Variance functions, detectability and bias: a re-evaluation

Background A recent study used simulated internal quality control data (4 specimens × 40 replicates) to investigate the use of variance functions in estimating limit of blank and limit of detection, as per ISO definitions. Small systematic negative biases were found (typically <1%), but subsequent investigation has shown that these estimates had unacceptably large uncertainties because of an inadequate simulation size. Methods The previous data generation and variance function estimations were repeated 25 times using a different random number generator seed on each occasion. The study was further extended by increasing data quantities 100-fold and by reducing the number of replicates per specimen (40 through 20, 10, 5 and 2). Results The previously reported negative biases were shown to be an artefact, and this was confirmed by simulations using 100-fold more data. Biases were <|0.1%| throughout with replication ≥20, but positive biases were found at lower replication; up to + 1.23% in the case of duplicates and large variances (e.g. some immunoassays) and up to + 0.2% in the case of duplicates and small variances. Conclusions The variance function provides essentially unbiased estimates of limit of blank and limit of detection at data replication ≥20 (bias: <1 part in 1000) and minimal biases at lower replication when measurement errors are small.