{"paper_id":"2c71e6f3-7b7c-47c7-9758-518ffd6d4a70","body_text":"Article\nMachine Learning Prediction of Biomarkers from SNPs and of\nDisease Risk from Biomarkers in the UK Biobank\nErik Widen 1*, Timothy G. Raben 1\n , Louis Lello 1,2* and Stephen D.H. Hsu 1,2\n/gid00030/gid00035/gid00032/gid00030/gid00038/gid00001/gid00033/gid00042/gid00045/gid00001\n/gid00048/gid00043/gid00031/gid00028/gid00047/gid00032/gid00046\nCitation: Erik Widen; Timothy G.\nRaben; Louis Lello and Stephen D.H.\nHsu . Preprints 2021, 1, 0.\nhttps://doi.org/\nReceived: preprint\nAccepted: preprint\nPublished: preprint\nPublisher’s Note: MDPI stays neutral\nwith regard to jurisdictional claims in\npublished maps and institutional affil-\niations.\n1 Michigan State University, Department of Physics and Astronomy, 567 Wilson Rd, East Lansing, MI 48824\n2 Genomic Prediction, Inc., 675 US Highway One, North Brunswick, NJ 08902\n* Correspondence: wideneri@msu.edu; (E.W); lellolou@msu.edu; (L.L)\nAbstract: We use UK Biobank data to train predictors for 48 blood and urine markers such as HDL,\nLDL, lipoprotein A, glycated haemoglobin, ... from SNP genotype. For example, our predictor\ncorrelates∼ 0.76 with lipoprotein A level, which is highly heritable and an independent risk factor\nfor heart disease. This may be the most accurate genomic prediction of a quantitative trait that\nhas yet been produced (specifically, for European ancestry groups). We also train predictors of\ncommon disease risk using blood and urine biomarkers alone (no DNA information). Individuals\nwho are at high risk (e.g., odds ratio of > 5x population average) can be identified for conditions\nsuch as coronary artery disease (AUC ∼ 0.75), diabetes (AUC ∼ 0.95), hypertension, liver and\nkidney problems, and cancer using biomarkers alone. Our atherosclerotic cardiovascular disease\n(ASCVD) predictor uses∼ 10 biomarkers and performs in UKB evaluation as well as or better than\nthe American College of Cardiology ASCVD Risk Estimator, which uses quite different inputs (age,\ndiagnostic history, BMI, smoking status, statin usage, etc.). We compare polygenic risk scores (risk\nconditional on genotype: (risk score| SNPs)) for common diseases to the risk predictors which result\nfrom the concatenation of learned functions (risk score| biomarkers) and (biomarker| SNPs).\nKeywords: Polygenic Scores, Disease Risk, Machine Learning, Atherosclerotic Cardiovascular Dis-\nease, Biomarkers\n1. Introduction\nModern machine learning (ML) methods have opened the door to using high dimen-\nsional inputs to predict health outcomes and risk. This paper concerns the application of\nsparse linear ML to genetic and health information in order to make predictions that could\nbe useful in a clinical setting. Recent work has highlighted that ML, especially polygenic\npredictors, have high potential impact in clinical settings [1–21]. The UK Biobank (UKB)[22]\ndataset includes single nucleotide polymorphisms (SNP) genotypes, medical diagnosis\ninformation, and extensive biomarker information (i.e., 48 quantitative outputs of blood\nand urine tests) for almost 500k individuals. In this article we describe ML investigations\nof the correlation structure between these three categories of data. As described in Figure 1,\nwe train:\n1. Polygenic Score (PGS) predictors of the quantitative biomarker test results from SNPs\nalone. These functions predict biomarker level conditional on genotype: PGS =\n(biomarker| SNPs).\nFor example, we predict measured lipoprotein A levels from SNPs, achieving a\ncorrelation of 0.76 between PGS and actual biomarker level. This may be the most\naccurate SNP prediction of a complex human trait yet accomplished.\n2. Biomarker Risk Scores which predict risk of a specific disease condition using only\nmeasured biomarkers as input: (risk score| biomarkers).\nFor example, our atherosclerotic cardiovascular disease (ASCVD) predictor uses∼10\nblood biomarkers to predict disease risk. We show that in UKB validation it predicts\ndisease risk as well as or better than the American College of Cardiology ASCVD Risk\nEstimator [23,24], which uses quite different inputs such as age, diagnostic history,\nbody mass index (BMI), smoking status, statin usage, etc. Liver and kidney problem\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \nNOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.\n\n2 of 20\nFigure 1. The four different types of predictors appearing in this paper.\nrisk prediction from biomarkers seems quite promising, based on our results. In total,\nwe investigate predictions for ASCVD, coronary artery disease (CAD), diabetes type\nI & II, hypertension, very inclusive definitions of kidney and liver problems, and\nobesity.\n3. Finally, by concatenating the predictors in 1 and 2 above, we build functions which\nmap genotype (SNPs) to disease risk, with biomarkers as an intermediate step. We de-\nnote these concatenated predictors as: (risk score| biomarkers| SNPs). We emphasize\nthat concatenation (i.e., F(G(x))) is not the same as training with both biomarkers\nand SNPs simultaneously used as features. The concatenated predictors only require\nSNPs as input, but use SNP predicted biomarker values as an intermediate step in\ncalculation of the predicted disease risk. These functions can be compared to standard\nPolygenic Risk Scores (PRS) computed directly from SNPs, using disease case status\nas the training phenotype: PRS = (risk score| SNPs).\nFor example, the concatenated function which maps SNPs→ biomarkers→ type 2\ndiabetes risk performs roughly as well as the PRS for type 2 diabetes (Area Under the\nReceiver operator characteristic Curve, AUC,∼ 0.64).\nFrom our investigations, we conclude that many biomarker levels are not just substan-\ntially heritable, but can be predicted with some accuracy from SNPs. This is true despite the\nfact that levels fluctuate from day to day for a specific individual! We also conclude that dis-\nease risk prediction from biomarkers alone, via (risk score\n| biomarkers), is potentially very\npowerful, and indeed complementary to existing methods for risk estimation. For example,\nwe show below that existing ASCVD risk predictors use different and complementary\ninformation to the biomarkers used in our ASCVD (risk score| biomarkers). Our results\nsuggest that combining this complementary information can lead to stronger prediction\nand perhaps new insights into heart disease. Significant analyses of the costs and benefits\nof additional inputs have been performed for the existing ASCVD predictor, which is in\nclinical use (e.g. [23,24]), including some of the features in our predictor. Our comparison\nis limited to risk predictor performance and in the UKB cohort only.\nWe validate all predictors using sibling data: most of the power to differentiate be-\ntween siblings (either in quantitative trait values or disease risk) persists despite similarity\nin childhood environments. We also test the fall off in power in distant ancestries (rela-\ntive to the European training population). The decline for SNP based predictors varies\nas expected with genetic distance, whereas biomarker prediction does not display this\npattern.\nThroughout this paper, we refer to the different biomarkers according to the abbrevia-\ntions listed in Table 1.\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n3 of 20\nTable 1. List of all studied blood and urine markers with abbreviations.\nAbbr. Full name Abbr. Full name Abbr. Full name\nABC Basophill count DBil Direct bilirubin PCT Platelet crit\nAEC Eosinophill count E2 Oestradiol phos Phosphate\nALB Albumin GGT Gamma glutamyltransferase PLT Platelet count\nALC Lymphocyte count gluc Glucose RBC Red blood cell (erythrocyte) count\nALP Alkaline phosphatase HbA1c Glycated haemoglobin (HbA1c) RET Reticulocyte count\nALT Alanine aminotransferase HCT Haematocrit percentage RF Rheumatoid factor\nAMC Monocyte count HDL HDL cholesterol SHBG Sex hormone binding globulin\nANC Neutrophill count Hgb Haemoglobin concentration T Testosterone\napoA Apolipoprotein A HLSR High light scatter reticulocyte\ncount\nTBil Total bilirubin\napoB Apolipoprotein B IGF1 IGF-1 TG Triglycerides\nAST Aspartate aminotransferase K Potassium in urine TP Total protein\nCa Calcium LDL LDL direct U Urea\nchol Cholesterol LpA Lipoprotein A UA Urate\nCr Creatinine MA Microalbumin in urine UCR Creatinine (enzymatic) in urine\nCRP C-reactive protein Na Sodium in urine vitD Vitamin D\nCysC Cystatin C NRBC Nucleated red blood cell count WBC White blood cell (leukocyte) count\n2. Materials and Methods\n• Subject data\nAll research in this paper uses data exclusively from the 2018 UKB release [ 22,25]\nand updates (see Supplementary Information for more details). All statements about sex\nor ancestry refer to the self-reported data within this dataset [ 26]. There is of course a\ncomplicated genetic substructure within each one of these subgroups [ 27–40], however,\nit has been repeatedly demonstrated that self-reporting provides sufficiently good data\nfor training purposes [ 41–45]1. We refer to the self-reported ancestries labeled white,\nAsian, Chinese, and black in UKB as European, South-Asian, East-Asian and African, in\naccordance with the guidelines in [46]. It has been repeatedly confirmed that the power\nof polygenic predictors is dependent on both the training and testing ancestries, and that\ngenerally the power of the prediction falls off as a function of genetic distance [47–50]. All\nindividuals with self-reported admixture were excluded from this study.