; the shortest M and Md DD(hours): 4.2(8.7) and 2.1(1.2-4.0) for South. For the Intervention by regions, West had the shortest values of M and Md MLOS: 3.4(8.3) and 1.3(0.9-2.8); PLOS: 3.5(8.3) and 1.4(0.9-2.9); and DD: 2.2(2.2) and 1.7(0.9-2.8). ANOVA Bonferroni corrected estimation showed p-values>0.05 for baseline and intervention. SRA predicted breakpoints for M MLOS on Aug-24 which matched IHI rules, for Md MLOS SRA predicted May-24 and IHI was Jul-24. For M PLOS, SRA predicted breakpoints on Jul-24 and IHI was Aug-24; for Md PLOS both SRA and IHI coincided on Jul-24. For M DD SRA predicted Jul-24, and IHI showed non-random variation after Jul-24.


Conclusions: 1) No statistically significant differences were detected among geographic regions. 2) SRA matched the IHI rules for mean (M) MLOS, median (Md) PLOS, and got close for other measures. 3) This approach provides a potential alternative to detect non-random variation in QI analyses.