Genetically informed, deep-phenotyped biobanks are an important research resource and it is imperative that the most powerful, versatile, and efficient analysis approaches are used. Here, we apply our recently developed Bayesian grouped mixture of regressions model (GMRM) in the UK and Estonian Biobanks and obtain the highest genomic prediction accuracy reported to date across 21 heritable traits. When compared to other approaches, GMRM accuracy was greater than annotation prediction models run in the LDAK or LDPred-funct software by 15% (SE 7%) and 14% (SE 2%), respectively, and was 18% (SE 3%) greater than a baseline BayesR model without single-nucleotide polymorphism (SNP) markers grouped into minor allele frequency–linkage disequilibrium (MAF-LD) annotation categories. For height, the prediction accuracy R 2 was 47% in a UK Biobank holdout sample, which was 76% of the estimated h SNP 2 . We then extend our GMRM prediction model to provide mixed-linear model association (MLMA) SNP marker estimates for genome-wide association (GWAS) discovery, which increased the independent loci detected to 16,162 in unrelated UK Biobank individuals, compared to 10,550 from BoltLMM and 10,095 from Regenie, a 62 and 65% increase, respectively. The average χ² value of the leading markers increased by 15.24 (SE 0.41) for every 1% increase in prediction accuracy gained over a baseline BayesR model across the traits. Thus, we show that modeling genetic associations accounting for MAF and LD differences among SNP markers, and incorporating prior knowledge of genomic function, is important for both genomic prediction and discovery in large-scale individual-level studies.

From the measurements, tests, and electronic health record data available in the UK Biobank data, we selected 12 blood based biomarkers, 3 of the most common heritable complex diseases, and 6 quantitative measures. The full list of traits, the UK Biobank coding of the data used, and the covariates adjusted for are given in Table S1. For the quantitative measures and blood-based biomarkers we adjusted the values by the covariates, removed any individuals with a phenotype greater or less than 7 SD from the mean (assuming these are measurement errors), and standardized the values to have zero mean and variance 1. 

For the common complex diseases, we determined disease status using a combination of information available. For high blood pressure (BP), we used self-report information of whether high blood pressure was diagnosed by a doctor (UK Biobank code 6150-0.0), the age high blood pressure was diagnosed (2966-0.0), and whether the individual reported taking blood pressure medication (6153-0.0, 6177-0.0). For type-2 diabetes (T2D), we used self-report information of whether diabetes was diagnosed by a doctor (2443-0.0), the age diabetes was diagnosed (2976-0.0), and whether the individual reported taking diabetes medication (6153-0.0, 6177-0.0). For cardiovascular disease (CAD), we used self-report information of whether a heart attack was diagnosed by a doctor (3894-0.0), the age angina was diagnosed (3627-0.0), and whether the individual reported heart problem diagnosed by a doctor (6150-0.0) the date of myocardial infarction (42000-0.0). For each disease, we then combined this with primary death ICD10 codes (40001-0.0), causes of operative procedures (41201-0.0), and the main (41202-0.0), secondary (41204-0.0) and inpatient ICD10 codes (41270-0.0). For BP we selected ICD10 codes I10, for T2D we selected ICD10 codes E11 to E14 and excluded from the analysis individuals with E10 (type-1 diabetes), and for CAD we selected ICD10 code I20-I29. Thus, for the purposes of this analysis, we define these diseases broadly simply to maximise the number of cases available for analysis. For each disease, individuals with neither a self-report indication or a relevant ICD10 diagnosis, were then assigned a zero value as a control.

We restricted our discovery analysis of the UK Biobank to a sample of European-ancestry individuals. To infer ancestry, we used both self-reported ethnic background (21000-0) selecting coding 1 and genetic ethnicity (22006-0) selecting coding 1. We also took the 488,377 genotyped participants and projected them onto the first two genotypic principal components (PC) calculated from 2,504 individuals of the 1,000 Genomes project with known ancestries. Using the obtained PC loadings, we then assigned each participant to the closest population in the 1000 Genomes data: European, African, East-Asian, South-Asian or Admixed, selecting individuals with PC1 projection < absolute value 4 and PC 2 projection < absolute value 3. Samples were excluded if in the UK Biobank quality control procedures they (i) were identified as extreme heterozygosity or missing genotype outliers; (ii) had a genetically inferred gender that did not match the self-reported gender; (iii) were identified to have putative sex chromosome aneuploidy; (iv) were excluded from kinship inference; (v) had withdrawn their consent for their data to be used. We used the imputed autosomal genotype data of the UK Biobank provided as part of the data release. We used the genotype probabilities to hard-call the genotypes for variants with an imputation quality score above 0.3. The hard-call-threshold was 0.1, setting the genotypes with probability <=0.9 as missing. From the good quality markers (with missingness less than 5% and p-value for Hardy-Weinberg test larger than 10-6, as determined in the set of unrelated Europeans) we selected those with minor allele frequency (MAF) > 0.0002 and rs identifier, in the set of European-ancestry participants, providing a data set 9,144,511 SNPs. From this we took the overlap with the Estonian Genome centre data described below to give a final set of 8,430,446 markers. For computational convenience we then removed markers in very high LD selecting one marker from any set of markers with LD R² > 0.8 within a 1MB window. These filters resulted in a data set with 458,747 individuals and 2,174,071 markers. We apply our GMRM model to each UK Biobank trait, running two short chains for 5000 iterations and combining the last 2000 posterior samples together. Here, we provide the posterior mean effect size estimates fo each SNP and the mixed-linear model association regression coefficient, SE, t-statistic, and association p-value.