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.
- Dilution experiment
- generalized Poisson distribution
- moment estimator
- optimal design
- validation of microbiological methods