\n• Phenotype data\nThe phenotypes included in the paper include self-reported UKB statuses, standard\n(ICD9, ICD10, OPCS3, OPCS4) codes, diagnosed conditions, thresholds, and combinations\nof all the previous items. Full details of how each phenotype is defined is given in the\nSupplementary Information.\n2.1. Predicting Biomarkers from SNPs\nThis work primarily focuses on LASSO [51], or compressed sensing [52–55]. LASSO\nwas chosen because it has been repeatedly shown that sparse, linear methods are among the\nmost successful in genetic prediction over a wide variety of traits[11,41,43]. Additionally,\nsparsity makes application and analysis of the predictors much more computationally\nefficient. As genetic predictors move into clinical settings, it will undoubtedly be the case\nthat optimal prediction algorithms will vary depending on phenotype and training data,\nbut LASSO currently serves as an excellent jack-of-all-trades. We used LASSO to predict the\n48 types of biomarkers listed in Table 1 from SNP data, and denote these type of predictors\nas (biomarker| SNPs).\n• Data and pre-processing\nUKB contains data from repeated visits and for samples with more than one measure-\nment of a certain biomarker the average value was taken. These raw measurements were\n1 Genetic prediction in general depends on non-trivial factors including population substructure, size of training sets, algorithms (e.g. sparse vs\nnon-sparse methods), heritability, environmental factors, and etc. Nonetheless, in many instances self-reported identity is sufficient for training.\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n4 of 20\nz-scored for men and women separately and consecutively age corrected by subtracting\na linear regression on age-biomarker data obtained from averaging the biomarker value\nfor all samples born the same year (biomarker-age plots are contained in Supplementary\nInformation). The parameters for the pre-processing were determined from training sets\nwith about 340k samples of European ancestry. Evaluation sets of about 20-40k Euro-\npean siblings and all non-European individuals were withheld entirely from training but\npre-processed with the same parameters.\nThe UKB genotypic data were quality controlled by excluding all SNPs with less\nthan 3% call success rate and also those with a minor allele frequency (MAF) < 0.001. All\nindividuals with less than 3% successfully called SNPs were also excluded and, again,\nany individual with self-reported mixed ancestry was excluded from this study entirely.\nFurthermore, only autosomal genetic information was used, including SNPs located on\nchromosomes 1-22 only.\n• Predictor training\nFive LASSO predictors were trained on each biomarker using cross-validation, ran-\ndomly drawing 1000 samples from the training set as validation set for each fold. The latter\nwere used to choose optimal values of the regularization parameter λ (see Supplementary\nInformation). The top performing predictor — as measured by correlation in the European\ncorresponding validation set — from each fold was retained providing some statistics for\nthe uncertainty estimates in the results. More details can be found in the Supplementary\nInformation.\n• Evaluation\nEach predictor for each biomarker was evaluated on its corresponding evaluation set\nconsisting of∼ 20-40k samples of European ancestry. To test the performance dependence\non ancestry we also applied the predictors to the 9k of South-Asian, 1500 of East-Asian,\nand 7k of African ancestry. In section 3.2.2, we report the correlation between the PGS and\nthe phenotypes as the performance metric for these continuous traits.\nSince environmental background, such as life style and diet, and indirect genetic\neffects have impacts on most of the biomarkers, we conducted a sibling evaluation. Siblings\ngenerally have more similar backgrounds than randomly chosen pairs, and are also more\ngenetically similar than unrelated individuals. Retained predictive power among siblings\nis hence a strong indication of direct genetic effects. Moreover, the amount of lost power as\ncompared to the general population can give some idea of the magnitude of environmental\neffects, e.g., from childhood environment. (There can also be genetic nurture [ 56–60]\neffects that are not analyzed here.) Childhood environments are more similar among\nsiblings than between unrelated individuals, and this comparison gives an indication of\nwhether the instantaneous biomarker measurements in adulthood are sensitive to the\neffects of childhood environment. To this end, we constructed both random pairs and\npairs of genetic siblings within the evaluation set of European ancestry. For each pair, we\ncalculated the difference in phenotype ∆phen and the difference in PGS ∆PGS and compared\nthe correlations between these quantities corr(∆phen, ∆PGS) within random and sibling\npairs, respectively.\n• Genetic architecture\nOne can define the variance accounted for by each SNPi in a predictor according to\nvariance accounted for by SNPi = β2\ni (1− fi) fi , (1)\nwhere fi is the MAF of SNP i. This is described in greater detail in the Supplementary\nInformation and in [42]. We use this alongside Manhattan-plots of the effect sizes β in the\nresults (section 3.1.1) to display the genetic architectures of the top 3 performing (biomarker\n| SNPs) predictors. Analogous plots for the rest of the (biomarker| SNPs) predictors are\ncontained in the Supplementary Information.\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n5 of 20\n2.2. Methods for disease prediction\nWe used two approaches to investigate whether biomarkers can be used to predict\ndisease risk, analogous to how blood tests are used clinically.\nApproach 1: We trained predictors to predict case/control status directly from phenotypes,\ni.e., using the direct biomarker measurements as features. We denote this type\nof predictor (risk score| biomarkers), or biomarker risk score.\nApproach 2: Second, we applied these already trained predictors to the predicted pheno-\ntypes, i.e., using the biomarker PGS output from the SNP-based predictors in\nsection 2.1 as input. As such, we obtain disease risk scores using only SNP data\nas input. We denote these concatenated predictors (risk score | biomarkers|\nSNPs).\nWe evaluated this strategy on eight different condition definitions and we present the\ndetails for the two approaches separately. This is done both to display the performance\ndependence on the two approaches and since the prediction from biomarkers in approach\n1 are very interesting in their own right.\n2.2.1. Approach 1: Predicting case status from biomarkers\n• Condition definitions\nBased on the available UKB data, we defined conditions for CAD, cancer, diabetes\ntype 1, diabetes type 2, hypertension, kidney problem, liver problem, and obesity. The\ndetailed definitions for each one of these are to be found in the Supplementary Information.\nIn general, we chose the definitions to be inclusive; kidney (liver) problem for example\ncontains almost all kidney (liver) related problems that are reported in UKB, whereas\ncancer refers to any type of cancer. Obesity was defined as a BMI over 30. The effects of\nchanging definitions are further discussed in section4.\n• Predictor training\nWe used 45 out of the 48 biomarkers as input features, dropping E2, MA, and RF\ndue to few available measurements, and taking the first available measurement for each\nsample. The raw data was pre-processed by sex specific z-scoring and then age correcting\nby subtracting a linear regression. Using LASSO, we then trained 5 predictors on the\ncase/control status, choosing optimal\nλ by five-fold cross-validation. The training was\ndone separately for men ( N = 106, 656) and women ( N = 86, 193) and on European\nancestry only.\n• Evaluation\nAs was done for the (biomarker| SNPs) in section 2.1, about 40k siblings of European\nancestry and all non-European individuals were kept separate from all training and were\nused as evaluation set. We measured the predictor performance by AUC and by odds\nratio plots. Additionally, we conducted sibling tests for the (risk score | biomarkers)\npredictors to test for environmental effects: we applied the predictors to pairs of siblings\nwith precisely one case and one control and report the fraction of correctly called affected\nsibling, juxtaposed with the same results for random pairs of one case and one control.\nIt should be emphasized here that we did not take date of onset into account in this\nstudy: disease status was considered on a \"life span\" (as far as UKB covers) basis such that\ncases could have onsets both prior to and after the time of the biomarker measurement.