Outlier Detection for Healthcare Quality Monitoring ‐ A Comparison of Four Approaches to Over-Dispersed Proportions

Outlier detection among over-dispersed proportions is important in healthcare quality monitoring. We had previously introduced control limits for double-square-root chart on the basis of prediction intervals from regression-through-origin and compared our approach to common outlier detection tests. In this study, we develop our approach further by adjusting the confidence level (in the spirit of Chauvenet's criterion and Bayesian thinking) and transforming the chart into an asymmetric funnel plot. We compare it to Laney's approach (p'-chart adapted for cross-sectional data), Spiegelhalter's approach (funnel plots based on multiplicative or additive regression models) and Carling's median rule. Comparisons are performed on simulated and real data. The simulations comprise ‘small’ (<0.2; highly right-skewed) and ‘large’ (>0.5; symmetrically distributed) proportions, drawn in samples of size 10–100 from lognormal distribution either without outliers or with one outlier added. The real data comprise hospital readmissions from the UK (used by Laney and Spiegelhalter) and business indicators of healthcare quality for Slovenian hospitals. In the simulations, Spiegelhalter's approach tended to yield very high false alarm rates, except the multiplicative version in very small samples. Laney's approach produced fewest false alarms but could not detect the outlier in very small samples among small proportions, and regardless of sample size among large proportions. Median rule performed similarly. Our approach performed the best overall, although it is slightly less liberal than median rule for small proportions, it appears to be the only generally useful approach for large proportions.