Using the variance function to estimate limit of blank, limit of detection and their confidence intervals

Implementing International Organization for Standardization definitions of limit of blank and limit of detection requires precision estimates from specimens devoid of analyte (blank specimens) and also from specimens located close to zero. Calculations are straightforward if errors are constant over the relevant concentration range but estimation of the relationship between variability and concentration (variance function) is necessary in the general case when errors are not constant. This study investigated the efficacy of incorporating the variance function into estimation of limit of blank, limit of detection and their confidence intervals.

Simulated data, designed to encompass the range of properties that would typically be observed in practice, consisted of four distinct relationships between variance and concentration, in combination with large and small variances and three concentration ranges. Four methods of estimating limit of blank were evaluated together with the accuracy of variance function derived estimates of limit of detection and the accuracy of symmetrical 95% confidence intervals constructed from limit of blank and limit of detection constituent variables.

Most limit of blank estimates and all limit of detection estimates showed systematic negative bias but, provided the data concentration range is not too small, the biases were consistently <1% with confidence interval coverages ranging from 92% to 95%. Estimating limit of blank by extrapolating the variance function to zero lost little in comparison with methods based on blank specimen data.

The variance function provides a convenient and reliable way of analyzing data from experiments evaluating detection capability and, provided certain assumptions are tenable, of estimating limit of blank and limit of detection as part of routine internal quality control.