The advent of cost-effective genotyping and sequencing methods have recently made it possible to ask questions that address the genetic basis of phenotypic diversity and how natural variants interact with the environment. We developed Camelot (CAusal Modelling with Expression Linkage for cOmplex Traits), a statistical method that integrates genotype, gene expression and phenotype data to automatically build models that both predict complex quantitative phenotypes and identify genes that actively influence these traits. Camelot integrates genotype and gene expression data, both generated under a reference condition, to predict the response to entirely different conditions. We systematically applied our algorithm to data generated from a collection of yeast segregants, using genotype and gene expression data generated under drug-free conditions to predict the response to 94 drugs and experimentally confirmed 14 novel gene-drug interactions. Our approach is robust, applicable to other phenotypes and species, and has potential for applications in personalized medicine, for example, in predicting how an individual will respond to a previously unseen drug.