The Evaluation of Statistical Methods for Estimating the Lower Limit of Detection

Abstract

In estimating a quantitative assay's lower limit of detection (LOD), standard deviation (SD) is the most common measure used to quantify the dispersion of the data, yet this LOD calculation method assumes that the low concentration samples follow a Gaussian distribution, which is not always true in reality. Here, a few LOD estimating methods that are based on different dispersion measures were investigated; each method's performance was evaluated across various distribution scenarios. Nine methods for LOD estimation that use different measures of data dispersion—SD, mean absolute deviation (MD), median absolute deviation, Gini's mean difference (GMD), percentiles (PCT), Algorithm A, S_n, Q_n, and inter-quartile range—were evaluated using both simulations and real-life datasets. LOD estimates calculated using different variability measures were compared to the true LOD value under different scenarios. A method was judged to be good if the method had a relatively stable formula, low bias, confidence interval that had shorter width, and achieved the desired level of frequency in covering the true value of LOD (coverage probability [CP]). First, the nine methods were screened for formula consistency across different distribution scenarios. Methods showing the greatest formula variation were removed from further analysis; the remaining methods were then examined and compared. The GMD-based method had a relatively stable formula and demonstrated the best overall performance with low bias, confidence interval of shorter width, and good CP across all situations. The PCT-based method only performed well if sample size was large. The MD-based method in general had larger bias than the GMD-based estimator. LOD estimates based on SD that assumes Gaussian distribution in all scenarios will often generate poor results. Instead, the GMD-based estimator, a method with a simple formula so is easy to use in practice, demonstrated robust performance across varying situations.