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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml" lang="" xml:lang="">
<head>
<title>PCA Toolkit</title>
<meta charset="utf-8" />
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<textarea id="source">
class: title-slide center middle inverse
<br>
# Efficient toolkit <br> implementing best practices <br> for principal component analysis <br> of population genetic data
<br>
## Florian Privé
<br>
<br>
**Slides:** `https://privefl.github.io/paper4-bedpca/pca-toolkit.html`
---
## Motivation
<br>
Perform PCA analyses in iPSYCH quickly and following best practices.
<br>
--
<br>
## Disclaimer
<br>
Still unfinished work.
---
## Range of analyses
<br>
- Compute PCA on PLINK .bed files (with missing values)
- Perform pruning or clumping to reduce effect of Linkage Disequilibrium (LD)
- Further removing of long-range LD regions
- Detection of outlier samples?
- Detection of homogeneous samples -> Danes
- Projection of new individuals onto reference PCA space
- Ancestry matching
---
## Overview of existing methods
<br>
<img src="figures/method-overview.png" width="98%" style="display: block; margin: auto;" />
---
## Pruning and PCA
<br>
Method:
- Directly memory-map the bed file (access it as if it were a matrix in memory)
- Same PCA algorithm based on random projections, already used in PCA of R package bigstatsr (Privé et al. 2018) and in FlashPCA2 (Abraham et al. 2017).
--
<br>
Using 20 physical cores,
- takes 22 minutes to perform a first phase of clumping on 406,545 unrelated individuals genotyped over 504,139 variants, which reduces the number of variants to 261,307.
- then takes 34 minutes to compute the first 20 PCs using these 261,307 variants.
---
## Problem of LD: PC reported by UK Biobank
<img src="figures/UKBB-loadings1-40.svg" width="98%" style="display: block; margin: auto;" />
---
## Problem of LD: PC computed after LD removal
Method: Robust Mahalanobis distance on PC loadings + Gaussian Smoothing = removing long-range LD outliers.
<img src="figures/UKBB-loadings.svg" width="98%" style="display: block; margin: auto;" />
---
## Remaining structure: 16 PCs
<img src="figures/UKBB-PC1-20.png" width="85%" style="display: block; margin: auto;" />
---
## Computing PCs using a subset of individuals
When restricting British to 10K and Irish to 5K: capturing at least 40 PCs!
<br>
<img src="figures/UKBB-scores-restricted.png" width="95%" style="display: block; margin: auto;" />
---
## Detection of outlier samples in 1000G
Method: compare density around point with density around its K-Nearest Neighbours.
<img src="figures/outliers-1000G.svg" width="80%" style="display: block; margin: auto;" />
---
## Restricting to homogeneous individuals
Method: Robust Mahalanobis distance on PC scores (approx. `\(\chi^2(K)\)`).
<img src="figures/homogeneous.svg" width="85%" style="display: block; margin: auto;" />
---
## Projection of new individuals into reference PCA space
**Issue:** shrinkage bias when projecting new individuals (when p > n).
PCA on 60% of 1000G (**black**) / Projecting on remaining 40% (**red**):
<img src="figures/proj1000G-PC1-8.svg" width="95%" style="display: block; margin: auto;" />
Shrinkage factors: `1.01 1.02 1.07 1.09 1.51 1.68 1.94 1.40 2.88 3.17 2.90 2.92 3.23 5.13 5.25 5.04 4.58 5.69 6.26 6.32`.
---
## Projection of new individuals into reference PCA space
**Solution:** Online Augmentation, Decomposition, and Procrustes (OADP) projection (Zhang et al. 2019). We provide faster implementation.
PCA on 60% of 1000G (**black**) / OADP projection on remaining 40% (**blue**):
<img src="figures/proj1000G-PC1-8.svg" width="95%" style="display: block; margin: auto;" />
---
## Projection of new individuals into reference PCA space
**Limitation:** Projection on related individuals does not work.
PCA on 60% of 1000G (**black**) / OADP projection on same 60% (**blue**):
<img src="figures/proj1000G-related.svg" width="75%" style="display: block; margin: auto;" />
---
## Pipeline to compute PCs
<img src="figures/PCA-pipeline.svg" width="55%" style="display: block; margin: auto;" />
---
## Remaining problem: what is really PC16?
<img src="figures/UKBB-PC1-20.png" width="85%" style="display: block; margin: auto;" />
---
## Facts about PC16
<br>
- unchanged if we impute randomly (using allele frequencies)
- People with PC16 > 30
- have 36% correlation between PC16 and number of NAs per individuals (also 13% for PC1, 12% for PC3, 11% for PC13 and 14)
- from almost all assessment centers (data-field 54), batches (data-field 22000) and plates (data-field 22007)
- from different ancestries (data-field 21000)
- have between 0.2% and 3.7% of missing values
- loadings are almost all positives (not symmetric)
---
## Possible explanation: heterozygosity
<img src="figures/het-PC16.png" width="90%" style="display: block; margin: auto;" />
---
## Possible explanation: heterozygosity
<img src="figures/het-NA.png" width="90%" style="display: block; margin: auto;" />
---
class: inverse, center, middle
# Thanks!
<br>
<br>
<i class="fab fa-twitter "></i> [privefl](https://twitter.com/privefl) &nbsp;&nbsp;&nbsp;&nbsp; <i class="fab fa-github "></i> [privefl](https://github.com/privefl) &nbsp;&nbsp;&nbsp;&nbsp; <i class="fab fa-stack-overflow "></i> [F. Privé](https://stackoverflow.com/users/6103040/f-priv%c3%a9)
.footnote[Slides created via the R package [**xaringan**](https://github.com/yihui/xaringan).]
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