Modeling the genetic etiology of pharmacokinetic-pharmacodynamic links with the ARMA process

Substantial variability exists among different patients in response to drugs. The identification of genetic factors that contribute to the interpersonal differentiation has been an important task for pharmacogenetic research and drug discovery. In this article, we have derived a high-dimensional statistical model for unveiling the genetic machinery for drug response by integrating two different but biologically related processespharmacokinetics (PK) and pharmacodynamics (PD)into a genetic mapping framework. Using an integrated model of PK and PD, we can identify specific DNA sequence variants and test how they relate to the differential effect of the body to the drug (PK) and the effect of the drug on the body (PD). To effectively model a two-stage hierarchic structure of the covariance matrix at the PD and PK level, we have for the first time introduced an autoregressive moving-average (ARMA) process to the mixture-based likelihood function for sequence mapping. Closed-form estimates of the determinant and inverse of the ARMA-based covariance matrix are incorporated into the estimation step, which significantly increases the computational efficiency. Simulation studies have been performed to test the statistical behavior of our model. Potential applications of this model to pharmacogenetic research are discussed.