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Population Stratification

Causal privilege

Suppose we run an epidemiological study to understand the effect of variable A on variable B. We detect an association between A and B. There are three main possibilities.

  • Causality: A causes B.
graph LR
A(A) --> B(B);

classDef normal fill:transparent,stroke:transparent;
classDef conditioned fill:transparent,stroke:#444,stroke-width:2px;
class A,B normal;
  • Reverse causality: B causes A.
graph LR
B(B) --> A(A);

classDef normal fill:transparent,stroke:transparent;
classDef conditioned fill:transparent,stroke:#444,stroke-width:2px;
class A,B normal;
  • Confounding: A and B are both caused by a third factor C.
graph LR
C(C) --> A(A);
C --> B(B);

classDef normal fill:transparent,stroke:transparent;
classDef conditioned fill:transparent,stroke:#444,stroke-width:2px;
class A,B,C normal;

Determining what part of the association to attribute to each of these possibilities is a challenge that frustrates much traditional epidemiological research1.

A key advantage of genetic epidemiology is that it is causally privileged. Let A be a person's genotype and B be a phenotype of interest observed after birth. In general:

  • A person's genotype is fixed at birth, so reverse causality can be ruled out.
  • Most kinds of environmental effects do not affect a person's genotype, so environmental confounding can be ruled out.

Thus a genotype-phenotype association is much more likely to reflect a causal effect than a general epidemiological association.

This causal privilege is a significant advantage, but it does not mean that genetic studies are free of causal inference considerations. One such consideration is population stratification2.

Types of stratification

Genetic population stratification

Genetic population stratification occurs when the population under study contains multiple subpopulations, and mating within a subpopulation has historically been more common than mating across subpopulations. Normally, linkage disequilibrium in humans decays to zero at a distance of a few megabases, and does not cross chromosomal boundaries. Genetic population stratification changes this. For example SNP P on chromosome 1 and SNP Q on chromosome 2 may both be more common in a subpopulation than in the general population due to historical non-random mating. Thus having P increases your odds of being a member of the subpopulation, which increases your odds of having Q. P and Q are therefore correlated, despite being on different chromosomes. The concept is illustrated in the causal diagram below.

graph LR
C(Subpopulation) --> A(SNP P);
C --> B(SNP Q);


classDef normal fill:transparent,stroke:transparent;
classDef conditioned fill:transparent,stroke:#444,stroke-width:2px;
class A,B,C normal;

Suppose now that P has a true causal effect on the phenotype of interest but Q does not. The long-range correlation between P and Q will produce a GWAS association of Q with the phenotype, creating the false impression of causal GWAS hit in the vicinity of Q. See below.

graph LR
C(Subpopulation) --> A(SNP P);
C --> B(SNP Q);
A --> D(Phenotype)


classDef normal fill:transparent,stroke:transparent;
classDef conditioned fill:transparent,stroke:#444,stroke-width:2px;
class A,B,C,D normal;

The non-causal association is induced by the backdoor path:

\[ Q \gets \text{Subpopulation} \to P \to \text{Phenotype}. \]

Environmental population stratification

It is common for different subpopulations to be exposed to different environments. These different environments may differentially affect the phenotype of interest. This phenomena is called environmental population stratification. On its own, environmental population stratification does not confound GWAS results.

However, if both genetic and environmental population stratification are present, environmental stratification can combine with genetic stratification to induce non-causal GWAS associations. Having both genetic and environmental stratification is common: genetically distinct people often inhabit distinct environments. A possible instance of this kind of confounding is illustrated below

graph LR
C(Subpopulation) --> D(Environment);
C --> E(SNP)
D --> B(Phenotype)


classDef normal fill:transparent,stroke:transparent;
classDef conditioned fill:transparent,stroke:#444,stroke-width:2px;
class B,C,D,E normal;

In the scenario illustrated by the diagram, a non-causal association will be induced between the SNP and the phenotype due to the backdoor path:

\[ \text{SNP}\gets\text{Subpopulation}\to \text{Environment} \to \text{Phenotype}. \]

Note that even in the extreme case where the phenotype is entirely environmental and does not depend on genetics at all, a combination of genetic and environmental population stratification can induce widespread genotype-phenotype association.

Adjusting for stratification

We have established that although associations from genetic studies are causally privileged, they can still be confounded by population stratification. So what can be done? There are a variety of techniques to mitigate the effects of population stratification.

Controlling for PCs

The classical causal inference strategy to remove confounding is to adjust for the confounder, which in our case is subpopulation membership. This strategy is illustrated in the causal diagram below, where (as is traditional in the causal inference literature) we draw a box around conditioned variables.

graph LR
C(Subpopulation) --> D(Environment);
C --> E(SNP)
D --> B(Phenotype)


classDef normal fill:transparent,stroke:transparent;
classDef conditioned fill:transparent,stroke:#444,stroke-width:2px;
class B,D,E normal;
class C conditioned;

By conditioning on the subpopulation, we break the non-causal association between the phenotype and the SNP.

Unfortunately, human population structure is sufficiently that it is difficult to see how we could ever gather information to fully condition on all possible subpopulation memberships. Thus, we must use some kind of proxy. Population genetics research indicates a person's membership in human subpopulations can be well-approximated by the allocation of their genotype to genetic principal components3. Thus, a strategy to approximately adjust for confounding due to population stratification is as follows

  • Let \(X\in\mathbb{R}^{N\times M}\) denote the genotype matrix.

REGENIE

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Downstream adjustment: LDSC

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  1. Miguel A Hernán and James M Robins. Causal inference. 2010. URL: https://miguelhernan.org/whatifbook. ↩

  2. Saloni Dattani, David M Howard, Cathryn M Lewis, and Pak C Sham. Clarifying the causes of consistent and inconsistent findings in genetics. Genetic epidemiology, 46(7):372–389, 2022. URL: https://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fgepi.22459. ↩

  3. Alkes L Price, Nick J Patterson, Robert M Plenge, Michael E Weinblatt, Nancy A Shadick, and David Reich. Principal components analysis corrects for stratification in genome-wide association studies. Nature genetics, 38(8):904–909, 2006. ↩