\nPrediction in this sense means what can we predict about current or future case status only\nknowing a set of momentary biomarker values. Temporal prediction tests (i.e., prospective\nprediction) are deferred to later work.\n2.2.2. Approach 2: Predicting case status from PGS of biomarkers\nTo form predictors taking SNP data as input, we concatenated the PGS predictors\nfrom section 2.1 with the biomarker predictors from approach 1, what we call (risk score|\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n6 of 20\nbiomarkers| SNPs). The disease predictors (risk score| biomarkers) were taken as is from\nApproach 1 and applied to the z-scored PGS output of the predictors in section 2.1. No\nfurther training was done and the performance was evaluated as for and compared with\nthe (risk score| biomarkers) predictors.\nLpA TBil DBil PLT HDL PCT RBC apoA ALP IGF1 UA apoB\n0.0\n0.2\n0.4\n0.6\n European South Asian East Asian African\nSHBG TG Hgb HCT LDL HLSR TP chol ANC CysC AEC ALB\n0.0\n0.1\n0.2\n0.3\n0.4\nHbA1c AMC WBC phos Cr GGT U ALT AST CRP T RET\n0.0\n0.1\n0.2\n0.3\nABC Na gluc ALC UCR K RF Ca vitD MA NRBC E2\n0.00\n0.05\n0.10\nFigure 2. Correlations between PGS and phenotype vary from very strong to effectively zero, depending on the\nbiomarker, and fall off with genetic distance from the training population. The mean of the PGS-phenotype corre-\nlation for evaluation sets are listed for all 48 biomarkers, ordered according to the results within Europeans — the ancestry\nfor the training population. The error bars represent± the standard deviation for 5 different predictors trained on slightly\ndifferent training sets. The dotted line is there to aid graphical comparisons across the rows. The LASSO predictor of\nlipoprotein A achieves a correlation of 0.759 within European ancestry, which is the highest correlation for a polygenic trait\nwe are aware of. The correlation fall-off for the other ancestries generally follows the order European > South Asian > East\nAsian > African. Note that the sample sizes for these ancestries are much smaller.\n2.3. Comparison with ASCVD Risk Estimator\nThe ASCVD Risk Estimator [ 24] is a widely used tool to aid clinicians in risk esti-\nmations of and preventative care against atherosclerotic cardiovascular disease. We used\nthis well-established resource to benchmark the approach of (risk score| biomarkers) pre-\ndictors by training a predictor on this condition specifically. ASCVD aggregates several\nsub-diagnoses and exists in different versions. Hard ASCVD includes acute coronary\nsyndromes, death by coronary heart disease, a history of myocardial infarction, and fatal\nand non-fatal stroke. A more general (extended) ASCVD definition additionally includes\nstable or unstable angina, coronary or other arterial revascularization, transient ischemic\nattack, and peripheral arterial disease presumed to be of atherosclerotic origin. We used a\nUKB specific extended definition, detailed in the Supplementary Information. The ASCVD\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n7 of 20\nRisk Estimator requires the input: age, sex, race, systolic and diastolic blood pressure,\ntotal cholesterol, HDL, LDL, history of diabetes, smoking status, time since quit smoking\n(if applicable), whether on hypertension treatment, whether on a statin, and whether on\naspirin. It can also use previous data for follow-ups but we restricted our analysis to \"first\nvisit patients\" only. All of these data fields can be found in some form in the UKB (the exact\nfield choices are listed in the Supplementary Information).\nThe outputs of the ASCVD Risk Estimator are (up to) three risk estimates: 10 year risk,\nlifetime risk, and optimal risk, all given as a percentage. Since our UKB data only cover\napproximately 10 years from the first biomarker measurement, we exclusively used the 10\nyear risk output. We applied the underlying function of the ASCVD Risk Estimator to the\ncorresponding data in UKB and obtained a 10 year risk estimate for 358,650 individuals\nfor whom we also had an ASCVD case/control status. Strictly speaking, the ASCVD Risk\nEstimator was developed for North American cohorts and and based on hard ASCVD\nbut, as seen in section 3.3, performed very well also in the cohorts of the UKB using the\nextended definition. Note, however, the current comparison is not intended as a rigorous\ntest for deployment.\nWe then trained a (risk score| biomarkers) predictor on case/control status, analo-\ngously to approach 1 in section 2.2, but using ordinary linear regression on the z-scored\nbiomarker measurements. This outputs a risk score which we mapped to absolute risk\nestimates in percentages as follows. The risk scores obtained from applying the predictor on\nthe training data were binned and, within each bin, the disease prevalence was calculated\nfrom the case/control statuses as an estimated risk for samples with the corresponding risk\nscores. This discrete mapping was then made continuous using rolling averages and linear\ninterpolation. For details see Supplementary Information.\n2.3.1. Combination of predictor from biomarkers and the ASCVD Risk Estimator\nIn the results section 3.3, we show that the ASCVD (risk score| biomarkers) predictor\nand the ASCVD Risk Estimator are making complementary predictions. We therefore also\ntested a combination of them. We made a linear regression on all the input features from\nthe two predictors combined (48 continuous and 8 discrete variables), z-scoring the discrete\nvariables from the ASCVD Risk Estimator input so that everything was on the same scale.\nIn addition, we made a second regression also including the output of the ASCVD Risk\nEstimator to capture the non-linearities within that function. These regressions were made\nand evaluated on the same training and evaluation sets as for the (risk score| biomarkers)\npredictors.\n3. Results\n3.1. Predicting Biomarkers from SNPs\nThe performance of the (biomarker| SNPs) predictors ranges from the highest phenotype-\nPGS correlation for a polygenic predictor we are aware of to no predictive power what-\nsoever. We present the results in order of correlation within European ancestry inFigure\n2. The best performing predictor is for lipoprotein A at a correlation of ∼ 0.76. This is\nnot too surprising as lipoprotein A levels are well-known to be highly heritable [61–64],\nrelated to the LPA gene and other loci [65–74], and thus do not greatly vary by life style\nor environment 2. Yet, it is a striking example of predictive power. After lipoprotein A,\nwe find correlations almost evenly distributed within the correlation range 0.1-0.59 and a\ngroup of 7 almost uncorrelated biomarkers at the bottom. In the same Figure 2, we have\nincluded the performance within the non-European ancestries. Being trained on European\nancestry only, the predictors suffer the now familiar [49,50] fall-off pattern according to\ngenetic distance, with performance generally being successively worse for South-Asian,\nEast-Asian, and African ancestries.\n2 Lipoprotein A has long been studied because of its association with CAD, atherosclerotic risk, liver problems, metabolism, and even cancer. Further\ndiscussion can be found in the review [75]\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n8 of 20\nLpA TBil DBil PLT HDL PCT RBC ALP apoA UA SHBG apoB\n0.00\n0.25\n0.50\n0.75\n random sib sib_0.5 sib_1.0 sib_1.5\nFigure 3. Sibling comparisons of correlation between difference in phenotype and difference in PGS, i.e.,\ncorr(∆phen, ∆PGS), show that most of the correlation is retained also for pairs that share similar environmental back-\ngrounds. UKBs ˜40k siblings of European ancestry were paired either randomly or as genetic siblings and were used as\ntest set. The correlations between the pairs’ differences in phenotype and their differences in PGS was then calculated for\neach biomarker, ordered above from strongest to weakest correlation. The error bars indicate± the standard deviations\nfor 5 predictors trained on slightly different training sets. The additional three bars labeled sib 0.5, sib 1.0 and sib\n1.5, are the results when restricting to siblings with phenotype differences larger than 0.5, 1 and 1.5 standard deviations,\nrespectively. Two siblings are likely to have more similar environmental backgrounds than random pairs, affecting the\nsimilarity of late-life biomarker measurements independently from (direct) genetic effects. This could explain the decreased\ncorrelation for siblings as compared to random pairs. Yet, the remaining correlations are strong evidence that the predictors\ncapture some direct genetic effects on the biomarkers. The comprehensive figure for all biomarkers can be found in the\nSupplementary Information.