FUNCTIONAL PRINCIPAL VARIANCE COMPONENT TESTING FOR A GENETIC ASSOCIATION STUDY OF HIV PROGRESSION

Abstract

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.

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

Fig. 1.

Manhattan plot for set-based testing on chromosome 6. Position on x-axis for each test is determined by the middle SNP (5th of 10) in the set. The dotted line corresponds to the threshold for rejection at FDR 0.1.

Fig. 2.

P-values in significant regions on the −log₁₀ scale. Large symbols correspond to set-based tests, and for illustration small symbols correspond to tests for individual SNPs. Triangles represent p-values computed in BHP010, and diamonds BHP011. Circles represent combined set-based p-values, which are of primary interest and are connected by lines. Combined p-values that are below the FDR threshold are in color, as are their corresponding component p-values.

Fig. 3.

Disease progression by minor allele burden in most significant SNP set. Estimated lCD4 and lVL are grouped by number of loci in SNP set with any minor alleles and averaged. For clarity, just those individuals with 2, 3, 8, and 9 loci are included. Lines correspond to estimates of the conditional mean based on FPCA.

Fig. 4.

Empirical type I error rates for tests performed at various levels, based on 10⁶ simulations.

Fig. 5.

Power to detect β using Q (FPVC), $\overline{Q}$ (FPVC Re-fitted), and Q_lin (Linear). β values are listed on the x-axis.

Fig. 6.

Power to detect β using Q (FPVC), Q_B (B-splines), and Q_p (Polynomial). β values are listed on the x-axis.