Estimation of the limit of detection for quantal response bioassays

A comparison of spiking experiments to estimate the detection proportion of qualitative microbiological methods

The detection proportion of a qualitative microbiological test method is the probability to detect a single micro-organism. A general expression for the moment estimator of the detection proportion is provided. It depends on the distribution of the spikes used in a validation study through its moment-generating function. Several forms of spiking experiments are compared on their estimation performance using simulations and assuming a generalized Poisson distribution (GPD) for the spikes. The optimal design, which minimizes the mean squared error of our proposed moment estimator, depends on the dispersion parameter of the GPD. The design that uses just one spiked solution instead of multiple solutions is optimal for Poisson and overdispersed Poisson and it is robust against distributions for the spikes.

Validation of qualitative microbiological test methods

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.

A comparison of test statistics for the recovery of rapid growth-based enumeration tests

This paper considers five test statistics for comparing the recovery of a rapid growth-based enumeration test with respect to the compendial microbiological method using a specific nonserial dilution experiment. The finite sample distributions of these test statistics are unknown, because they are functions of correlated count data. A simulation study is conducted to investigate the type I and type II error rates. For a balanced experimental design, the likelihood ratio test and the main effects analysis of variance (ANOVA) test for microbiological methods demonstrated nominal values for the type I error rate and provided the highest power compared with a test on weighted averages and two other ANOVA tests. The likelihood ratio test is preferred because it can also be used for unbalanced designs. It is demonstrated that an increase in power can only be achieved by an increase in the spiked number of organisms used in the experiment. The power is surprisingly not affected by the number of dilutions or the number of test samples. A real case study is provided to illustrate the theory.