Controlling the FDR in GWAS with population structure

Matteo Sesia (University of Southern California)

CSGI 2022 | July 7th, 2022

Traditional approach: testing marginal associations

Methods: univariate regression, permutations, linear mixed models.

\begin{align*} \text{marginal association} \quad & \neq \quad \text{causation} \\ Y {\; \not\!\perp\!\!\!\perp \;} X_j \quad & \qquad X_j \rightarrow Y \end{align*}

Variants on same chromosome are not independent of each other (linkage disequilibrium, population structure, familial relatedness).

Testing conditional associations

Partition the variables into (contiguous) groups.

\begin{align*} \underbrace{X_1, X_2, X_3}_{G_1},\underbrace{X_4, X_5}_{G_2}, \underbrace{X_6, X_7}_{G_3}, \underbrace{X_8, X_9, X_{10}}_{G_4} \end{align*}

Conditional hypotheses: \begin{align*} \mathcal{H}_{0,g} : Y {\; \perp\!\!\!\perp \;} X_g \mid X_{-g}. \end{align*}

• Larger groups: easier to reject the null
• Smaller groups: more informative discoveries

Control the false discovery rate: the expected proportion of spurious discoveries.

Model-X framework: \begin{align*} (X^i,Y^i) \overset{}{\sim} P_{XY} = P_X \cdot P_{Y \mid X}, \qquad X^i \in \mathbb{R}^p, Y^i \in \mathbb{R}. \end{align*} Model $P_X$, make inferences about $P_{Y \mid X}$.

Preview of discoveries (simulated phenotype)

Genotypes and knockoffs

Knockoff are synthetic variables that "look like", but are not identical to, the genotypes.

Knockoffs preserve allele frequencies, linkage disequilibrium, and population structure.

Knockoffs as negative control variables

Main strength of knockoffs: they can be used as negative control variables with any model, including complicated multivariate and machine learning models.

Tutorial

A toy genetic dataset containing 1000 artificial samples typed at 2000 loci (divided between chromosome 21 and 22) is available from the software repository.

Download the repository, enter the main directory, and compile the snpknock2 C++ program by typing in your terminal:

cd snpknock2
make
cd ..

After a successful compilation, you can execute the script analyze.sh.

./analyze.sh

This will first verify whether the system dependencies and then carry out an entire association analysis.

This analysis consists of 4 main modules.

Module 1: partition the genome

Partition the available SNPs into contiguous groups at different levels of resolution, based on the genetic distance information.

Module 2: generate knockoffs

Generate knockoff genotypes for all specified genome partitions.

Module 2: inspect the knockoffs

Compute goodness-of-fit-diagnostics for the knockoffs.

Module 3: test statistics

Compute knockoff test statistics for all groups of SNPs, separately for each specified genome partition.

Module 4: knockoff filter

The last module applies the knockoff filter and reports any discoveries.

Visualize the results

The final results can be visualized interactively with the script visualize.sh, which will launch a Shiny app in your browser.

./visualize.sh

To learn more

References:

• False discovery rate control in genome-wide association studies with population structure. M. Sesia, S. Bates, E. Candès, J. Marchini, C. Sabatti. Proceedings of the National Academy of Sciences, 2021. https://doi.org/10.1073/pnas.2105841118
• Multi-resolution localization of causal variants across the genome. M. Sesia, E. Katsevich, S. Bates, E. Candès, C. Sabatti Nature Communications, 2020. https://doi.org/0.1038/s41467-020-14791-2
• Gene hunting with hidden Markov model knockoffs. M. Sesia, C. Sabatti, E. Candès. Biometrika, 2019. https://doi.org/10.1093/biomet/asy033

Other recent works:

• Searching for robust associations with a multi-environment knockoff filter. S. Li, M. Sesia, Y. Romano, E. Candès, C. Sabatti. Biometrika, 2021. https://doi.org/10.1093/biomet/asab055

• Searching for interactions. Individualized conditional independence testing under model-X with heterogeneous samples and interactions. M. Sesia, T. Sun. (2022, Under review) https://arxiv.org/abs/2205.08653