Non-Inferiority Testing on the Accuracy of Two Qualitative Microbiological Methods on Paired Binary Data

Before implementing a new microbiological test method in pharmaceutical industry, it is required to assess whether it matches or surpasses the detection of microorganisms of the current microbiological method. The United Stated Pharmacopoeia Chapter 1223 (USP < 1223>) proposes two statistical approaches for testing non-inferiority of two qualitative microbiological methods when they can both test the same samples (paired design). The first approach compares the positive rates of the two methods. The non-inferiority test is not influenced by the performance of the methods alone, it is also affected by the spiked bacterial density. The second approach compares most probable numbers (MPNs) between the two methods, but the MPN assumes that the microbiological methods are perfect. To address the two above mentioned flaws, a generalized MPN (gMPN) approach is being proposed. Estimators for the accuracy, detection proportion, and bacterial density parameter are being derived using the method of moments. It will be shown that estimation of the accuracy and detection proportion has limited to no bias, but the bias for the bacterial density can become substantial. A test statistic for non-inferiority of accuracy, along with a sample size formula, is presented, showing nominal Type I error and appropriate power. The proposed approach is demonstrated using real data.