## Abstract

This paper considers a statistical model for the detection mechanism of qualitative microbiological test methods with a parameter for the detection proportion (the probability to detect a single organism) and a parameter for the false positive rate. It is demonstrated that the detection proportion and the bacterial density cannot be estimated separately, not even in a multiple dilution experiment. Only the product can be estimated, changing the interpretation of the most probable number estimator. The asymptotic power of the likelihood ratio statistic for comparing an alternative method with the compendial method, is optimal for a single dilution experiment. The bacterial density should either be close to two CFUs per test unit or equal to zero, depending on differences in the model parameters between the two test methods. The proposed strategy for method validation is to use these two dilutions and test for differences in the two model parameters, addressing the validation parameters specificity and accuracy. Robustness of these two parameters might still be required, but all other validation parameters can be omitted. A confidence interval-based approach for the ratio of the detection proportions for the two methods is recommended, since it is most informative and close to the power of the likelihood ratio test. Copyright (c) 2014 John Wiley & Sons, Ltd.

Original language | English |
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Pages (from-to) | 120-128 |

Number of pages | 9 |

Journal | Pharmaceutical Statistics |

Volume | 14 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2015 |

## Keywords

- accuracy
- detection proportion
- specificity
- false positives
- limit of detection
- generalized most probable number estimator