Introduction to Bayesian Statistical Inference

We present basic concepts of Bayesian statistical inference. We briefly introduce the Bayesian paradigm. We present the conjugate priors; a computational convenient way to quantify prior information for tractable Bayesian statistical analysis. We present tools for parametric and predictive inference, and particularly the design of point estimators, credible sets, and hypothesis tests. These concepts are presented in running examples. Supplementary material is available from GitHub.

Discovery and prioritization of variants and genes for kidney function in >1.2 million individuals

Genes underneath signals from genome-wide association studies (GWAS) for kidney function are promising targets for functional studies, but prioritizing variants and genes is challenging. By GWAS meta-analysis for creatinine-based estimated glomerular filtration rate (eGFR) from the Chronic Kidney Disease Genetics Consortium and UK Biobank (n = 1,201,909), we expand the number of eGFRcrea loci (424 loci, 201 novel; 9.8% eGFRcrea variance explained by 634 independent signal variants). Our increased sample size in fine-mapping (n = 1,004,040, European) more than doubles the number of signals with resolved fine-mapping (99% credible sets down to 1 variant for 44 signals, ≤5 variants for 138 signals). Cystatin-based eGFR and/or blood urea nitrogen association support 348 loci (n = 460,826 and 852,678, respectively). Our customizable tool for Gene PrioritiSation reveals 23 compelling genes including mechanistic insights and enables navigation through genes and variants likely relevant for kidney function in human to help select targets for experimental follow-up.

The Comparison between Visually and Auditory Oddball Tasks in the EEG Experiment with Healthy Subjects

Purpose: We compare the two oddball tasks for auditory and visually in the healthy subjects with the EEG experiment. In this regard, we compare three different dimensions of the EEG, including regional, longitudinal, and functional effects. The regional dimension defines as the region of the brain, the longitudinal dimension is the repetition of the stimuli, and the functional dimension is the whole curve of ERP, evoked related potential, instead of the only amplitude and latency of it. We also study the trial effects for each stimulus in each task. Materials and Methods: Seventeen healthy patients, 11 of whom are males, have participated in this study. The dataset was downloaded from the internet. The EEG dataset was cleaned. There are three trials and each has a total of 25 target stimuli per group. The functional data analysis, Hybrid principal component analysis, were used to estimate three effects among two different visually and auditory oddball tasks. The 95% Bayesian credible sets were estimated with three trials of each stimulus and each group. The Generalized Additive Mixed Model was used for studying the effect of trials as random effects. Results: The first eigenfunctions of functional and longitudinal dimensions and first and second eigenvector of regional dimensions were estimated. The 95% Bayesian credible sets indicated that the variability between trials exists and is different for each stimulus and each target. The GAMM model indicates that the interaction effects in the functional dimension are statistically significant for both tasks. The interaction effect in the longitudinal dimension is not statistically significant in the Auditory Task and is statistically significant in the visual task. The brain regions are statistically significant and the main effect of the target stimuli is significant for auditory (P-Value: <0.00) and is not significant for the visual tasks (P-Value: >0.06). The interaction effect for target stimuli and the region of the brain is only significant for Occipital, Parietal, and Right Temporal (P-values < 0.05) for the auditory task. The random effects of trials are statistically significant in most of them. Conclusion: The functional data analysis provides many statistical methods to analyze the EEG dataset. The HPCA can capture the functional-longitudinal and regional dimensions and we also study the new dimension, trials with GAMM. The different regions of the brain have not the same activity in these two tasks. The repeating of the stimuli has a positive effect on complex tasks. The between trial's variability are statistically significant, and we conclude to study this effect to show the stability of the trials.

Discovery and prioritization of variants and genes for kidney function in >1.2 million individuals

ABSTRACTChronic kidney disease (CKD) has a complex genetic underpinning. Genome-wide association studies (GWAS) of CKD-defining glomerular filtration rate (GFR) have identified hundreds of loci, but prioritization of variants and genes is challenging. To expand and refine GWAS discovery, we meta-analyzed GWAS data for creatinine-based estimated GFR (eGFRcrea) from the Chronic Kidney Disease Genetics Consortium (CKDGen, n=765,348, trans-ethnic) and UK Biobank (UKB, n=436,581, Europeans). The results (i) extend the number of eGFRcrea loci (424 loci; 201 novel; 8.9% eGFRcrea variance explained by 634 independent signals); (ii) improve fine-mapping resolution (138 99% credible sets with ≤5 variants, 44 single-variant sets); (iii) ascertain likely kidney function relevance for 343 loci (consistent association with alternative biomarkers); and (iv) highlight 34 genes with strong evidence by a systematic Gene PrioritiSation (GPS). We provide a sortable, searchable and customizable GPS tool to navigate through the in silico functional evidence and select relevant targets for functional investigations.

The Trans-Ancestral Genomic Architecture of Glycaemic Traits

Glycaemic traits are used to diagnose and monitor type 2 diabetes, and cardiometabolic health. To date, most genetic studies of glycaemic traits have focused on individuals of European ancestry. Here, we aggregated genome-wide association studies in up to 281,416 individuals without diabetes (30% non-European ancestry) with fasting glucose, 2h-glucose post-challenge, glycated haemoglobin, and fasting insulin data. Trans-ancestry and single-ancestry meta-analyses identified 242 loci (99 novel; P<5×10-8), 80% with no significant evidence of between-ancestry heterogeneity. Analyses restricted to European ancestry individuals with equivalent sample size would have led to 24 fewer new loci. Compared to single-ancestry, equivalent sized trans-ancestry fine-mapping reduced the number of estimated variants in 99% credible sets by a median of 37.5%. Genomic feature, gene-expression and gene-set analyses revealed distinct biological signatures for each trait, highlighting different underlying biological pathways. Our results increase understanding of diabetes pathophysiology by use of trans-ancestry studies for improved power and resolution.