The diagnostic accuracy of quality control rules

Internal quality control in clinical chemistry laboratories are based on analyzing samples of stable control materials among the patient samples. The control results are interpreted by using quality control rules that usually are designed to detect systematic errors. The best rules have a high probability of error detection (P_ed), i.e. to detect the maximal allowable (critical) systematic error and a low probability of false rejection (P_fr, false alarm). In this work we show that quality control rules can be represented by points on a ROC curve which appears when P_ed is plotted against P_fr and only the control limit is varied. Further, we introduce a new method for choosing the optimal control limit, analogous to choosing the optimal operating point on the ROC curve of a diagnostic test. This decision needs knowledge of the pretest probability of a critical systematic error, the benefit of detecting it when it occurs and the cost of false alarm. The ROC curve analysis showed that if rules based on N = 2 are used, mean rules outperform Westgard rules because the ROC curve of the mean rules was lying above the ROC curves of the Westgard rules. A mean rule also had a lower maximum expected increase in the number of unacceptable patient results reported during the presence of an out-of-control error condition (Max E(N_UF)) than comparable Westgard rules.