Optimal spiking experiment for non-inferiority of qualitative microbiological methods on accuracy with multiple microorganisms

The European and United States Pharmacopoeia demand a non-inferiority 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, non-inferiority studies require large numbers of test samples for a proposed non-inferiority 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 non-inferiority, 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 data set and demonstrate good performance of our method using simulation studies.