Sample size determination for Emax model, equivalence / non-inferiority test and drug combination in fixed dose trials.

Sample size determination is one of the most important aspects in clinical designs. Careful selection of appropriate sample sizes can not only save economic and human resources, but also improve model performance and efficiency. We first explore the sample sizes of Emax model for a simple one group crossover design. Emax model is the one of the most frequently used models defining the relationship of drug efficacy with respect to its dosing levels in pharmacokinetic /pharmacodynamic studies. In frequentist approach, sample sizes are determined by desired accuracy for the parameter of interest ED₅₀. Non-linear mixed effects model is applied to emphasize the within subjects correlation. To allow for different magnitudes of variability of the population parameters in the Emax model, we proposed three different model structures to account for the random effects. In Bayesian approach, sample sizes are determined by desired coverage, average of posterior variances and lengths for the parameter of interest ED₅₀. In our simulation studies, sampling priors are used to generate the data, and non-informative priors are utilized to represent ignorance of key model parameters. Sample sizes for comparative studies are then discussed in Bayesian approach. In the absence of gold standard, sample sizes are determined by the measures of average posterior variances and lengths for the ratio of marginal probabilities of two screening tests; whereas in the presence of gold standard, sample sizes are evaluated under the same criterion to the measures of sensitivity and specificity. Non-informative priors are utilized in this study as well. We have also considered the problem of drug combination in fixed dose trials to test whether a drug mixture, which may combine two or more agents, is more ‘effective’ than each of its components. Informative priors are derived for component drugs and a non-informative prior is assumed for the drug mixture. Sample sizes are evaluated by posterior standard errors, average probability of more effectiveness and Bayesian power.