Fast linear mixed model computations for genome-wide association studies with longitudinal data.

Genome-wide association studies are characterized by a huge number of statistical tests performed to discover new disease-related genetic variants [in the form of single-nucleotide polymorphisms (SNPs)] in human DNA. Many SNPs have been identified for cross-sectionally measured phenotypes. However, there is a growing interest in genetic determinants of the evolution of traits over time. Dealing with correlated observations from the same individual, we need to apply advanced statistical techniques. The linear mixed model is popular but also much more computationally demanding than fitting a linear regression model to independent observations. We propose a conditional two-step approach as an approximate method to explore the longitudinal relationship between the trait and the SNP. In a simulation study, we compare several fast methods with respect to their accuracy and speed. The conditional two-step approach is applied to relate SNPs to longitudinal bone mineral density responses collected in the Rotterdam Study.