Sufficient direction factor model and its application to gene expression quantitative trait loci discovery

Rapid improvement in technology has made it relatively cheap to collect genetic data, however statistical analysis of existing data is still much cheaper. Thus, secondary analysis of singlenucleotide polymorphism, SNP, data, i.e., reanalysing existing data in an effort to extract more information, is an attractive and cost-effective alternative to collecting new data. We study the relationship between gene expression and SNPs through a combination of factor analysis and dimension reduction estimation. To take advantage of the flexibility in traditional factor models where the latent factors are not required to be normal, we recommend using semiparametric sufficient dimension reduction methods in the joint estimation of the combined model. The resulting estimator is flexible and has superior performance relative to the existing estimator, which relies on additional assumptions on the latent factors. We quantify the asymptotic performance of the proposed parameter estimator and perform inference by assessing the estimation variability and by constructing confidence intervals. The new results enable us to identify, for the first time, statistically significant SNPs concerning gene-SNP relations in lung tissue from genotype-tissue expression data.