Association Studies with Imputed Variants Using Expectation-Maximization Likelihood-Ratio Tests

<div><p>Genotype imputation has become standard practice in modern genetic studies. As sequencing-based reference panels continue to grow, increasingly more markers are being well or better imputed but at the same time, even more markers with relatively low minor allele frequency are being imputed with low imputation quality. Here, we propose new methods that incorporate imputation uncertainty for downstream association analysis, with improved power and/or computational efficiency. We consider two scenarios: I) when posterior probabilities of all potential genotypes are estimated; and II) when only the one-dimensional summary statistic, imputed dosage, is available. For scenario I, we have developed an expectation-maximization likelihood-ratio test for association based on posterior probabilities. When only imputed dosages are available (scenario II), we first sample the genotype probabilities from its posterior distribution given the dosages, and then apply the EM-LRT on the sampled probabilities. Our simulations show that type I error of the proposed EM-LRT methods under both scenarios are protected. Compared with existing methods, EM-LRT-Prob (for scenario I) offers optimal statistical power across a wide spectrum of MAF and imputation quality. EM-LRT-Dose (for scenario II) achieves a similar level of statistical power as EM-LRT-Prob and, outperforms the standard Dosage method, especially for markers with relatively low MAF or imputation quality. Applications to two real data sets, the Cebu Longitudinal Health and Nutrition Survey study and the Women’s Health Initiative Study, provide further support to the validity and efficiency of our proposed methods.</p></div

Rejection Sampling vs. Dosage Approximation for Estimation.

<p>MAF: Minor allele frequency.</p><p>MSE: Mean square error.</p><p>Rejection Sampling vs. Dosage Approximation for Estimation.</p

One-sample T-test for Type I Error.

<p>*: <i>P</i>-value <5E-4.</p><p>One-sample T-test for Type I Error.</p

Associated Variants with <i>R²</i>≤0.3 in the CLHNS Study.

<p>*: Coordinates are in genome build 37.</p><p>Bold with †: The most significant <i>p</i>-value among the four methods.</p><p>Bold without †: The second most significant <i>p</i>-values among the four methods.</p>#<p>: Truth was established by regressing phenotype on true genotypes.</p><p>Associated Variants with <i>R²</i>≤0.3 in the CLHNS Study.</p

Spearman Correlation with Gold Standard <i>P</i>-values.

<p>The Spearman correlation (Y-axis) between gold standard <i>p</i>-values and <i>p</i>-values from different methods is displayed across a spectrum of MAF and <i>R²</i>.</p

Computing Time: Mixture Method vs EM-LRT-Prob.

<p>The computing time of the Mixture method and our proposed EM-LRT-Prob method is displayed across a range of sample sizes. For each sample size, computing time is averaged across 2,000 simulated datasets.</p

Q–Q Plot for Null Variants with Low Imputation Quality in the CLHNS Study.

<p>The observed (Y-axis) vs. expected (X-axis) –log₁₀[<i>p</i>-values] are shown for 1,135 SNPs in the CLHNS data set. These SNPs are considered to be under the null hypothesis (true <i>p</i>-value >5×10⁻⁶), and all have low imputation quality (<i>R</i>²<0.3).</p

Type I Error at Significance Level = 5E-02.

<p>Type I Error at Significance Level = 5E-02.</p

Associated Variants with MAF <5% in the WHI Study.

<p>*: The most significant <i>p</i>-value among the two methods.</p><p>Associated Variants with MAF <5% in the WHI Study.</p

Power Comparison.

<p>The statistical power (Y-axis) of the different methods is shown across a spectrum of <i>R²</i> and MAF.</p