\nThe results from the sibling comparison can be seen in Figure 3. On average, there\nis a∼ 26% drop in correlation when comparing differences within random pairs and\ndifferences within sibling pairs. The figure also shows that siblings that are separated by\nmore than 0.5, 1.0, and 1.5 times the standard deviation in phenotype are predicted with\nincreased correlation. The sibling comparisons for the other biomarkers can be found in\nthe Supplementary Information.\n3.1.1. Genetic Architecture\nPolygenic predictors have shown to usually use information spread over the entire\ngenome, even when enforcing sparsity [11,41,42,45]. In Figure 4, we illustrate the genetic\narchitectures behind three of the top performing (biomarker| SNPs) predictors with Man-\nhattan plots of the effect sizes β and the variance accounted for in eq. (1), accumulated\nacross chromosomes 1-22 (the Supplementary Information contains figures for all biomark-\ners). It shows that both biomarkers with a few very strong loci and biomarkers with an\nevenly distributed dependence can be predicted well. Let us make a few remarks on the\ntop 5 performing predictors (see Supplementary Information for the direct bilirubin and\nplatelet count plots):\n• The lipoprotein A predictor is as expected totally dominated by the single locus on\nchromosome 6, the gene carrying its name LPA.\n• The total bilirubin predictor is very similar to the one for direct bilirubin. GWASes\nhave implicated many variants on all but chromosome 15 (according to a GWAS\nCatalog[\n76] trait search) but most have a very minor impact on our predictor. For\nexample, [77] reported a locus on chromosome 19 but although there are groups of\nmoderately large β in this region, the entire chromosome 19 does not account for more\nthan∼ 1% of total variance in our predictors.\n• GWASes for direct bilirubin in the literature [77,78] are generally dominated by vari-\nants in gene UGT1A on chromosome 2. The LASSO predictors pick these up too. In\naddition, there is another∼ 17% variance accounted for by the locus at chromosome\n12, also known[ 78]. Chromosomes 6 and 19 account for ∼ 1% variance each and\nhave no generally listed loci. The βi with the largest magnitude corresponds to SNP\nrs908327 on chromosome 1. It has SNPs in linkage disequilibrium (LD) that have been\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n9 of 20\nlinked to triglycerides[79] but not directly to bilirubin, to our knowledge. It has a very\nsmall MAF, however, and does not account for much variance.\n• The predictor for platelet count is very polygenic with the variance accounted for\nalmost evenly distributed across all 22 chromosomes. Chromosome 12 provides a\nsmall deviation from this pattern, accounting for∼ 14% of the variance, partly due to\na locus near one end.\n• The predictor for HDL is also highly polygenic. Previous GWASes have recorded loci\nat all but chromosome 13, which has no large magnitude βi but still accounts for∼ 1%\nof the total variance.\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2122\n-1.5\n-1.0\n-0.5\n0.0\n0.00\n0.25\n0.50\n0.75\n1.00\nLpA    (# : 2915 ± 304, corr: 0.76)\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2122\n-0.6\n-0.4\n-0.2\n0.0\n0.2\n0.00\n0.25\n0.50\n0.75\n1.00\nvariance accounted for\nTBil    (# : 9771 ± 3004, corr: 0.59)\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2122\nchromosome\n-0.4\n-0.2\n0.0\n0.2\n0.4\n0.00\n0.25\n0.50\n0.75\n1.00\nHDL    (# : 20553 ± 825, corr: 0.45)\nFigure 4. Manhattan plots of LASSO β — superimposed with the aggregate single snp variance accounted for — show\nboth highly localized as well as widely polygenic architectures. The predictor for Lipoprotein A is almost entirely\ndetermined by the well-known gene LPA in chromosome 6; the top 50 SNPs in this region account for ∼ 95% of the\naggregate single SNP variance. In contrast, HDL has an almost uniform distribution of the variance accounted for across all\nthe 22 autosomal chromosomes, despite some loci with high magnitude β-coefficients. (The difference being due to the\nMAF in equation (1).) The most significant genetic loci are discussed further in the main text. The plot titles include the\nachieved PGS-phenotype correlation and mean number of non-zero β± the standard deviation for the 5 predictors trained\non each trait.\n3.2. Predicting Disease Risk\nThe results for the disease risk predictors are divided into sections corresponding to\nthe (risk score| biomarkers) from approach 1 and (risk score| biomarkers| SNPs) from\napproach 2, respectively.\n3.2.1. Predicting case status from biomarkers\nThe performance of the (risk score| biomarkers) predictors was evaluated and are\nreported as AUCs and odds ratio plots in Figure 5. With training optimized for European\nancestry, we regard the results for this ancestry as the main results and provide the per-\nformance in other ancestries for reference. The results vary with the condition. Within\nEuropean ancestry, they range from an AUC of .53 (.60) for cancer for women (men) up to\n∼ .95 for diabetes type 1 (both sexes). As a comparison, we report below on an ASCVD\npredictor with an AUC of∼ .76 which performs risk prediction as well as or better than\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n10 of 20\n○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○\n○\n○\n○\n△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△ △ △ △ △ △ △ △ △ △ △ △\n△\n△\n△\n○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○\n○\n○\n○\n△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△△ △ △ △ △ △ △ △ △ △ △\n△\n△\n△\n0 20 40 60 80 100\n0\n35\n70\n105\n140\n175\n0\n35\n70\n105\n140\n175\nPRS Percentile\nOdds Ratio\ndiabetes 1\ndiabetes 2\n○○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○\n○\n○\n○\n○\n△△ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △\n△\n△\n○○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○\n○\n○\n○\n△△ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △\n△\n△\n○○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○\n○ ○\n△△ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △\n△ △\n0 20 40 60 80 100\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nPRS Percentile\nOdds Ratio\nobesity\nkidney\nliver\n○○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○\n○ ○ ○\n○\n○\n○\n○ ○\n○\n○ ○\n△△ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △\n△\n△\n○○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○\n○\n○\n○ ○\n○ ○\n○\n△△ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △\n△\n△\n○○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○\n○\n○\n○\n△△ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △ △\n△\n0 20 40 60 80 100\n0\n4\n8\n0\n4\n8\nPRS Percentile\nOdds Ratio\nhypertension\nCAD\ncancer\nCAD\ncancer\ndiabetes 1\ndiabetes 2\nhypertension\nkidney \nliver \nobesity\n0.5\n0.6\n0.7\n0.8\n0.9\n1.0\nAUC - women\nCAD\ncancer\ndiabetes 1\ndiabetes 2\nhypertension\nkidney \nliver \nobesity\n0.5\n0.6\n0.7\n0.8\n0.9\n1.0\nAUC - men\nEuropean South Asian East Asian African\nFigure\n5. The predictive power of (risk score| biomarkers) can single out high risk individuals with over 10x odds ratio\nfor many traits, and AUCs > 0.7 for most traits including tests across ancestry. Left: inclusive odds ratio (OR) plots for\ndiabetes type 1/2, obesity, kidney problem, liver problem, hypertension, CAD, and any cancer trained and validated on the\nEuropean population. Horizontal axis indicates individuals at that percentile and above in PRS. Marker is for predictors\ntrained and validated on men and marker △ for predictors trained and validated on women. Error bars represent the\nstandard error of the mean value with a contribution coming from computing the OR and a contribution from including 5\npredictors. Right: AUCs for (risk score| biomarkers) predictors separately trained on men and women. All predictors are\ntrained on the European population and then validated on European, South Asian, East Asian, and African populations.\nThe error bars indicate the standard deviations for 5 different predictors and do not reflect the significant uncertainties\narising from limited available statistics (sample sizes are listed in Supplementary Information).\nthe American College of Cardiology ASCVD Risk Estimator. We discuss this in detail\nbelow in section 4. The odds ratio plots show a wide range of results that also vary with\ncondition. Figure 5 separates conditions into groups based on the odds ratios of the high\nrisk outliers. The strength of the diabetes predictors is probably due to their use of blood\nbiomarkers (e.g. HbA1c) which are standard diagnostic indicators for diabetes. That this\nstandard diagnostic indicator is so highly ranked lends confidence to the results of the\ngeneral methodology.\nThere are some differences in performance for men and women, most notably in\ncancer (possibly due to sex specific cancer variants). The differences are condition specific\nand viewed across all conditions the performance is similar. We delay a more detailed\nanalysis of these differences to future study. The reported performance variations across\nthe different ancestries are notably smaller and show less of a consistent pattern than what\nis the usual case for prediction from genetic information; this is expected since predicting\nfrom biomarkers stays on a higher biological level and does not involve issues such as LD\npatterns and tag SNPs etc. Note, however, that these results are limited by the available\nstatistics, see Supplementary Information for the case/control numbers for each ancestry.