Optimal Spiking Experiment for Noninferiority of Qualitative Microbiological Methods on Accuracy With Multiple Microorganisms

Abstract

The European and United States Pharmacopoeia demand a noninferiority study on the detection of microorganisms when an alternate qualitative microbiological method is intended to replace the compendial microbiological method. However, without imposing any modeling assumptions or constraints, noninferiority studies require large numbers of test samples for a proposed noninferiority criterion of 0.7 or higher for each microorganism. When we can assume that the accuracy of the alternate method with respect to the compendial method is homogeneous across microorganisms, a joint statistical analysis of the data from all microorganisms can be used to help reduce the sample size dramatically. For this situation, we provide a test statistic for noninferiority, an optimal spiking experiment, and a sample size calculation approach under only mild modeling assumptions of the microorganism-specific detection proportions. We illustrate our approach on a real dataset and demonstrate good performance of our method using simulation studies.

Keywords:

• Limit of detection
• Maximum likelihood
• Microbiological validation
• Sensitivity
• Specificity

Notes

1 This equation actually has a solution whenever the observed positive rates ${\overline{Y}}_{21}$ and ${\overline{Y}}_{22}$ are not equal to the same boundary value as we will see for the second equation in (A.1) in Scenarios 2 to 5. Thus, one of the positive rates is allowed to be equal to the boundary, as long as the other is not. However, characteristics of the solution depend on whether or not the positive rates are at a boundary zero or not.

Additional information

Funding

This work is part of the research program Rapid Micro Statistics with project number 15990, which is (partly) financed by the Dutch Research Council (NWO).