<p>To answer the first part of your question, the dependent and independent variable of X-WAS is kind of arbitrary and dependent on the question you asked. But it gradually becomes a convention in the field after the initial name and concept are accepted by the community. For example, GWAS from the very beginning is written as <code>condition ~ SNP</code>, and there is no doubt about it. Later, people did something like <code>condition ~ gene expression</code> and called it TWAS, which is also widely accepted now. In your case, MWAS is indeed <code>metabolite ~ condition</code>, and the only important thing is to know the convention in the research community so people are on the same page when they talk to each other.</p>

<p>As for why running GWAS using single SNP. In a GWAS, it is typical to use 500K to 7M SNPs. So this is a large number. It is obvious that we cannot include all the SNP in one single model, then the question becomes how many SNPs to include in each model, and how to choose those SNPs. This is very hard to decide. Also, due to link disequilibrium, many SNPs are correlated, which means co-linearity, a thing you want to avoid in linear models. It is not clear how to correctly interpret the effect sizes in a model with many SNPs as well. Therefore, due to feasibility, simplicity, and interpretability, it might be best to perform regression on every single SNP.</p>

<p>Now since we are running GWAS in an SNP-by-SNP fashion, there are a lot of work that needs to be done after GWAS in order to find the true causal SNP. Many fine-mapping methods have been developed to tackle this problem.</p>

<p>Interestingly, there are some multi-variate GWASs methods, but they do not come in the flavor of simple linear models. Instead, sometimes complex Bayesian statistics are used, for instance.</p>

CC BY-SA 4.0
2020-03-26T16:34:50.567Z
2020-03-26T16:34:50.567Z
Phoenix Mu
<p>I started reading some papers on X-wide association studies, where X can be metabolome, epigenome, etc... The authors usually describe which are the dependent and which are the independent variables of their models. Taking as an example a metabolome-wide association study (MWAS), the authors use as model the following: <code>metabolite</code> ~ <code>condition</code>. That is, each metabolite is considered the dependent variable and the condition (e.g., smoker vs. non-smoker) is considered the independent variable. I was a little bit confused, so I looked into an example study using GWAS: in this case the model can be written as <code>condition</code> ~ <code>SNPs</code>, which is what I would expect (knowing nothing about GWAS but something about Data Science) and quite the opposite from the MWAS described above.</p>

<p>Does the choice of the dependent variable depend on the questions asked in the study, or does it exist some sort of <em>agreement</em>? Moreover, regarding the GWAS model described above, I read that usually researchers fit a model for each SNP: what's wrong with fitting a model which consists of several independent variables (i.e., <code>y ~ SNP_1 + SNP_2 + ... + SNP_N</code>)?</p>

CC BY-SA 4.0
2023-06-14T20:49:10.763Z
Fitting a model that consists of many independent variables is done, but serves a different purpose. There is nothing inherently wrong with it. A GWAS answers the question "given phenotype and genotype data, which genotypes are associated with the phenotype?" Your proposal answers a question more like "given phenotype and genotype data, how can we best predict phenotype with genotypes?"
BigMistake
CC BY-SA 4.0
2023-06-15T03:17:14.337Z
See also: https://biology.stackexchange.com/questions/111538/why-would-greml-in-gcta-treat-snp-effects-as-random-effects/111539#111539
BigMistake
<gwas><linear-regression><logistic-regression>
GWAS, MWAS, EWAS: what are the (in)dependent variables?
# GWAS, MWAS, EWAS: what are the (in)dependent variables?

(Asked by: username_0 on 2020-03-26)

I started reading some papers on X-wide association studies, where X can be metabolome, epigenome, etc... The authors usually describe which are the dependent and which are the independent variables of their models. Taking as an example a metabolome-wide association study (MWAS), the authors use as model the following: `metabolite` ~ `condition`. That is, each metabolite is considered the dependent variable and the condition (e.g., smoker vs. non-smoker) is considered the independent variable. I was a little bit confused, so I looked into an example study using GWAS: in this case the model can be written as `condition` ~ `SNPs`, which is what I would expect (knowing nothing about GWAS but something about Data Science) and quite the opposite from the MWAS described above.

Does the choice of the dependent variable depend on the questions asked in the study, or does it exist some sort of *agreement*? Moreover, regarding the GWAS model described above, I read that usually researchers fit a model for each SNP: what's wrong with fitting a model which consists of several independent variables (i.e., `y ~ SNP_1 + SNP_2 + ... + SNP_N`)?

**Tags:** gwas, linear-regression, logistic-regression
> **Comments:**
> **username_1**: Fitting a model that consists of many independent variables is done, but serves a different purpose. There is nothing inherently wrong with it. A GWAS answers the question "given phenotype and genotype data, which genotypes are associated with the phenotype?" Your proposal answers a question more like "given phenotype and genotype data, how can we best predict phenotype with genotypes?"  
> **username_1**: See also: https://biology.stackexchange.com/questions/111538/why-would-greml-in-gcta-treat-snp-effects-as-random-effects/111539#111539  

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## 1 answers

### Answer by username_2 on 2020-03-26. Score: 3 | Accepted answer

To answer the first part of your question, the dependent and independent variable of X-WAS is kind of arbitrary and dependent on the question you asked. But it gradually becomes a convention in the field after the initial name and concept are accepted by the community. For example, GWAS from the very beginning is written as `condition ~ SNP`, and there is no doubt about it. Later, people did something like `condition ~ gene expression` and called it TWAS, which is also widely accepted now. In your case, MWAS is indeed `metabolite ~ condition`, and the only important thing is to know the convention in the research community so people are on the same page when they talk to each other.

As for why running GWAS using single SNP. In a GWAS, it is typical to use 500K to 7M SNPs. So this is a large number. It is obvious that we cannot include all the SNP in one single model, then the question becomes how many SNPs to include in each model, and how to choose those SNPs. This is very hard to decide. Also, due to link disequilibrium, many SNPs are correlated, which means co-linearity, a thing you want to avoid in linear models. It is not clear how to correctly interpret the effect sizes in a model with many SNPs as well. Therefore, due to feasibility, simplicity, and interpretability, it might be best to perform regression on every single SNP.

Now since we are running GWAS in an SNP-by-SNP fashion, there are a lot of work that needs to be done after GWAS in order to find the true causal SNP. Many fine-mapping methods have been developed to tackle this problem.

Interestingly, there are some multi-variate GWASs methods, but they do not come in the flavor of simple linear models. Instead, sometimes complex Bayesian statistics are used, for instance.


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