\nIn Figure 6, we also include two examples of the LASSO coefficients for CAD and\ntype 2 diabetes. For CAD, we find mostly well-known biomarkers with the highest weight,\nsuch as LDL, apolipoprotein B, total cholesterol and HDL. However, for women cystatin C\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n11 of 20\n-0.01 0.00 0.01\nAEC\nRET\nWBC\nSHBG\nUA\nAMC\nCr\nPLT\nALB\nK\nCRP\nU\nRBC\nUCR\nphos\nHCT\nTP\nALP\nIGF1\nALT\nHLSR\nCa\nvitD\nLpA\nGGT\nAST\nHDL\nchol\nCysC\nHbA1c\napoB\nLDL\n-0.05 0.00 0.05\nU\nALC\nTP\nALP\nCa\nT\nPCT\nNa\nRET\nCysC\nCRP\nvitD\nPLT\nRBC\nAEC\nHgb\nALT\nTBil\nCr\nAMC\ngluc\nSHBG\nGGT\nANC\nHDL\nDBil\nLpA\nHLSR\nHbA1c\nchol\napoB\nLDL\nCAD\n0.00 0.05\napoB\nTBil\nLpA\nABC\nNRBC\nNa\nALT\nWBC\nAEC\nT\nU\nALP\nRBC\nDBil\nHgb\nANC\nTP\nLDL\nPCT\nCa\nALB\nIGF1\nvitD\nGGT\nUA\nCr\nTG\nCysC\nHLSR\ngluc\nchol\nHbA1c\n0.0 0.1\nCRP\nAMC\nK\nIGF1\napoA\nAEC\nTG\nAST\nHCT\nABC\nPLT\nUA\nCa\nPCT\nSHBG\nvitD\nphos\nDBil\nALP\nT\nANC\nALB\nCr\nGGT\nHDL\nRBC\nLDL\nCysC\nHLSR\nchol\ngluc\nHbA1c\ndiabetes 2\nFigure 6. Predictors for phenotypes\nlike CAD and type 2 diabetes from\nbiomarkers are dominated by a top\nfew inputs.\nRelative weights of each\nbiomarker within predictors for CAD\nand type 2 diabetes. women and men\nwhile error bars indicate± standard de-\nviations from the mean of five predictors.\nThe most impactful biomarkers are very\nwell-known but we highlight cystatin C\nas surprisingly frequent among the mod-\nerately strong coefficients. Correspond-\ning plots for all condition predictors are\nshown in the Supplementary Informa-\ntion.\nappears at fourth place, which to our knowledge is not often used in this context. Cystatin\nC also is the fifth most influential biomarker in the diabetes type 2 predictor for both sexes,\nwhile these predictors are dominated by the standard biomarker glycated haemoglobin.\nIn fact, cystatin C is among the more important biomarkers for most of our predictors.\nCoefficients for all conditions are listed in the Supplementary Information.\nWe investigated the presence of non-linear effects for (risk score | biomarkers) by\nextending the input features with all possible quadratic interactions among the seven most\ninfluential biomarkers for each condition. We saw no effect on the performance in either\ndirection and conclude that the effects of the biomarkers on all the listed conditions appear\nto be linear to very good approximation.\n3.2.2. Predicting case status from PGS of biomarkers\nThe concatenated predictors (risk score | biomarkers| SNPs) suffer a significant\ndrop in performance, as can be seen in Figure 7. The imprecise predictors (biomarker\n| SNPs) introduce a lot of noise and, exacerbated further by the uncertainty in the (risk\nscore| biomarkers) predictors, the concatenation does in general not lead to meaningful\npredictions. A notable exception are the diabetes predictors. The combination of reasonably\ncorrelated PGS for the most important biomarkers and the exceptionally high AUCs for\nthese predictors lead to an average AUC of ∼ .63 for the type 2 diabetes (risk score |\nbiomarkers| SNPs) predictor. This is comparable to what we have achieved in the past\nby training SNP-based LASSO directly on type 2 diabetes status[ 11]. Furthermore, the\ntwo different types of predictors (risk score| biomarkers| SNPs) and (risk score| SNPs)\ncapture somewhat complementary information, as shown in Figure 8. The sum of the two\ntypes of risk scores reaches an AUC of∼ .67. It is unclear why the use of biomarkers as an\nintermediate step adds additional information relative to training directly with SNPs as\nfeatures and case status as the phenotype. We leave this as an interesting topic for future\nresearch.\nThe sibling evaluation of the disease risk predictors, described in section 2.2, is re-\nported in Figure 9. The fraction of sibling pairs with one case and one control called\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n12 of 20\nCAD\ncancer\ndiabetes 1\ndiabetes 2\nhypertension\nkidney \nliver \nobesity\n0.500\n0.525\n0.550\n0.575\n0.600\n0.625\n0.650\n0.675\n women\nmen\nFigure 7. AUCs for (risk score\n| biomarkers| SNPs) predictors\ndrop significantly as compared\nto (risk score | biomarkers) in\nFigure 5 and only the diabetes\npredictors reach par with other\nmethods. The predictors were\nevaluated on 9016 (9607) white\nwomen (men) and the error bars\nindicate± the standard deviation\nfor 5 different predictors.\n-4 -3 -2 -1 0 1 2 3 4\n(risk score|SNPs)\n-3\n-2\n-1\n0\n1\n2\n3\n(risk score|biomarkers|SNPs)\nctrl\ncase\nFigure 8. Risk scores predicted\nfrom SNPs (risk score | SNPs)\nand from PGS of biomarkers\n(risk score| biomarkers| SNPs)\ndo not always agree, here exem-\nplified by type 2 diabetes data\nfor men. Both predictors predict\ncase status directly from SNPs\nalone. Their outputs correlate\n∼\n0.37 with a linear regression coef-\nficient of∼ 0.39. In the noise, they\ncapture some complementary in-\nformation: the sum of the risk\nscores achieves an AUC of∼ 0.67\nwhile the SNP and PGS based\npredictors individually achieve\nAUCs of∼ 0.63 and∼ 0.65, re-\nspectively.\ncorrectly ranged from pure chance for cancer and liver problems, while reaching∼ 0.9 for\ndiabetes type 1 and 2, using the (risk score| biomarkers) predictors. The accuracy dropped\nsignificantly for the (risk score| biomarkers| SNPs) predictors, as expected; no predictor of\nthis type reached a correctly called fraction above 0.6.\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n13 of 20\nCAD\ncancer\ndiabetes 1\ndiabetes 2\nhypertension\nkidney \nliver \nobesity\n0.6\n0.7\n0.8\n0.9\n475 813 349 447 1831 371 292 1395\nCAD\ncancer\ndiabetes 1\ndiabetes 2\nhypertension\nkidney \nliver \nobesity\n0.45\n0.50\n0.55\n0.60\n47 113 34 53 216 32 38 166\nFigure\n9. The fractions of sibling pairs with precisely one case and one control called correctly are\ngenerally high for (risk\nscore| biomarkers) but not much better than chance when predicting\nfrom genotypes using (risk\nscore| biomarkers| SNPs). The pairs were considered correctly called\nif the PRS was higher for the affected sibling, without any restriction on the size of the separation.\nNumber of included sibling pairs differed for the two types of predictors and are listed at the top. The\nerror bars indicate± the standard deviation for five different predictors for (risk score| biomarkers)\nand for 5× 5 concatenation combinations of predictors in the (risk score| biomarkers| SNPs).\n3.3. Comparison with ASCVD Risk Estimator\nTo illustrate the performance of the (risk score| biomarkers) predictor for ASCVD\nand to compare it with the ASCVD Risk Estimator, we used the risk percentage output as\ndescribed in section 2.3. The ASCVD Risk Estimator was built using American cohorts of\nseparately European and African ancestry. Due to the similarities with the UKB population,\nwe deemed it could be applied somewhat fairly to the entire UKB, whereas we used the\nwithheld evaluation set of∼ 40k of European ancestry for the (risk score| biomarkers)\npredictor. The result is shown in Figure 10, in which the predicted risks were binned and\nthe actual disease prevalence within each bin was calculated, labeled \"Actual risk\". Both\npredictors give very accurate risk estimates, with increasing uncertainty for individuals\nwith high predicted risk. However, although they do assign correct risk estimates for bins\ntaken as a whole, they do not always agree on who is at low versus high risk. The scatter\nplot in Figure 10 shows their individual distributions and occasional disagreements. Their\npartially complementary predictions are further highlighted in the risk heat map in Figure\n10 and utilized below in a combined predictor.\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n14 of 20\n0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8\nPredicted risk\n0.0\n0.2\n0.4\n0.6\n0.8\nActual risk\n(risk|biomarkers)\nASCVD Risk Est.\nSNP\n0.0 0.1 0.2 0.3 0.4 0.5 0.6\nRisk acc. to ASCVD Risk Est.\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\nRisk acc. to (risk|biomarkers)\nFigure 10. The ASCVD (risk score | biomarkers)\nand the ASCVD Risk Estimator both make accu-\nrate risk predictions but with partially complemen-\ntary information. Left:\nPredicted risk by (risk score|\nbiomarkers), the ASCVD Risk Estimator and a (risk\nscore| SNPs) predictor were binned and compared\nto the actual disease prevalence within each bin. The\ngray 1:1 line indicates perfect prediction. Shaded re-\ngions are 95% confidence intervals obtained from 100\nfold bootstrap estimates of the prevalence in each bin.\nThe ASCVD Risk Estimator was applied to 340k UKB\nsamples while the others were applied to an eval-\nuation set of 28k samples, all of European ancestry.