Bayesian semiparametric joint models for functional predictors.

Motivated by the need to understand and predict early pregnancy loss using hormonal indicators of pregnancy health, this paper proposes a semiparametric Bayes approach for assessing the relationship between functional predictors and a response. A multivariate adaptive spline model is used to describe the functional predictors, and a generalized linear model with a random intercept describes the response. Through specifying the random intercept to follow a Dirichlet process jointly with the random spline coefficients, we obtain a procedure that clusters trajectories according to shape and according to the parameters of the response model for each cluster. This very flexible method allows for the incorporation of covariates in the models for both the response and the trajectory. We apply the method to post-ovulatory progesterone data from the Early Pregnancy Study and find that the model successfully predicts early pregnancy loss.