On the Estimation of POD and LOD of Qualitative Microbiological Assays from a Multi-Laboratory Validation Study

Jarvis et al. in 2019 (J. AOAC Int. 102: 1617-1623) estimated the mean laboratory effect (µ), standard deviation of laboratory effects (σ), probability of detection (POD), and level of detection (LOD) from a multi-laboratory validation study of qualitative microbiological assays using a random intercept complementary log-log model. Their approach estimated σ based on a Laplace approximation to the likelihood function of the model, but estimated µ from a fixed effectmodel due to a limitation in the MS Excel spreadsheet which was used by the authors to develop a calculation tool.

We compared the estimates of µ and σ from three approaches (the Laplace approximation that estimates µ and σ simultaneously from the random intercept model, adaptive Gauss-Hermite quadrature (AGHQ), and the method of Jarvis et al.) and introduced an R Shiny app to implement the AGHQ using the widely used "lme4" R package.

We conducted a simulation study to compare the accuracy of the estimates of µ and σ from the three approaches and compared the estimates of µ, σ, LOD, etc. between the R Shiny app and the spreadsheet calculation tool developed by Jarvis et al. for an example dataset.

Our simulation study shows that, while the three approaches produce similar estimates of σ, the AGHQ has generally the best performance for estimating µ (and hence mean POD and LOD). The differences in the estimates between the R Shiny app and the spreadsheet were demonstrated using the example dataset.

The AGHQ is the best method for estimating µ, POD, and LOD.

The user-friendly R Shiny app provides a better alternative to the spreadsheet.