Robustification of GWAS to explore effective SNPs addressing the challenges of hidden population stratification and polygenic effects

Genome-wide association studies (GWAS) play a vital role in identifying important genes those is associated with the phenotypic variations of living organisms. There are several statistical methods for GWAS including the linear mixed model (LMM) which is popular for addressing the challenges of hidden population stratification and polygenic effects. However, most of these methods including LMM are sensitive to phenotypic outliers that may lead the misleading results. To overcome this problem, in this paper, we proposed a way to robustify the LMM approach for reducing the influence of outlying observations using the β-divergence method. The performance of the proposed method was investigated using both synthetic and real data analysis. Simulation results showed that the proposed method performs better than both linear regression model (LRM) and LMM approaches in terms of powers and false discovery rates in presence of phenotypic outliers. On the other hand, the proposed method performed almost similar to LMM approach but much better than LRM approach in absence of outliers. In the case of real data analysis, our proposed method identified 11 SNPs that are significantly associated with the rice flowering time. Among the identified candidate SNPs, some were involved in seed development and flowering time pathways, and some were connected with flower and other developmental processes. These identified candidate SNPs could assist rice breeding programs effectively. Thus, our findings highlighted the importance of robust GWAS in identifying candidate genes.

Accuracy and sensitivity of different Bayesian methods for genomic prediction using simulation and real data

The main objectives of this study were to compare the prediction accuracy of different Bayesian methods for traits with a wide range of genetic architecture using simulation and real data and to assess the sensitivity of these methods to the violation of their assumptions. For the simulation study, different scenarios were implemented based on two traits with low or high heritability and different numbers of QTL and the distribution of their effects. For real data analysis, a German Holstein dataset for milk fat percentage, milk yield, and somatic cell score was used. The simulation results showed that, with the exception of the Bayes R, the other methods were sensitive to changes in the number of QTLs and distribution of QTL effects. Having a distribution of QTL effects, similar to what different Bayesian methods assume for estimating marker effects, did not improve their prediction accuracy. The Bayes B method gave higher or equal accuracy rather than the rest. The real data analysis showed that similar to scenarios with a large number of QTLs in the simulation, there was no difference between the accuracies of the different methods for any of the traits.

Efficient estimation of reduced-rank partial envelope model in multivariate linear regression

In order to further improve the efficiency of parameter estimation and reduce the number of estimated parameters, we adopt dimension reduction ideas of partial envelope model proposed by [Su and Cook, Partial envelopes for efficient estimation in multivariate linear regression, Biometrika 98 (2011) 133–146.] to center on some predictors of special interest. Based on the research results of [Cook et al., Envelopes and reduced-rank regression, Biometrika 102 (2015) 439–456.], we combine partial envelopes with reduced-rank regression to form reduced-rank partial envelope model which can reduce dimension efficiently. This method has the potential to perform better than both. Further, we demonstrate maximum likelihood estimators for the reduced-rank partial envelope model parameters, and exhibit asymptotic distribution and theoretical properties under normality. Meanwhile, we show selections of rank and partial envelope dimension. At last, under the normal and non-normal error distributions, simulation studies are carried out to compare our proposed reduced-rank partial envelope model with the other four methods, including ordinary least squares, reduced-rank regression, partial envelope model and reduced-rank envelope model. A real data analysis is also given to support the theoretic claims. The reduced-rank partial envelope estimators have shown promising performance in extensive simulation studies and real data analysis.