Impact of small sample sizes on the internal quality control: statistical uncertainties in the determination of root mean square deviations with respect to the sample mean (RMSD) or to a target value (RMSTD)

Insufficient statistics due to small considered sample sizes can cause distinct problems in internal quality control (IQC) approaches. This issue concerns most of the currently applied IQC concepts either directly (if a root-mean-square-deviation metric is evaluated) or indirectly (if the IQC concept facilitates a standard deviation that was self-evaluated based on a very limited number (n≤30) of control measures). In clinical chemistry a famous example for the latter case is the common implementation of the Westgard Sigma Rules approach. This study quantifies the statistical uncertainties in the determination of root mean square (total) deviations related to the sample mean (RMSD) or to a target value (RMSTD). It is clearly shown that RMS(T)D values based on small data sets with n<50 samples are accompanied by a significant statistical uncertainty that needs to be considered in adequate IQC limit definitions. Two mathematical models are derived to reliably estimate an optimal adaptation function to adjust IQC limits to short charts of control measures. This article provides the theoretical background for the novel IQC method “Statistical Monitoring by Adaptive RMSTD Tests” (SMART) intended to monitor limited available numbers of recent control measures (usually n<20). The study also addresses a general problem in specificity of an IQC resulting from too small sample sizes during the evaluation period of the applied in-control standard deviation.