Power Calculation of Multi-step Combined Principal Components with Applications to Genetic Association Studies

Principal component analysis (PCA) is a useful tool to identify important linear combination of correlated variables in multivariate analysis and has been applied to detect association between genetic variants and human complex diseases of interest. How to choose adequate number of principal components (PCs) to represent the original system in an optimal way is a key issue for PCA. Note that the traditional PCA, only using a few top PCs while discarding the other PCs, might significantly lose power in genetic association studies if all the PCs contain non-ignorable signals. In order to make full use of information from all PCs, Aschard and his colleagues have proposed a multi-step combined PCs method (named mCPC) recently, which performs well especially when several traits are highly correlated. However, the power superiority of mCPC has just been illustrated by simulation, while the theoretical power performance of mCPC has not been studied yet. In this work, we attempt to investigate theoretical properties of mCPC and further propose a novel and efficient strategy to combine PCs. Extensive simulation results confirm that the proposed method is more robust than existing procedures. A real data application to detect the association between gene TRAF1-C5 and rheumatoid arthritis further shows good performance of the proposed procedure.