\nUpper right shows a scatter plot and distributions of\nthe risk predicted by (risk score| biomarkers) versus\nthe risk predicted by the ASCVD Risk Estimator for\nthe 28k Europeans in the evaluation set. The (risk\nscore\n| biomarkers) distribution has a longer tail of\nhigh predicted risk, providing the tighter confidence\ninterval in this region. The left plot y-axis is the actual\nprevalence within the horizontal and vertical cross-\nsections, as illustrated with the shaded bands corre-\nsponding to the hollow squares to the left. Notably,\nboth predictors perform well despite the differences\nin assigned stratification. The hexagons are an over-\nlay of the lower right heat map of actual risk within\neach bin (numbers are bin sizes). Both high risk edges\nhave varying actual prevalence but with a very strong\nenrichment when the two predictors agree.\n0.0 0.1 0.2 0.3 0.4 0.5 0.6\nRisk acc. to ASCVD Risk Est.\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\nRisk acc. to (risk|biomarkers)\n4437\n343\n56\n37\n7\n3170\n771\n273\n199\n68\n5\n982\n566\n278\n226\n88\n5\n374\n332\n186\n199\n84\n5\n100\n128\n89\n110\n56\n4\n29\n39\n39\n66\n33\n7\n5\n10\n10\n30\n15\n1\n2\n4\n9\n11\n4\n2\n1\n8\n9\n1\n3\n1\n1\n1\n4276\n419\n121\n41\n10\n2243\n489\n183\n109\n32\n1124\n372\n238\n113\n42\n481\n241\n136\n96\n30\n169\n75\n42\n42\n21\n36\n14\n23\n20\n25\n14\n8\n9\n9\n12\n4\n3\n3\n2\n4\n3\n2\n2\n3\n1\n2\n1\n2\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nActual risk\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n15 of 20\n0.0 0.2 0.4 0.6 0.8\nPredicted risk\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nActual risk\nUKB only\nUKB + ASCVD R.E.\n0.00 0.05\nSHBG\nSBP\nTBil\nquitSmoke\nGGT\nALT\nRBC\nHLSR\nHCT\nSEX\nDBil\nHbA1c\nANC\ndiabetes\nCysC\nALC\nDBP\nAGE\napoA\nWBC\nhyperTreat\nstatin\naspirin\nUKB only\n0.00 0.05\nchol\ngluc\nLpA\nTBil\nGGT\nALT\nHCT\nRBC\nHLSR\nquitSmoke\nDBil\nHbA1c\nANC\nCysC\nALC\nDBP\napoA\ndiabetes\nWBC\nrisk_10y\nhyperTreat\nstatin\naspirin\nUKB + ASCVD R.E.\nFigure 12. The risk prediction using both 45 biomarkers and all the ASCVD Risk Estimator input improves perfor-\nmance as compared to Figure 10, in particular for high risk individuals, and is very good all the way up to risk levels\nof 80%. The figure compares two predictors: a combined ASCVD predictor using all 45 biomarkers plus all the input\nfields (age, sex, etc.) used by the ASCVD Risk Estimator, using UKB data only, and a predictor using the same input plus\nthe ASCVD Risk Estimator output, labeled UKB + ASCVD R.E. The latter does not perform notably better, although the\nASCVD Risk Estimator output “risk_10y” corresponds to the fourth strongest coefficient. Both perform better than both the\n(risk score| biomarkers) and ASCVD Risk Estimator individually, confirming their complementary nature shown in the heat\nmap, Figure 10. The shaded areas in the left panel again indicate 95% confidence intervals obtained by 100 fold bootstrap\ncalculations of the actual prevalence in each risk bin. Figures with all coefficients can be found in the Supplementary\nInformation.\n3.3.1. Combination of predictor from biomarkers and the ASCVD Risk Estimator\nSince the ASCVD Risk Estimator and the (risk score | biomarkers) predictor use\ndifferent input and give complementary predictions, we combined them into a a very\nreliable risk predictor, superseding both the former. The risk estimates are compared with\nactual disease prevalence in Figure 12 for two versions of the combined predictor: (1)\na linear regression on the biomarkers and all of the input going into the ASCVD Risk\nEstimator, and (2) a similar regression but also including the output of the ASCVD Risk\nEstimator. Their top coefficients are listed in the same figure.\n4. Discussion\nUK Biobank data include about 500k individuals, for each of whom the following are\nrecorded: SNP genotype, biomarker (blood, urine) test results, and case status for most\ncommon disease conditions. We have explored the pattern of correlations between these\nthree distinct data types using machine learning.\nWe have shown that SNPs can be used to predict quantitative values of biomarkers\nby training new polygenic scores (PGS) for biomarker prediction. We note that the day\nto day fluctuation of these biomarker levels suppresses the quality of prediction. A more\nstable phenotype (e.g., average value of biomarker measured on multiple occasions) would\nprobably be even better predicted from SNPs alone.\nAs is typical for current genomic predictors, we find predictive power falls off sig-\nnificantly with genetic distance from the (European) training population. This highlights\nthe importance of increasing ancestry diversity in genetic data collection. As genetic\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n16 of 20\npredictors begin to find clinical applications, lack of diversity can exacerbate healthcare\ninequalities[48,80] (a larger list of associated ethical issues is highlighted in [44]).\nWe showed that biomarkers can be used as input to predict common disease risk.\nSome of these (risk score| biomarkers) predictors (e.g., ASCVD, diabetes) are very strong\nand may even surpass risk predictors in widespread clinical use. The combined predictor\ntrained using both biomarkers and ASCVD Risk Estimator inputs clearly outperforms the\nlatter in our comparison, at least for individuals at very high risk. It should be emphasized\nhere that we did not perform the careful evidence review nor the statistical analysis that\nunderlie the ASCVD Risk Estimator [23] and our comparison did not take into account the\ntime of diagnosis. As such, our ASCVD predictor presented here is merely a comparative\nexample and is not intended for clinical use in its current form. Yet, this naive approach\nperforms remarkably well, utilizing the large statistical power of the UKB.\nIn the case of liver and kidney disease, we are not aware of other quantitative risk\npredictors that can be evaluated from biomarkers alone. Our results suggest that further\nresearch in this direction is warranted.\nWe note that (risk score| biomarkers) prediction quality does not exhibit the pattern of\nfall-off with genetic distance as previously found with genomic predictors3. For example,\nCAD and ASCVD predictors work well in all major ancestry groups despite using a\nEuropean training sample. Further investigation is needed.\nWe studied concatenated predictor functions, which map SNPs to biomarkers to\nrisk. In general, there were significant declines in performance. The magnitudes of these\ndeclines were perhaps expected for correlation chains of generic, high dimensional, vectors\nwith similar pairwise correlations. Of the (risk score| biomarkers| SNPs) predictors, only\nthe type 2 diabetes predictor performs well: AUC of ∼ .63. This is in fact comparable\nto what we have achieved in the past by training SNP-based LASSO directly on type 2\ndiabetes status. Furthermore, the two different types of predictors (risk score| biomarkers\n| SNPs) and (risk score| SNPs) capture somewhat complementary information, as shown\nin Figure 8. The sum of the two types of risk scores reaches an AUC of∼ .67. It is unclear\nwhy the use of biomarkers as an intermediate step adds additional information relative to\ntraining directly with SNPs as features and case status as the phenotype. We leave this as\nan interesting topic for future research.\nAuthor Contributions: Authors, listed alphabetically according to last name, contributed in the\nfollowing ways: conceptualization, L.L., S.H. and E.W.; methodology, L.L., T.G.R., S.H., E.W.; software,\nL.L., T.G.R., and E.W.; validation, L.L., T.G.R., E.W.; formal analysis, L.L., T.G.R., E.W.; investigation,\nL.L., T.G.R., E.W.; resources, S.H.; data curation, L.L., T.G.R., and E.W.; writing — original draft\npreparation, L.L., T.G.R., S.H., and E.W.; writing — review and editing, L.L., T.G.R., S.H., E.W.;\nvisualization, T.G.R. and E.W.; supervision, S.H.; project administration, S.H.; funding acquisition,\nS.H.; All authors have read and agreed to the published version of the manuscript.\nFunding: This research received no external funding.\nData Availability Statement: The predictors described in the paper are available to other researchers\nupon request.\nAcknowledgments: Computational resources provided by the Michigan State University High-\nPerformance Computing Center. The authors thank Dr. Andrew Siskind (UC Irvine) and Dr. Pui-Yan\nKwok (Academia Sinica UC San Francisco) for fruitful discussions and correspondence. The authors\nacknowledge acquisition of datasets via UK Biobank Main Application 15326.\nConflicts of Interest:\nStephen Hsu is a founder, shareholder and serves on the Board of Directors\nof Genomic Prediction, Inc. (GP). Louis Lello is an employee and shareholder of GP . These roles\nhad no impact in the design of the study; in the collection, analyses, or interpretation of data; in the\nwriting of the manuscript, or in the decision to publish the results. EW and TR declare no competing\ninterests.\n3 Previous GWAS and PGS studies generally see a fall off behavior, but there are occasional exceptions (e.g. [81]).