The Annals of Applied Statistics

Functional principal variance component testing for a genetic association study of HIV progression

Denis Agniel, Wen Xie, Myron Essex, and Tianxi Cai

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HIV-1C is the most prevalent subtype of HIV-1 and accounts for over half of HIV-1 infections worldwide. Host genetic influence of HIV infection has been previously studied in HIV-1B, but little attention has been paid to the more prevalent subtype C. To understand the role of host genetics in HIV-1C disease progression, we perform a study to assess the association between longitudinally collected measures of disease and more than 100,000 genetic markers located on chromosome 6. The most common approach to analyzing longitudinal data in this context is linear mixed effects models, which may be overly simplistic in this case. On the other hand, existing flexible and nonparametric methods either require densely sampled points, restrict attention to a single SNP, lack testing procedures, or are cumbersome to fit on the genome-wide scale. We propose a functional principal variance component (FPVC) testing framework which captures the nonlinearity in the CD4 and viral load with low degrees of freedom and is fast enough to carry out thousands or millions of times. The FPVC testing unfolds in two stages. In the first stage, we summarize the markers of disease progression according to their major patterns of variation via functional principal components analysis (FPCA). In the second stage, we employ a simple working model and variance component testing to examine the association between the summaries of disease progression and a set of single nucleotide polymorphisms. We supplement this analysis with simulation results which indicate that FPVC testing can offer large power gains over the standard linear mixed effects model.

Article information

Ann. Appl. Stat., Volume 12, Number 3 (2018), 1871-1893.

Received: November 2015
Revised: July 2017
First available in Project Euclid: 11 September 2018

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Genomic association studies HIV disease progression functional principal component analysis longitudinal data mixed effects models variance component testing


Agniel, Denis; Xie, Wen; Essex, Myron; Cai, Tianxi. Functional principal variance component testing for a genetic association study of HIV progression. Ann. Appl. Stat. 12 (2018), no. 3, 1871--1893. doi:10.1214/18-AOAS1135.

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Supplemental materials

  • Supplementary proofs and plots. We provide the derivation of the form of the score statistic, proof of its null distribution, and supporting assumptions. And we include the form of the eigenfunctions for the HIV data analysis.