Additional file 1: of Fast and robust adjustment of cell mixtures in epigenome-wide association studies with SmartSVA

Further methodological details, notes, and additional results. (PDF 3644 kb

Distribution of interaction test lambdaGC in ECLIPSE.

<p>We derived the genomic inflation factor (<i>λ</i>_<i>GC</i>) of the standard interaction test using across sub-groups stratified based on P_{<i>TF</i>.<i>marg</i>}, the <i>p</i>-value for association between the target gene and the candidate transcription factors (TFs). Grey bars present the total number of interaction tests falling in each strata. Four approaches were performed: i) no normal rank-transformation of the expression data (<i>std</i>), ii) HC3 correction of the effect estimate variance to account for heteroscedasticity (<i>h</i>3), iii) normal rank-transformation of expression data (<i>rkt</i>), and iv) HC3 correction and normal rank-transformation of expression data (<i>rkt</i>.<i>h</i>3).</p

Effect of non-linear transformation on interaction effects.

<p>We defined an outcome <i>Y</i> as a function of a single nucleotide polymorphism <i>G</i> with a minor allele frequency of 0.1, an exposure <i>E</i> normally distributed with mean 5 and variance 1, and a right-skewed normal distributed residual term <i>ε</i>. In the framework of this analysis, TF mRNA level is considered as an exposure <i>E</i>. We generated two datasets of 10,000 individuals for the two scenarios. In a) <i>G</i> and <i>E</i> have only main effects and each explain 20% of the variance of <i>Y</i>. In b) <i>G</i> and <i>E</i> main effects each explain 10% of the outcome variance, but also have an interaction effect explaining 20% of the variance of <i>Y</i>. Upper panels show <i>Y</i> as a function of <i>E</i> by genotypic class and trend slope from a standard linear regression. Lower panels show the same data plotted after a rank-normal transformation (<i>rkt</i>) of <i>Y</i>. Interaction effect (observed as differences in slope by genotypic class) appears or disappears depending on the transformation applied to <i>Y</i>. <i>P</i>-values for interaction are indicated in red.</p

Gene expression data pre-processing pipeline.

<p>Standard pre-processing methods applied to gene expression data prior to expression quantitative trait locus analysis. Note that alternative strategies are also used. For example step 2 is sometimes skipped and confounding factors (e.g. batch) are included in the model tested as covariates. Others have also applied step 3 before step 2.</p

Robustness comparison.

<p>QQplots over series of 8 million replicates where an outcome <i>Y</i> is simulated as a function of a genetic variant <i>G</i>, an unmeasured exposure <i>E</i>, an interaction between <i>G</i> and <i>E</i>, and in 50% of the replicates a measured exposure <i>Z</i>. In the framework of this analysis, <i>Z</i> and <i>E</i> are considered as measured and unmeasured TF mRNA level, respectively. The validity of five tests is evaluated by comparing the observed -log₁₀ (p-value) against the expected -log₁₀ (p-value) when testing for the null interaction between a <i>G</i> and <i>Z</i>. The tests include a standard linear regression using main and interaction terms only (STD), heteroscedasticity consistent-based tests using effect estimates from STD (HC0 and HC3), linear regression using binary-transformed <i>Z</i> (BIN), and a saturated model including a main effect of <i>Z</i>² and each genotype coded as dummy variable (SAT). We considered coded allele frequency (CAF) of 0.05 (first row), 0.3 (middle row) and 0.5 (bottom row), and sample size <i>N</i> of 100, 500, 1,000 and 5,000. We randomly draw <i>E</i>, <i>Z</i>, and <i>ε</i>, the residual of <i>Y</i> from either a normal or a right-skewed normal distribution. For each scenario we derived the genomic inflation factor <i>λ</i>_<i>GC</i>.</p

When a true interaction can bias interaction screening.

<p>A quantitative outcome <i>Y</i> is defined as a linear function of a SNP <i>G</i>, an unmeasured exposure <i>E</i>, a measured exposure <i>Z</i>, and an interaction between <i>G</i> by <i>E</i>, with effect <i>γ</i>_<i>G</i>, <i>γ</i>_<i>E</i>, <i>γ</i>_<i>Z</i>, and <i>γ</i>_<i>GE</i>, respectively (as defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0173847#pone.0173847.e001" target="_blank">Eq 1</a>). All predictors were standardized to have mean 0 and variance 1. In the framework of this analysis, TF mRNA level is considered as an exposure <i>E</i>. We vary <i>γ</i>_<i>GE</i> so that the interaction term explains between 0 and 30% of the variance of <i>Y</i>. For simplicity we assume that, when relevant, the main effect of either <i>G</i>, <i>E</i>, or <i>Z</i> explains the same amount of variance as the interaction effect and set <i>ε</i> so that the variance of <i>Y</i> equals 1. Using this model we simulated series of 10,000 replicates, each including 400 individuals and tested for interaction between <i>G</i> and <i>Z</i> using a model not including the unmeasured exposure <i>E</i> (as defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0173847#pone.0173847.e003" target="_blank">Eq 2</a>), in the absence of main effect of the predictors (<i>γ</i>_<i>G</i> = <i>γ</i>_<i>E</i> = <i>γ</i>_<i>Z</i> = 0), panel <i>a</i>) or when including a main effect of <i>G</i> (<i>γ</i>_<i>G</i> ≠ 0, panel <i>b</i>), a main effect of <i>E</i> (<i>γ</i>_<i>E</i> ≠ 0), panel <i>b</i>), or a main effect of <i>G</i> (<i>γ</i>_<i>Z</i> ≠ 0, panel <i>d</i>). Upper panels show the increase in the residual variance of the outcome <i>δ</i> minus <i>ε</i> (so that models are comparable) stratified by genotypic class while increasing the interaction effect <i>γ</i>_<i>GE</i>. Lower panels show the type I error rate <i>α</i> at a <i>p</i>-value threshold of 0.05 for the interaction tests between <i>G</i> and <i>Z</i> derived for each series of 10,000 replicates.</p

Top 5 interaction signals for four different analytical strategies.

<p>Top 5 interaction signals for four different analytical strategies.</p

Descriptive statistics of 11127 study participants.

*<p>Missing Information: NHS = 175, 5.1% of participants with item non-response, 0.1% with item non-response >2 out of 8 items; HPFS = 328, 1.1% of participants with item nonresponse, 0.1% with item non-response >2 out of 8 items.</p>**<p>Missing Information: NHS = 1093 (726 due to death) 4.1% of participants with item non-response, 0.2% with item non-response >2 out of 8 items; HPFS = 479 (294 due to death), 5.1% of participants with item non-response, 0.2% with item non-response >2 out of 8 items.</p

Most statistically significant Single Nucleotide Polymorphisms based on GWAS Results from Meta-Analysis of 7 Cohorts (p<1×10−5).

<p>Chr = Chromosome, A1 = coded allele, A2 = non-coded allele.</p>*<p>Number of SNPs within 250 kb of indicator SNP, linkage disequilibrium threshold of R2≥0.5, and p for association <0.01.</p

Genome wide association plot (Manhattan plot), phobic anxiety in the Nurses' Health Study and the Health Professionals Follow-up Study (n = 11,127).

<p>Genome wide association plot (Manhattan plot), phobic anxiety in the Nurses' Health Study and the Health Professionals Follow-up Study (n = 11,127).</p