Population substructure and control selection in genome-wide association studies

Abstract

Determination of the relevance of both demanding classical epidemiologic criteria for control selection and robust handling of population stratification (PS) represents a major challenge in the design and analysis of genome-wide association studies (GWAS). Empirical data from two GWAS in European Americans of the Cancer Genetic Markers of Susceptibility (CGEMS) project were used to evaluate the impact of PS in studies with different control selection strategies. In each of the two original case-control studies nested in corresponding prospective cohorts, a minor confounding effect due to PS (inflation factor lambda of 1.025 and 1.005) was observed. In contrast, when the control groups were exchanged to mimic a cost-effective but theoretically less desirable control selection strategy, the confounding effects were larger (lambda of 1.090 and 1.062). A panel of 12,898 autosomal SNPs common to both the Illumina and Affymetrix commercial platforms and with low local background linkage disequilibrium (pair-wise r(2)<0.004) was selected to infer population substructure with principal component analysis. A novel permutation procedure was developed for the correction of PS that identified a smaller set of principal components and achieved a better control of type I error (to lambda of 1.032 and 1.006, respectively) than currently used methods. The overlap between sets of SNPs in the bottom 5% of p-values based on the new test and the test without PS correction was about 80%, with the majority of discordant SNPs having both ranks close to the threshold. Thus, for the CGEMS GWAS of prostate and breast cancer conducted in European Americans, PS does not appear to be a major problem in well-designed studies. A study using suboptimal controls can have acceptable type I error when an effective strategy for the correction of PS is employed.

Figure 1. A diagram for the three main sets of SNPs used in the text.

The first set of PCA SNPs is used to identify hidden population substructure. The set of genomic control SNPs is used to evaluate the over-dispersion factor in a given study, as well as in the proposed permutation procedure to select relevant PCs for the correction of PS. The second set of PCA SNPs is used to validate findings from the first set of PCA SNPs. In applications, only the first set of PCA SNPs is recommended.

Figure 2. Samples represented by their first two principal components.

Principal components (PC, the 1^st along the horizontal direction, the 2^nd along the vertical direction)) were obtained by applying the PCA on the joint sample of PLCO prostate cancer and NHS breast cancer studies. A) First two PCs for subjects from the PLCO prostate cancer study. B) First two PCs for subjects from the NHS breast cancer study.

Figure 3. Q-Q plot based on the test without PC adjustment.

For each of the four analyses, the Q-Q plot is based on P-values (in log10 scale) that correspond to the 1 d.f. Wald test on 475,116 testing autosomal SNPs by assuming an additive risk model (in logit scale) and without PC adjustment. A) Results for the original prostate cancer study (prostate cancer cases and controls from PLCO). B) Result for the reconstructed prostate cancer study using external controls (prostate cancer cases from PLCO, and external controls from NHS). C) Results for the original breast cancer study (breast cancer cases and controls from NHS). D) Results for the reconstructed breast cancer study using external controls (breast cancer cases from NHS, and external controls from PLCO).

Figure 4. Q-Q plot based on the test with PC adjustment.

For each of the four analyses, the Q-Q plot is based on P-values (in log10 scale) that correspond to the 1 d.f. Wald test on 475,116 testing autosomal SNPs by assuming an additive risk model (in logit scale) and with PC adjustment. The PCs used in adjustment are selected by the proposed permutation procedure. A) Results for the original prostate cancer study (prostate cancer cases and controls from PLCO). B) Results for the reconstructed prostate cancer study using external controls (prostate cancer cases from PLCO, and external controls from NHS). C) Results for the original breast cancer study (breast cancer cases and controls from NHS). D) Results for the reconstructed breast cancer study using external controls (breast cancer cases from NHS, and external controls from PLCO).

Figure 5. SNP ranking correlation in prostate cancer studies.

In each plot, SNPs' rankings based on the 1 d.f. Wald test on 475,116 testing autosomal SNPs without PC adjustment are compared with their rankings based on the 1 d.f. Wald test with adjustment for PCs chosen by the permutation procedure. The SNPs in blue are ranked among the top 5% by tests both with and without PC adjustment. The SNPs in green and orange are ranked among the top 5% by only one of the tests. A) Results based on the original prostate cancer study (prostate cancer cases and controls from PLCO). The 1^st PC was chosen for PS correction. B) Results based on the reconstructed prostate cancer study using external controls (prostate cancer cases from PLCO, and external controls from NHS). The 1^st, 2^nd and 4^th PCs were chosen for PS correction.

Figure 6. The conditional ranking distribution for the original PLCO prostate cancer study.

Each plot shows the histogram of ranks according to the test without PC adjustment for SNPs ranked within a given range by the test with the adjustment for the 1^st PC (chosen by the proposed permutation procedure). The ranking ranges (%) are shown on the horizontal axis. The frequencies (%) are shown on the vertical axis. A) The histogram of ranks for SNPs ranked in the top 0–1% by the test with PC adjustment. B) The histogram of ranks for SNPs ranked in the top 1–2% by the test with PC adjustment. C) The histogram of ranks for SNPs ranked in the top 2–3% by the test with PC adjustment. D) The histogram of ranks for SNPs ranked in the top 3–4% by the test with PC adjustment. E) The histogram of ranks for SNPs ranked in the top 4–5% by the test with PC adjustment.

Figure 7. The conditional ranking distribution for the reconstructed prostate cancer study using external controls.

Each plot shows the histogram of ranks according to the test without PC adjustment for SNPs ranked within a given range by the test with the adjustment for the 1^st, 2^nd, and 4^th PCs (chosen by the proposed permutation procedure). The ranking ranges (%) are shown on the horizontal axis. The frequencies (%) are shown on the vertical axis. A) The histogram of ranks for SNPs ranked in the top 0–1% by the test with PC adjustment. B) The histogram of ranks for SNPs ranked in the top 1–2% by the test with PC adjustment. C) The histogram of ranks for SNPs ranked in the top 2–3% by the test with PC adjustment. D) The histogram of ranks for SNPs ranked in the top 3–4% by the test with PC adjustment. E) The histogram of ranks for SNPs ranked in the top 4–5% by the test with PC adjustment.