Ancestry in GWAS

How would our ancestry influence GWAS analysis? Why it is problematic?

Ancestry

Intro

Another cool aspect of genetics is ancestry. As generation passes, each individual may carry similar but still different genetic ancestral composition as their families (like hybrids). Some genetic companies (i.e. 23andMe) sell kits for customers to learn more about their genetics, both health wise and ancestry wise.

So how does this area apply to statistical genetics? Well, ancestry has its connection with GWAS. Besides, scientists can apply mathematical methods to better infer one’s ancestry by machine learning, in other words, we can guess estimation of one’s origin!

Ancestry can be a confounder in GWAS

GWAS analyzes the statistical association between SNPs and our trait of interest. In observational studies, ancestry can actually be a confounder of GWAS. Confounder is a variable that both associates with the predictor and the response variable.

Above is an simple DAG graph

People with different ancestry can have very different performance on genotype: for example, for a SNP, people with European ancestry may have different allele frequencies and different distribution of alleles compared to people with Asian ancestry. Ancestry may also associate with the trait. Therefore, if we do not stratify and control for the confounding variable, we may end up having a spurious outcome in GWAS. This concept is especially important to keep in mind when carrying out observational studies.

After adjusting for ancestry, our GWAS model (marginal regression) would look like:

\[ E[y|x_j,A] = \beta_0 +\beta_j x_j+\gamma A \]

where:

However, what should we do when we do not have information on ancestry for a particular data set? Then, we have to infer their ancestry, and here is how powerful PCA is.

An essential approach with inferring ancestry: Principal Component Analysis

What do we do when we do not know one’s ancestral decomposition? Well, luckily, after analyzing many individuals’ ancestral and making them into a huge database, statisticians can utilize previous knowledge and make guesses on an individual’s ancestry even though it is unknown. How do we achieve this? One of the essential, and popular methods to analyze such problems is to use Principal Component Analysis, short for PCA.

PCA is a machine learning algorithm, which can predict outcomes for new data, using information we gained from previous data.

Here are some important key highlights about PCA:

  1. It is a technique to reduce the complexity of high dimensional data to low dimensions by “summarizing the variables”, achieved by expressing principal components (PCs) in terms of linear combination of predictors.
  2. The criteria for determining the expression of PCs is to choose the one which maximizes the variation of the variable values. Therefore, this technique is called “dimension reduction” since we have fewer dimensions from variables.
  3. It is called an unsupervised algorithm, meaning there is no response variable we are interested in, instead, we want PCA tells us how my distribution of data looks like by forming some clustering groups.

Here is a youtube video explains PCA very well (adapted from Prof. Leslie Myint).

For your interest and better understanding of PCA conceptually, here is a link to a discussion forum to analog PCA concepts with characteristics in wines!

What is beneficial and special about PCA?

Recall from last section where we mention that ancestry may be a confounder in GWAS: since PCA captures the information that summarizes ancestry information,we can include them in our analysis easily just as adding a linear term to the original marginal regression model (but this is just for ONE SNP!).

\[ E[Y|X_j,PC_1,PC_2]=\beta_0+\beta_1x_j+\beta_2PC_1+\beta_3 PC_2+... \]

By PCA, we can efficiently and effectively replace the predictors we have with new variables (PCs). In other words, we can create fewer, new variables that help us capture all the traits from our samples. Since the PCs are linear combination of the old predictors, the PC will look like:

\[ PC_1 = a_{11}x_1+a_{12}x_2+...+a_{1p}x_p\\ \] \[ PC_2 = a_{21}x_1+a_{22}x_2+...+a_{2p}x_p\\ ...\\ \]

\[ PC_p = a_{p1}x_1+a_{p2}x_2+...+a_{pp}x_p\\ \]

Note: \(PC_1\) ALWAYS explains the most variability in our data: considering all possible linear combinations; \(PC_2\) ALWAYS explains the second most variability in the data; same as \(PC_3\). The variance explained by PC decreases with further PCs.

The amazing thing about PCA here is that the algorithm automatically clusters the data into different dimensions, allowing us to see patterns very easily. In this context, the “patterns” mean genetic ancestry! For an exemplar visualization, here is a figure from the paper “Genes mirror geography within Europe.” (Novembre et al., 2008.)

example of how PC1 and PC2 reflecting European genetic ancestry

The cited paper mainly characterized 3000 European individuals genotyped at lots of DNA sites to find out patterns of their population structure. The letters in the figure recorded their reported geographic information.

PCA Vocab

After learning what PCA is, there are some terms you should know for PCA as well!

That’s it!

Lab: Applying PCA

You’ve come to a lot of understanding of our work today! In this section, we will take a look at what PCA results look like and explore their meanings.

Understand PCA output

Here is a screenshot from my PCA analysis demo. I have 15 SNPs (SNP 1-15). Can you see how many PCs do we have? What do numbers in each column mean?

PCA output form

Summary:

  1. There are 15 PCs for our data set.

  2. The “standard deviation” column explains the variability (more specifically, standard deviation is the sqaure root of variance explained) each PC captures. PC1 has the greatest standard as we expect, it decreases with the sequence.

  3. The “rotation” column are the loadings. For example, in PC1, the most important variables are SNP 1 and SNP2 because they share the most absolute value of the loadings (since PC1 captures the most variability, it indicates that SNP 1 and SNP 2 contribute to it very much!!). This picture only captures loadings from PC1 to PC6.

PC score visualization

Let’s create plot showing the score for the top PCs: PC1, 2. to visualize data patterns. What do you learn from this plot?

PC1 scores V.S. PC2 scores

The magic of PCA shows that even if we have no knowledge about the ancestry, PCA automatically grouped them by the PCs. It seems like we have a pattern between two population groups (mainly by PC1, that is where the score differs the most across two groups).

However, given this strong and powerful algorithm, PCA results sometimes still get its own limitations. Since an individual’s genotype may depend on their ancestry, people with mixed ancestry inherit different genetic materials from their parents (or grandparents), therefore, for some SNPs they may carry differently. If we were to carry out PCA on this group of people, we need to more carefully intepret the results.

The topic about “alleles’ narrative potential” is also important, or, problematic in GWAS and ancestry studies. For example, in biology, there are situations where one type of allele may functionally outdo the other one, and resulting different phenotypic traits in them (complete dominance). There are also concepts in biology such as multiple alleles, incomplete dominance, codominance. Therefore, when we carry out GWAS and adjusting for ancestry, we may or may not intepret their genotype the same way, thus posing a challenge for researchers to understand the results fully and correctly.

Outro

We briefly explored a widely-used method for inferring ancestry: PCA. We’ve seen how ancestry can be a potential confounder in our GWAS analysis, and the way we should address this problematic factor is to include them into the model by adding PC elements. In real life study, researchers have also been using this technique to group elements, shrinking variables, and effectively learn information from a huge data set.