Non-inferiority testing for qualitative microbiological methods: Assessing and improving the approach in USP 1223.

The United States Pharmacopoeia (USP) presents two approaches for showing non-inferiority of an alternate qualitative microbiological method versus a compendial method. One approach compares the positive rates for the alternate and compendial methods at one spike level, while the other one compares multiple most probable number (MPN) estimates from a multi-spike design using a t-test. In this paper, we discuss these approaches under certain assumptions and propose a third approach that can be used for both single and multiple dilutions, which we call the generalized MPN (gMPN) approach. Simulations, using Poisson distributed numbers of microorganisms in test samples, confirm that the USP approach based on rates is not suitable, that the USP approach based on MPNs is appropriate for non-inferiority, but the gMPN approach outperforms the MPN-based approach and is therefore recommended.

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.

Optimal and maximin sample sizes for multicentre cost-effectiveness trials.

This paper deals with the optimal sample sizes for a multicentre trial in which the cost-effectiveness of two treatments in terms of net monetary benefit is studied. A bivariate random-effects model, with the treatment-by-centre interaction effect being random and the main effect of centres fixed or random, is assumed to describe both costs and effects. The optimal sample sizes concern the number of centres and the number of individuals per centre in each of the treatment conditions. These numbers maximize the efficiency or power for given research costs or minimize the research costs at a desired level of efficiency or power. Information on model parameters and sampling costs are required to calculate these optimal sample sizes. In case of limited information on relevant model parameters, sample size formulas are derived for so-called maximin sample sizes which guarantee a power level at the lowest study costs. Four different maximin sample sizes are derived based on the signs of the lower bounds of two model parameters, with one case being worst compared to others. We numerically evaluate the efficiency of the worst case instead of using others. Finally, an expression is derived for calculating optimal and maximin sample sizes that yield sufficient power to test the cost-effectiveness of two treatments.

Sample size calculation in cost-effectiveness cluster randomized trials: optimal and maximin approaches.

In this paper, the optimal sample sizes at the cluster and person levels for each of two treatment arms are obtained for cluster randomized trials where the cost-effectiveness of treatments on a continuous scale is studied. The optimal sample sizes maximize the efficiency or power for a given budget or minimize the budget for a given efficiency or power. Optimal sample sizes require information on the intra-cluster correlations (ICCs) for effects and costs, the correlations between costs and effects at individual and cluster levels, the ratio of the variance of effects translated into costs to the variance of the costs (the variance ratio), sampling and measuring costs, and the budget. When planning, a study information on the model parameters usually is not available. To overcome this local optimality problem, the current paper also presents maximin sample sizes. The maximin sample sizes turn out to be rather robust against misspecifying the correlation between costs and effects at the cluster and individual levels but may lose much efficiency when misspecifying the variance ratio. The robustness of the maximin sample sizes against misspecifying the ICCs depends on the variance ratio. The maximin sample sizes are robust under misspecification of the ICC for costs for realistic values of the variance ratio greater than one but not robust under misspecification of the ICC for effects. Finally, we show how to calculate optimal or maximin sample sizes that yield sufficient power for a test on the cost-effectiveness of an intervention.