A new profile likelihood confidence interval for the mean probability of detection in collaborative studies of binary test methods

A confidence interval for the probability of detection across laboratories (LPOD) for qualitative methods, described in the AOAC INTERNATIONAL guidelines for validation of microbiological methods for food and environmental surfaces, is considered. It is demonstrated that under certain conditions, the observed confidence of this confidence interval can be rather low, so that statistical minimum requirements are not fulfilled. A new profile likelihood confidence interval based on a latent random laboratory effect approach is proposed. Observed confidence levels for this confidence interval demonstrate its applicability already for a small number of laboratories.