EMGM2024

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# Quality Control of GWAS Summary Statistics

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## Florian Privé 
### Aarhus Univ, Denmark
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---

### GWAS summary statistics

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- `\(\hat{\gamma}_j\)` &mdash; the GWAS effect size of variant `\(j\)` (marginal effect),

- `\(\text{se}(\hat{\gamma}_j)\)` &mdash; its standard error,

- `\(z_j = \frac{\hat{\gamma}_j}{\text{se}(\hat{\gamma}_j)}\)` &mdash; the Z-score of variant `\(j\)`,

- `\(n_j\)` &mdash; the GWAS sample size associated with variant `\(j\)`,

- `\(f_j\)` &mdash; the allele frequency of variant `\(j\)`,

- `\(\text{INFO}_j\)` &mdash; the imputation INFO score of variant `\(j\)`

---

### The first quality control I already recommend

**Compare standard deviations** of genotypes estimated in 2 ways:

<br>

1.  - When linear regression was used 
    \begin{equation}
    \text{sd}(G_j) \approx \dfrac{\text{sd}(y)}{\sqrt{n_j \cdot \text{se}(\hat{\gamma}_j)^2 + \hat{\gamma}_j^2}}
    \end{equation}

- When logistic regression was used (case-control phenotype)
    \begin{equation}\label{eq:approx-sd-log}
    \text{sd}(G_j) \approx \dfrac{2}{\sqrt{n_j^\text{eff} \cdot \text{se}(\hat{\gamma}_j)^2 + \hat{\gamma}_j^2}}
    \end{equation}
<br>
2. \begin{equation}\text{sd}(G_j) \approx \sqrt{2 \cdot f_j \cdot (1 - f_j) \cdot \text{INFO}_j}\end{equation}

---

### Detect differences in per-variant GWAS sample sizes

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### Detect bias in total effective GWAS sample size

.pull_left[
<img src="figures/cad_quick_qc.png" width="100%" style="display: block; margin: auto;" />

<span class="footnote"> `\(N_\text{eff} = \frac{4}{1 / N_\text{ca} + 1 / N_\text{co}}\)` </span>
]

.pull_right[
<img src="figures/cad_neff_perstudy.png" width="70%" style="display: block; margin: auto;" />
]

---

### Detect low imputation INFO scores

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### Uncover an issue after correcting for INFO

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### Read more about this

<br>

- Privé, F., et al. (2022) "Identifying and correcting for misspecifications in GWAS summary statistics and polygenic scores." *Human Genetics and Genomics Advances* 3.4.

- Grotzinger, A.D., et al. (2023) "Pervasive downward bias in estimates of liability-scale heritability in genome-wide association study meta-analysis: a simple solution." *Biological Psychiatry* 93.1.

- Gazal, S., et al. (2018) "Functional architecture of low-frequency variants highlights strength of negative selection across coding and non-coding annotations." *Nature Genetics* 50.11.

- Privé, F. (2022) "Using the UK Biobank as a global reference of worldwide populations: application to measuring ancestry diversity from GWAS summary statistics." *Bioinformatics* 38.13.

---

### Additional (complementary) QC &#8212; DENTIST methodology

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GCTA method which compares reported Z-scores with imputed Z-scores.

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`\(\chi^2(1)\)` test statistic:
<img src="figures/eq-dentist.jpg" width="90%" style="display: block; margin: auto;" />

where `\(i\)` is the variant of interest, and `\(t\)` the variants used for imputing.

<br>

It is particularly good at detecting allelic errors (opposite effect).

.footnote[DENTIST citation: Chen, W., et al. (2021) "Improved analyses of GWAS summary statistics by reducing data heterogeneity and errors." *Nature Communications* 12.1.]

---

### Quick simulation to check DENTIST

<br>

Design:

- Use 145K variants on chromosome 22 with MAF > 0.005 and INFO > 0.8

- Simulate some phenotype with heritability of 0.1 and polygenicity of 0.01

- Compute the GWAS summary statistics using N=50K    
(Z-scores in [-20; 20], mostly in [-10; 10])

- For 1000 variants at random, assign them an opposite effect (allelic error)

<br>

Results:

- 802 true positives (TP, real errors) and 3209 false positives (FP)    
with DENTIST

- vs 686 TP and 9 FP    
with my alternative methodology

---

### Current project

- Check and improve the DENTIST methodology,    
to ideally get more power and less false positive

- As an <svg viewBox="0 0 581 512" style="height:1em;position:relative;display:inline-block;top:.1em;" xmlns="http://www.w3.org/2000/svg">  <path d="M581 226.6C581 119.1 450.9 32 290.5 32S0 119.1 0 226.6C0 322.4 103.3 402 239.4 418.1V480h99.1v-61.5c24.3-2.7 47.6-7.4 69.4-13.9L448 480h112l-67.4-113.7c54.5-35.4 88.4-84.9 88.4-139.7zm-466.8 14.5c0-73.5 98.9-133 220.8-133s211.9 40.7 211.9 133c0 50.1-26.5 85-70.3 106.4-2.4-1.6-4.7-2.9-6.4-3.7-10.2-5.2-27.8-10.5-27.8-10.5s86.6-6.4 86.6-92.7-90.6-87.9-90.6-87.9h-199V361c-74.1-21.5-125.2-67.1-125.2-119.9zm225.1 38.3v-55.6c57.8 0 87.8-6.8 87.8 27.3 0 36.5-38.2 28.3-87.8 28.3zm-.9 72.5H365c10.8 0 18.9 11.7 24 19.2-16.1 1.9-33 2.8-50.6 2.9v-22.1z"></path></svg> implementation

- [I NEED YOUR HELP]    
Do you have/know GWAS summary statistics with allelic errors?

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### Part of a larger project

- Provide some very well quality-controlled GWAS summary statistics

- In a standardized format

- Probably as a GitHub repo of R scripts,    
where each script processes a specific GWAS summary statistics file

---

### Take-home messages

<br>

- There can be many issues in GWAS summary statistics

- You can detect many of them by comparing SDs estimated in two ways

- You can detect other (complementary) issues with DENTIST

- DENTIST is currently prone to false positives; it needs to be improved

- I hope to provide QCed GWAS summary statistics for everyone to use

---

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## Thank you for your attention

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Presentation available at [bit.ly/qc_sumstats_EMGM](https://bit.ly/qc_sumstats_EMGM)

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.footnote[Slides created via the R package [**xaringan**](https://github.com/yihui/xaringan)]