Description Usage Details References Examples
An ExpressionSet object storing simulated genotype data. The minor allele frequency (MAF) of cases has the same prior as that of controls.
1 | data("esSim")
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In this simulation, we generate additive-coded genotypes for 3 clusters of SNPs based on a mixture of 3 Bayesian hierarchical models.
In cluster +, the minor allele frequency (MAF) θ_{x+} of cases is greater than the MAF θ_{y+} of controls.
In cluster 0, the MAF θ_{0} of cases is equal to the MAF of controls.
In cluster -, the MAF θ_{x-} of cases is smaller than the MAF θ_{y-} of controls.
The proportions of the 3 clusters of SNPs are π_{+}, π_{0}, and π_{-}, respectively.
We assume a “half-flat shape” bivariate prior for the MAF in cluster +
2h_{+}≤ft(θ_{x+}\right)h_{+}≤ft(θ_{y+}\right) I≤ft(θ_{x+}>θ_{y+}\right),
where I(a) is hte indicator function taking value 1 if the event a is true, and value 0 otherwise. The function h_{+} is the probability density function of the beta distribution Beta≤ft(α_{+}, β_{+}\right).
We assume θ_{0} has the beta prior Beta(α_0, β_0).
We also assume a “half-flat shape” bivariate prior for the MAF in cluster -
2h_{-}≤ft(θ_{x-}\right)h_{-}≤ft(θ_{y-}\right) I≤ft(θ_{x-}>θ_{y-}\right).
The function h_{-} is the probability density function of the beta distribution Beta≤ft(α_{-}, β_{-}\right).
Given a SNP, we assume Hardy-Weinberg equilibrium holds for its genotypes. That is, given MAF θ, the probabilities of genotypes are
Pr(geno=2) = θ^2
Pr(geno=1) = 2θ≤ft(1-θ\right)
Pr(geno=0) = ≤ft(1-θ\right)^2
We also assume the genotypes 0 (wild-type), 1 (heterozygote), and 2 (mutation) follows a multinomial distribution Multinomial≤ft\{1, ≤ft[ θ^2, 2θ≤ft(1-θ\right), ≤ft(1-θ\right)^2 \right]\right\}
We set the number of cases as 100, the number of controls as 100, and the number of SNPs as 1000.
The hyperparameters are α_{+}=2, β_{+}=5, π_{+}=0.1, α_{0}=2, β_{0}=5, π_{0}=0.8, α_{-}=2, β_{-}=5, π_{-}=0.1.
Note that when we generate MAFs from the half-flat shape bivariate priors, we might get very small MAFs or get MAFs >0.5. In these cased, we then delete this SNP.
So the final number of SNPs generated might be less than the initially-set number 1000 of SNPs.
For the dataset stored in esSim
, there are 872 SNPs.
83 SNPs are in cluster -, 714 SNPs are in cluster 0,
and 75 SNPs are in cluster +.
Yan X, Xing L, Su J, Zhang X, Qiu W. Model-based clustering for identifying disease-associated SNPs in case-control genome-wide association studies. Scientific Reports 9, Article number: 13686 (2019) https://www.nature.com/articles/s41598-019-50229-6.
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