Bayesian EMAX model with a mixture of normal distributions for dose-response in clinical trials

When a dose-response relationship is monotonic, the EMAX model has been shown to provide a good empirical fit for designing and analyzing dose-response data across a wide range of pharmaceutical studies. However, the EMAX model has never been applied to a finite mixture distribution. Motivated by a proposal investigating DHA dose effect on preterm birth (PTB, <37 weeks gestation) rate, we developed a Bayesian EMAX mixture model incorporating the three normal components finite mixture model into the EMAX framework. The proposed Bayesian EMAX mixture model analyzes gestational age as a continuous variable, which allows for statistically efficient estimates of PTB rate using various cut point with the same parsimonious model. For example, we can estimate the rate of early PTB (ePTB, <34 weeks gestation), PTB (<37 weeks gestation), and late-term birth (>41 weeks gestation) using the same model. We compared our proposed EMAX mixture model with an EMAX logistic model and an independent doses logistic model for a dichotomized endpoint using extensive simulations. Across the scenarios under consideration, the EMAX mixture model achieved higher power than the EMAX logistic model and the independent doses logistic model in detecting the effect of DHA supplementation on the PTB rate. The EMAX mixture model also resulted in smaller mean squared errors (MSE) in PTB rate estimates.