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Abstract:
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The most probable number (MPN) is a statistical estimation of the microbial density using binary data. Such data are obtained by assessing whether the substance of interest continues to remain detected in serially diluted samples. Conventionally, microbial densities are determined according to the MPN table which is based on three assumptions: 1) number of microorganisms is Poisson distributed; 2) substance is easily detected; and 3) test results are independent. However, test outcomes are often affected by experimental errors across diluted samples. In the proposed methodology, test results are conditionally independent given random effect which is captured by a frailty variable. The advantage of the proposed model over conventional method is that it allows simultaneous assessment of detection errors and microbial density estimation. The outline of this paper includes an introduction of the MPN method, concepts of frailty variables, mathematical detail of the proposed model and method of constructing confidence intervals. Finally, simulations are conducted with various sample sizes and parameter settings to demonstrate the robust performance of the model.
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