\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n17 of 20\nReferences\n1. Wray, N.R.; Yang, J.; Goddard, M.E.; Visscher, P .M. The genetic interpretation of area under the ROC curve in genomic profiling.\nPLoS genetics 2010, 6.\n2. Veenstra, D.L.; Roth, J.A.; Garrison Jr, L.P .; Ramsey, S.D.; Burke, W. A formal risk-benefit framework for genomic tests: facilitating\nthe appropriate translation of genomics into clinical practice. Genetics in Medicine 2010, 12, 686.\n3. Amir, E.; Freedman, O.C.; Seruga, B.; Evans, D.G. Assessing women at high risk of breast cancer: a review of risk assessment\nmodels. JNCI: Journal of the National Cancer Institute 2010, 102, 680–691. Oxford University Press.\n4. Euesden, J.; Lewis, C.M.; O’reilly, P .F. PRSice: polygenic risk score software. Bioinformatics 2014, 31, 1466–1468.\n5. Abraham, G.; Tye-Din, J.A.; Bhalala, O.G.; Kowalczyk, A.; Zobel, J.; Inouye, M. Accurate and Robust Genomic Prediction of\nCeliac Disease Using Statistical Learning. PLOS Genetics 2014, 10, 1–15. doi:10.1371/journal.pgen.1004137.\n6. Priest, J.R.; Ashley, E.A. Genomics in clinical practice, 2014.\n7. Jacob, H.J.; Abrams, K.; Bick, D.P .; Brodie, K.; Dimmock, D.P .; Farrell, M.; Geurts, J.; Harris, J.; Helbling, D.; Joers, B.J.; others.\nGenomics in clinical practice: lessons from the front lines. Science translational medicine 2013, 5, 194cm5–194cm5.\n8. Shieh, Y.; Shieh, Y.; Hu, D.; Ma, L.; Huntsman, S.; Gard, C.C.; Leung, J.W.T.; Tice, J.A.; Vachon, C.M.; Cummings, S.R.; Kerlikowske,\nK.; Ziv, E. Breast cancer risk prediction using a clinical risk model and polygenic risk score. Breast Cancer Research and Treatment\n2016, 159, 513–525.\n9. Bowdin, S.; Gilbert, A.; Bedoukian, E.; Carew, C.; Adam, M.P .; Belmont, J.; Bernhardt, B.; Biesecker, L.; Bjornsson, H.T.; Blitzer, M.;\nothers. Recommendations for the integration of genomics into clinical practice. Genetics in Medicine 2016, 18, 1075.\n10. Chatterjee, N.; Shi, J.; García-Closas, M. Developing and evaluating polygenic risk prediction models for stratified disease\nprevention. Nature Reviews Genetics 2016, 17, 392.\n11. Lello, L.; Raben, T.G.; Yong, S.Y.; Tellier, L.C.; Hsu, S.D.H. Genomic prediction of 16 complex disease risks including heart attack,\ndiabetes, breast and prostate cancer. Sci Rep 2019, 9, 1–16. [PMC6814833].\n12. Khera, A.V .; Chaffin, M.; Aragam, K.G.; Haas, M.E.; Roselli, C.; Choi, S.H.; Natarajan, P .; Lander, E.S.; Lubitz, S.A.; Ellinor, P .T.;\nKathiresan, S. Genome-wide polygenic scores for common diseases identify individuals with risk equivalent to monogenic\nmutations. Nature Genetics 2018, 50, 1219.\n13. Liu, L.; Kiryluk, K. Genome-wide polygenic risk predictors for kidney disease. Nature Reviews Nephrology 2018, 14, 723–724.\n14. Torkamani, A.; Wineinger, N.E.; Topol, E.J. The personal and clinical utility of polygenic risk scores. Nature Reviews Genetics 2018,\n19, 581.\n15. Khera, A.V .; Chaffin, M.; Wade, K.H.; Zahid, S.; Brancale, J.; Xia, R.; Distefano, M.; Senol-Cosar, O.; Haas, M.E.; Bick, A.; Aragam,\nK.G.; Lander, E.S.; Smith, G.D.; Mason-Suares, H.; Fornage, M.; Lebo, M.; Timpson, N.J.; Kaplan, L.M.; Kathiresan, S. Polygenic\nprediction of weight and obesity trajectories from birth to adulthood. Cell 2019, 177, 587–596. [PMC6661115].\n16. Nelson, H.D.; Pappas, M.; Cantor, A.; Haney, E.; Holmes, R. Risk assessment, genetic counseling, and genetic testing for\nBRCA-related cancer in women: updated evidence report and systematic review for the US Preventive Services Task Force. Jama\n2019, 322, 666–685.\n17. Meisner, A.; Kundu, P .; Zhang, Y.D.; Lan, L.V .; Kim, S.; Ghandwani, D.; Pal Choudhury, P .; Berndt, S.I.; Freedman, N.D.;\nGarcia-Closas, M.; Chatterjee, N. Combined Utility of 25 Disease and Risk Factor Polygenic Risk Scores for Stratifying Risk of\nAll-Cause Mortality. American Journal of Human Genetics 2020, 107, 418–431. doi:10.1016/j.ajhg.2020.07.002.\n18. Lewis, C.M.; Vassos, E. Polygenic risk scores: from research tools to clinical instruments. Genome medicine 2020, 12, 1–11.\n19. Lewis, A.C.; Green, R.C. Polygenic risk scores: from research tools to clinical instruments. Genome medicine 2021, 13, 14.\n20. Kulm, S.; Marderstein, A.; Mezey, J.; Elemento, O. A systematic framework for assessing the clinical impact of polygenic risk\nscores. medRxiv 2021, pp. 2020–04.\n21. Wray, N.R.; Lin, T.; Austin, J.; McGrath, J.J.; Hickie, I.B.; Murray, G.K.; Visscher, P .M. From basic science to clinical application of\npolygenic risk scores: a primer. JAMA psychiatry 2021, 78, 101–109.\n22. Bycroft, C.; Freeman, C.; Petkova, D. The UK Biobank resource with deep phenotyping and genomic data. Nature, 562, 203–209.\n23. Lloyd-Jones, D.M.; Braun, L.T.; Ndumele, C.E.; Smith Jr, S.C.; Sperling, L.S.; Virani, S.S.; Blumenthal, R.S. Use of risk assessment\ntools to guide decision-making in the primary prevention of atherosclerotic cardiovascular disease: a special report from the\nAmerican Heart Association and American College of Cardiology. Circulation 2019, 139, e1162–e1177.\n24. ASCVD Risk Estimator Plus. Available online: http://tools.acc.org/ASCVD-Risk-Estimator-Plus/#!/calculate/estimate/\n(accessed on 29-03-2021).\n25. UK Biobank.\n26.\nBycroft, C.; Freeman, C.; Petkova, D.; Band, G.; Elliott, L.T.; Sharp, K.; Motyer, A.; Vukcevic, D.; Delaneau, O.; O’Connell, J.; Cortes,\nA.; Welsh, S.; McVean, G.; Leslie, S.; Donnelly, P .; Marchini, J. Genome-wide genetic data on 500,000 UK Biobank participants.\nbioRxiv 2017, [https://www.biorxiv.org/content/early/2017/07/20/166298.full.pdf]. doi:10.1101/166298.\n27. Price, A.L.; Patterson, N.J.; Plenge, R.M.; Weinblatt, M.E.; Shadick, N.A.; Reich, D. Principal components analysis corrects for\nstratification in genome-wide association studies. Nature genetics 2006, 38, 904–909.\n28. Novembre, J.; Johnson, T.; Bryc, K.; Kutalik, Z.; Boyko, A.R.; Auton, A.; Indap, A.; King, K.S.; Bergmann, S.; Nelson, M.R.; others.\nGenes mirror geography within Europe. Nature 2008, 456, 98–101.\n29. Mathieson, I.; McVean, G. Differential confounding of rare and common variants in spatially structured populations. Nature\ngenetics 2012, 44, 243–246.\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n18 of 20\n30. Bhatia, G.; Gusev, A.; Loh, P .R.; Finucane, H.; Vilhjálmsson, B.J.; Ripke, S.; Purcell, S.; Stahl, E.; Daly, M.; de Candia, T.R.; others.\nSubtle stratification confounds estimates of heritability from rare variants. BioRxiv 2016, p. 048181.\n31. Dandine-Roulland, C.; Bellenguez, C.; Debette, S.; Amouyel, P .; Génin, E.; Perdry, H. Accuracy of heritability estimations in\npresence of hidden population stratification. Scientific reports 2016, 6, 1–10.\n32. Guo, J.; Wu, Y.; Zhu, Z.; Zheng, Z.; Trzaskowski, M.; Zeng, J.; Robinson, M.R.; Visscher, P .M.; Yang, J. Global genetic differentiation\nof complex traits shaped by natural selection in humans. Nature communications 2018, 9, 1–9.\n33. Rosenberg, N.A.; Edge, M.D.; Pritchard, J.K.; Feldman, M.W. Interpreting polygenic scores, polygenic adaptation, and human\nphenotypic differences. Evolution, medicine, and public health 2019, 2019, 26–34.\n34. Sohail, M.; Maier, R.M.; Ganna, A.; Bloemendal, A.; Martin, A.R.; Turchin, M.C.; Chiang, C.W.; Hirschhorn, J.; Daly, M.J.;\nPatterson, N.; Neale, B.; Mathieson, I.; Reich, D.; Sunyaev, S.R. Polygenic adaptation on height is overestimated due to\nuncorrected stratification in genome-wide association studies. Elife 2019, 8, e39702.\n35. Barton, N.; Hermisson, J.; Nordborg, M. Population genetics: Why structure matters. Elife 2019, 8, e45380.\n36. Berg, J.J.; Harpak, A.; Sinnott-Armstrong, N.; Joergensen, A.M.; Mostafavi, H.; Field, Y.; Boyle, E.A.; Zhang, X.; Racimo, F.;\nPritchard, J.K.; others. Reduced signal for polygenic adaptation of height in UK Biobank. Elife 2019, 8, e39725.\n37. Wray, N.R.; Kemper, K.E.; Hayes, B.J.; Goddard, M.E.; Visscher, P .M. Complex trait prediction from genome data: contrasting\nEBV in livestock to PRS in humans: genomic prediction. Genetics 2019, 211, 1131–1141.\n38. Bitarello, B.D.; Mathieson, I. Polygenic scores for height in admixed populations. G3: Genes, Genomes, Genetics 2020, 10, 4027–4036.\n39. Trochet, H.; Hussin, J. Fine-scale population structure confounds genetic risk scores in the ascertainment population. bioRxiv\n2020.\n40. Refoyo-Martínez, A.; Liu, S.; Jørgensen, A.M.; Jin, X.; Albrechtsen, A.; Martin, A.R.; Racimo, F. How robust are cross-population\nsignatures of polygenic adaptation in humans? BioRxiv 2021, pp. 2020–07.\n41. Lello, L.; Avery, S.G.; Tellier, L.; Vazquez, A.I.; de los Campos, G.; Hsu, S.D. Accurate genomic prediction of human height.\nGenetics 2018, 210, 477–497. [PMC6216598].\n42. Yong, S.Y.; Raben, T.G.; Lello, L.; Hsu, S.D. Genetic Architecture of Complex Traits and Disease Risk Predictors. Scientific Reports\n2020, 10. [PMC7374622].\n43. Lello, L.; Raben, T.G.; Hsu, S.D.H. Sibling validation of polygenic risk scores and complex trait prediction. Scientific Reports 2020,\n10, 13190. [PMC7411027], doi:10.1038/s41598-020-69927-7.