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I am learning about genome-wide association studies (GWAS) and I know that they are used to see whether certain SNPs are associated with a disease of interest. From everything that I have watched and read about GWAS, it seems to me that GWAS can only be used to analyse SNPs in relation to a disease.

However, I was wondering whether GWAS can be used to analyse gene deletions in relation to a specific disease. For example, if you are interested in seeing whether a deletion of a certain gene X is associated with a disease like intellectual disability.

Would it be feasible to recruit thousands of people with intellectual disability and thousands of controls and then sequence their genomes and see whether the deletion of a specific gene is significantly associated with intellectual disability?

I cannot see how else scientists can determine if deletion of a specific gene has a meaningful association with a disease. I know that many mutations in intellectual disability patients are de novo and rare, so it is hard to find a large sample size of intellectual disability patients with a specific mutation. Many journal papers focusing on the deletion of a gene in relation to intellectual disability just reference the cases of individuals carrying the deletion reported in the literature/databases, and use that as evidence to justify the gene as a candidate gene worth investigating.

However, if you have a very small cohort (e.g. < 10) of patients with intellectual disability carrying deletion of a specific gene (and have no other detected mutations), is this strong enough evidence to say that this gene is a plausible candidate for the intellectual disability?

In biological research, how many people with a disease need to be carrying a specific gene mutation in order for that gene to be considered a candidate gene for the disease (is there a minimum value)?

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Genomic analysis of copy number variants is routine for GWAS purposes. Here is one early example. In that case I believe they used array CGH rather than sequencing but the principle is the same, and it is more cost effective with sequencing now.

I suggest that you look into the literature of power analysis for GWAS studies. Here is one publication, here are some course materials on the topic.

This is really a statistical question rather than a biological question, at its root.

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Short answer: about a million people.

Check out Cochran's formula: enter image description here

In reality, here's a paper that discusses it more (still using pretty simple assumptions):

"Our results indicate that predictive models for many complex traits, including a variety of human disease susceptibilities (e.g., with additive heritability h 2∼0.5), can be extracted from data sets comprised of n⋆∼100s individuals, where s is the number of distinct causal variants influencing the trait. For example, given a trait controlled by ∼10 k loci, roughly a million individuals would be sufficient for application of the method."

This subject is a lot more rich than I can do justice to here. There have been a handful of papers published on this.

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