Theoretical Basis for the Identification of Allelic Variants That Encode Drug Efficacy and Toxicity

Almost all drugs that produce a favorable response (efficacy) may also produce adverse effects (toxicity). The relative strengths of drug efficacy and toxicity that vary in human populations are controlled by the combined influences of multiple genes and environmental influences. Genetic mapping has proven to be a powerful tool for detecting and identifying specific DNA sequence variants on the basis of the haplotype map (HapMap) constructed from single-nucleotide polymorphisms (SNPs). In this article, we present a novel statistical model for sequence mapping of two different but related drug responses. This model is incorporated by mathematical functions of drug response to varying doses or concentrations and the statistical device used to model the correlated structure of the residual (co)variance matrix. We implement a closed-form solution for the EM algorithm to estimate the population genetic parameters of SNPs and the simplex algorithm to estimate the curve parameters describing the pharmacodynamic changes of different genetic variants and matrix-structuring parameters. Extensive simulations are performed to investigate the statistical properties of our model. The implications of our model in pharmacogenetic and pharmacogenomic research are discussed.