Selecting the Best Method among Several: Bayesian and Classical Data Analyses Comparison in a Complex Microbiological Validation Setting

摘要

Statistical procedures to compare new methods to gold standards, after validation of microbiological food methods, exist. However, evaluation of the best microbiological detection method among several is more challenging; there is little precedent in scientific literature. Our work compares Bayesian hierarchical (BH), Bayesian logistic Anova-like (BL-AL) and Classical logistic (CL) models using an original validation study, based on Health Canada's Microbiological Methods Committee guidelines. The validation study design includes 6 microbiological methods, 13 food panels of 20 samples each, and 10 laboratories, and theoretically generates 780 sub-groups, reduced to 198 after quality review. In classical statistics this would lead to 231 null hypothesis tests, requiring significance level (α) correction for multiple comparisons. Assuming non-informative priors, BH and BL-AL estimations include meaningful parameters (e.g. method detection rate (DR), DR differences between methods, etc.), reallocate their credibility based on observed data, and provide posterior distributions and 95% high credibility intervals (HCI). Joining HCI with pre-defined Regions of Practical Equivalence (ROPEs) allows for null hypotheses decision making: rejection, acceptance, or no decision. BH and BL-AL give similar results and posteriors. Posteriors' modes are nearly identical to best-estimates computed with CL. Statistical conclusions will be similar between BH, BL-AL and CL if, and only if, significance level (a) is corrected for multiple comparisons. Nevertheless only Bayesian allows null hypotheses acceptance and a clean ranking of the 6 microbiological methods using posterior densities within, below, and above ROPE limits. Using flat priors, it isn't surprising to find similarities between Bayesian and Classical methods. However, while avoiding classical paradigm misinterpretation issues, the Bayesian framework provides informative and meaningful results with no multiple comparison issues.