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Therefore, Figure 3 illustrates the ability of the algorithm to select relevant covariates while intrinsically incorporating shrinkage of effect estimates.
Shrinkage of effect estimates is a widely established method in statistical modelling [ 18, 19] and tends to produce a more stable solution leading to an improved prediction accuracy of the model [ 20- 22], even though an increase of the model bias (towards underlying data) has to be accepted.
To avoid some of the complications in model selection, saturated models have been proposed in which genetic effects from all possible explanatory markers are collected simultaneously into the model and their identifiability is increased by prior assumptions that result in shrinkage of effect sizes towards zero [ 1, 4, 13].
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In Bayes A and Bayes Cπ, the shrinkage of effects is marker specific, while in BLUP all markers are penalized equally.
Other genomic prediction models such as GREML assume equal contributions of each SNP to the total variability, and generally include shrinkage of effects of individual SNP effects by modelling them as random effects.
In the LASSO, the distribution of SNP effects are assigned a double exponential (DE) prior as which states that the marker-specific prior is Gaussian, with marker-specific shrinkage of effects depending on τ, which is in turn controlled by the prior distribution of the regularization parameter (p [ 37].
This value τ followed an exponential distribution Exp, where λ is a regularization parameter for the shrinkage of marker effect estimates.
However, some shrinkage of the effect might be expected when GST is provided by centres that were not involved in the development of GST.
The SNP ASEs estimated by GBLUP and BayesCπ had a Spearman correlation of 0.85, but had a Pearson correlation of only 0.56 due to the strong shrinkage of large effect SNPs in GBLUP (due to the assumption that all SNPs are drawn from a distribution with a common variance) and the strong shrinkage of small effect SNPs in BayesCπ.
Details of the method are described in Additional file 3. Briefly, GWAS implemented with this SBayes method consists of two steps as the statistical model underlying this method combines noise reduction and shrinkage of SNP effect components.
Nevertheless, all models showed good calibration after correction for differences in 5-year survival between the development and validation cohorts, and shrinkage of the effect of the predictors on survival.
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