Commensurate Priors on a Finite Mixture Model for Incorporating Repository Data in Clinical Trials.

Docosahexaenoic acid (DHA) is a good source of fat that can be taken up through food, such as fish, or taken as a supplement. Evidence is building that DHA provides a high yield, low risk strategy to reduce preterm birth and/or low birth weight. These births are great costs to society. A recently completed phase III trial revealed that higher birth weight and gestational age were associated with DHA dosed at 600 mg/day. In this paper we take a posterior predictive approach to assess impacts of these findings on public health. Simple statistical models are not adequate for accurate posterior predictive distribution estimation. Of particular interest is a paper by Schwartz et al. (2010) who discovered that the joint distribution of birth weight and gestational age is well modeled by a finite mixture of three normal distributions. Data from our own clinical trial exhibit similar features. Using the mean and variance-covariance matrices from Schwartz et al. (2010) and flexible commensurate priors (Hobbs et al., 2012) for the mixing parameters, we estimate the effect of DHA supplementation on the over 20,000 infants born in hospitals demographically similar to the hospital where the clinical trial was conducted.