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I have a list of Genes with their alleles (RS IDs) associated with a specific condition. I have to find their genotyping data and the beta values from published studies. I looked through several studies and none of them had anything mentioned about the said terms?

Apparently its for calculating the polygenic score of the listed SNPs. Does that mean the genotyping data is the allelic possibilities and beta score as effect size? Effect size is the population size (n)?

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The beta statistic is a common output field produced by programs that carry out genome-wide associations. There's a good explanation here.

I interpret a beta statistic as the degree to which a change in genotype from the reference allele alters the phenotype of interest. The association (and beta statistic) can be negative or positive. It should always be tied to a particular variant, usually called the "risk allele".

The beta statistic is related to the number of individuals found in each group with a particular genotype. In that sense it could be argued to be related to the population size (at least, assuming pre-grouping of populations by genotype), but that's not a typical interpretation.

The GWAS catalogue is a good place to start off looking for data associated with GWAS:

https://www.ebi.ac.uk/gwas/home

However, I think that's for summary statistics. If someone has asked you for raw genotype data, that is trickier to get, and tends to depend on the condition. Genotype data is personally-identifying information, and there are lots of issues associated with a blanket public release of such information, which is why it's so hard to find.

Without more information on the particular phenotype, I can't give much guidance, but useful places to look for most traits are dbGaP and UK Biobank. Both of those data sources need forms filled out and approved (to demonstrate an ethically-responsible research aim) in order to access genotype-level data.

There are a few public datasets around that include data uploaded by individuals (who have explicitly consented to their genotype data being public), but it tends to be trait-specific.

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