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

Background: 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.

Objective: 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.

Methods: 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.

Results: 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.

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

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