\n44. Raben, T.G.; Lello, L.; Widen, E.; Hsu, S.D.H. From Genotype to Phenotype: polygenic prediction of complex human traits, 2021,\n[arXiv:q-bio.GN/2101.05870].\n45. Privé, F.; Aschard, H.; Blum, M. Efficient Implementation of Penalized Regression for Genetic Risk Prediction. Genetics 2019,\n212, 65–74.\n46. Wand, H.; Lambert, S.A.; Tamburro, C.; Iacocca, M.A.; O’Sullivan, J.W.; Sillari, C.; Kullo, I.J.; Rowley, R.; Dron, J.S.; Brockman, D.;\nVenner, E.; McCarthy, M.I.; Antoniou, A.C.; Easton, D.F.; Hegele, R.A.; Khera, A.V .; Chatterjee, N.; Kooperberg, C.; Edwards, K.;\nVlessis, K.; Kinnear, K.; Danesh, J.N.; Parkinson, H.; Ramos, E.M.; Roberts, M.C.; Ormond, K.E.; Khoury, M.J.; Janssens, A.C.J.;\nGoddard, K.A.; Kraft, P .; MacArthur, J.A.; Inouye, M.; Wojcik, G.L. Improving reporting standards for polygenic scores in risk\nprediction studies, 2020. doi:10.1101/2020.04.23.20077099.\n47. Carlson, C.S.; Matise, T.C.; North, K.E.; Haiman, C.A.; Fesinmeyer, M.D.; Buyske, S.; Schumacher, F.R.; Peters, U.; Franceschini, N.;\nRitchie, M.D.; Duggan, D.J.; Spencer, K.L.; Dumitrescu, L.; Eaton, C.B.; Thomas, F.; Young, A.; Carty, C.; Heiss, G.; Le Marchand,\nL.; Crawford, D.C.; Hindorff, L.A.; Kooperberg, C.L.; for the PAGE Consortium. Generalization and Dilution of Association\nResults from European GWAS in Populations of Non-European Ancestry: The PAGE Study. PLOS Biology\n2013, 11, 1–11.\ndoi:10.1371/journal.pbio.1001661.\n48. Martin, A.R.; Gignoux, C.R.; Walters, R.K.; Wojcik, G.L.; Neale, B.M.; Gravel, S.; Daly, M.J.; Bustamante, C.D.; Kenny, E.E. Human\ndemographic history impacts genetic risk prediction across diverse populations. The American Journal of Human Genetics 2017,\n100, 635–649.\n49. Huang, H.; Ruan, Y.; Feng, Y.C.A.; Chen, C.Y.; Lam, M.; Sawa, A.; Martin, A.; Qin, S.; Ge, T. Improving Polygenic Prediction in\nAncestrally Diverse Populations.\n50. Privé, F.; Aschard, H.; Carmi, S.; Folkersen, L.; Hoggart, C.; O’Reilly, P .F.; Vilhjálmsson, B.J. High-resolution portability of 245\npolygenic scores when derived and applied in the same cohort. medRxiv 2021.\n51. Tibshirani, R. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological) 1996,\n58, 267–288.\n52. Donoho, D.L.; Tanner, J. Sparse nonnegative solution of underdetermined linear equations by linear programming. Proceedings of\nthe National Academy of Sciences 2005, 102, 9446–9451. doi:10.1073/pnas.0502269102.\n53. Donoho, D.; Stodden, V . Breakdown Point of Model Selection When the Number of Variables Exceeds the Number of Observations.\nThe 2006 IEEE International Joint Conference on Neural Network Proceedings. IEEE, 2006. doi:10.1109/ijcnn.2006.246934.\n54. Donoho, D.L.; Maleki, A.; Montanari, A. Message-passing algorithms for compressed sensing. Proceedings of the National Academy\nof Sciences 2009, 106, 18914–18919. doi:10.1073/pnas.0909892106.\n55. Donoho, D.L.; Tanner, J. Precise Undersampling Theorems.Proceedings of the IEEE2010, 98, 913–924. doi:10.1109/jproc.2010.2045630.\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n19 of 20\n56. Wertz, J.; Moffitt, T.E.; Agnew-Blais, J.; Arseneault, L.; Belsky, D.W.; Corcoran, D.L.; Houts, R.; Matthews, T.; Prinz, J.A.;\nRichmond-Rakerd, L.S.; others. Using DNA from mothers and children to study parental investment in children’s educational\nattainment. Child development 2019, 00, 1–17.\n57. Kong, A.; Thorleifsson, G.; Frigge, M.L.; Vilhjalmsson, B.J.; Young, A.I.; Thorgeirsson, T.E.; Benonisdottir, S.; Oddsson, A.;\nHalldorsson, B.V .; Masson, G.; others. The nature of nurture: Effects of parental genotypes. Science 2018, 359, 424–428.\n58. Bates, T.C.; Maher, B.S.; Medland, S.E.; McAloney, K.; Wright, M.J.; Hansell, N.K.; Kendler, K.S.; Martin, N.G.; Gillespie, N.A.\nThe nature of nurture: Using a virtual-parent design to test parenting effects on children’s educational attainment in genotyped\nfamilies. Twin Research and Human Genetics 2018, 21, 73–83.\n59. Belsky, D.W.; Domingue, B.W.; Wedow, R.; Arseneault, L.; Boardman, J.D.; Caspi, A.; Conley, D.; Fletcher, J.M.; Freese, J.; Herd, P .;\nothers. Genetic analysis of social-class mobility in five longitudinal studies. Proceedings of the National Academy of Sciences 2018,\n115, E7275–E7284.\n60. Trejo, S.; Domingue, B.W. Genetic nature or genetic nurture? Introducing social genetic parameters to quantify bias in polygenic\nscore analyses. Biodemography and Social Biology 2018, 64, 187–215.\n61. Boerwinkle, E.; Leffert, C.C.; Lin, J.; Lackner, C.; Chiesa, G.; Hobbs, H.H.; others. Apolipoprotein (a) gene accounts for greater\nthan 90% of the variation in plasma lipoprotein (a) concentrations. The Journal of clinical investigation 1992, 90, 52–60.\n62. Kraft, H.; Köchl, S.; Menzel, H.; Sandholzer, C.; Utermann, G. The apolipoprotein (a) gene: a transcribed hypervariable locus\ncontrolling plasma lipoprotein (a) concentration. Human genetics 1992, 90, 220–230.\n63. Austin, M.; Sandholzer, C.; Selby, J.; Newman, B.; Krauss, R.; Utermann, G. Lipoprotein (a) in women twins: heritability and\nrelationship to apolipoprotein (a) phenotypes. American journal of human genetics 1992, 51, 829.\n64. Rao, F.; Schork, A.J.; Maihofer, A.X.; Nievergelt, C.M.; Marcovina, S.M.; Miller, E.R.; Witztum, J.L.; O’Connor, D.T.; Tsimikas,\nS. Heritability of biomarkers of oxidized lipoproteins: twin pair study. Arteriosclerosis, thrombosis, and vascular biology 2015,\n35, 1704–1711.\n65. Frank, S.L.; Klisak, I.; Sparkes, R.S.; Mohandas, T.; Tomlinson, J.E.; McLean, J.W.; Lawn, R.M.; Lusis, A.J. The apolipoprotein (a)\ngene resides on human chromosome 6q26–27, in close proximity to the homologous gene for plasminogen. Human genetics 1988,\n79, 352–356.\n66. Drayna, D.T.; Hegele, R.A.; Hass, P .E.; Emi, M.; Wu, L.L.; Eaton, D.L.; Lawn, R.M.; Williams, R.R.; White, R.L.; Lalouel, J.M.\nGenetic linkage between lipoprotein (a) phenotype and a DNA polymorphism in the plasminogen gene. Genomics 1988,\n3, 230–236.\n67. Lindahl, G.; Gersdorf, E.; Menzel, H.J.; Duba, C.; Cleve, H.; Humphries, S.; Utermann, G. The gene for the Lp (a)-specific\nglycoprotein is closely linked to the gene for plasminogen on chromosome 6. Human genetics 1989, 81, 149–152.\n68. Clarke, R.; Peden, J.F.; Hopewell, J.C.; Kyriakou, T.; Goel, A.; Heath, S.C.; Parish, S.; Barlera, S.; Franzosi, M.G.; Rust, S.;\nothers. Genetic variants associated with Lp (a) lipoprotein level and coronary disease. New England Journal of Medicine\n2009,\n361, 2518–2528.\n69. Tsimikas, S.; Hall, J.L. Lipoprotein (a) as a potential causal genetic risk factor of cardiovascular disease: a rationale for increased\nefforts to understand its pathophysiology and develop targeted therapies. Journal of the American College of Cardiology 2012,\n60, 716–721.\n70. Nikpay, M.; Goel, A.; Won, H.H.; Hall, L.M.; Willenborg, C.; Kanoni, S.; Saleheen, D.; Kyriakou, T.; Nelson, C.P .; Hopewell,\nJ.C.; others. A comprehensive 1000 Genomes–based genome-wide association meta-analysis of coronary artery disease. Nature\ngenetics 2015, 47, 1121.\n71. Kettunen, J.; Demirkan, A.; Würtz, P .; Draisma, H.H.; Haller, T.; Rawal, R.; Vaarhorst, A.; Kangas, A.J.; Lyytikäinen, L.P .; Pirinen,\nM.; others. Genome-wide study for circulating metabolites identifies 62 loci and reveals novel systemic effects of LPA. Nature\ncommunications 2016, 7, 1–9.\n72. Mack, S.; Coassin, S.; Rueedi, R.; Yousri, N.A.; Seppälä, I.; Gieger, C.; Schönherr, S.; Forer, L.; Erhart, G.; Marques-Vidal, P .; others.\nA genome-wide association meta-analysis on lipoprotein (a) concentrations adjusted for apolipoprotein (a) isoforms. Journal of\nlipid research 2017, 58, 1834–1844.\n73. Schmidt, K.; Kraft, H.G.; Parson, W.; Utermann, G. Genetics of the Lp (a)/apo (a) system in an autochthonous Black African\npopulation from the Gabon. European journal of human genetics 2006, 14, 190–201.\n74. Hoekstra, M.; Chen, H.Y.; Rong, J.; Dufresne, L.; Yao, J.; Guo, X.; Tsai, M.Y.; Tsimikas, S.; Post, W.S.; Vasan, R.S.; others. Genome-\nwide association study highlights APOH as a novel locus for lipoprotein (a) levels—brief report. Arteriosclerosis, Thrombosis, and\nVascular Biology 2021, 41, 458–464.\n75. Schmidt, K.; Noureen, A.; Kronenberg, F.; Utermann, G. Structure, function, and genetics of lipoprotein (a). Journal of lipid research\n2016, 57, 1339–1359.\n76. Buniello, A.; MacArthur, J.A.L.; Cerezo, M.; Harris, L.W.; Hayhurst, J.; Malangone, C.; McMahon, A.; Morales, J.; Mountjoy,\nE.; Sollis, E.; Suveges, D.; Vrousgou, O.; Whetzel, P .L.; Amode, R.; Guillen, J.A.; Riat, H.S.; Trevanion, S.J.; Hall, P .; Junkins, H.;\nFlicek, P .; Burdett, T.; Hindorff, L.A.; Cunningham, F.; Parkinson, H. The NHGRI-EBI GWAS Catalog of published genome-wide\nassociation studies, targeted arrays and summary statistics 2019. Nucleic acids research 2019, 47, D1005–D1012.\n77. Coltell, O.; Asensio, E.M.; Sorlí, J.V .; Barragán, R.; Fernández-Carrión, R.; Portolés, O.; Ortega-Azorín, C.; Martínez-Lacruz, R.;\nGonzález, J.I.; Zanón-Moreno, V .; Gimenez-Alba, I.; Fitó, M.; Ros, E.; Ordovas, J.M.; Corella, D. Genome-wide association study\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted April 5, 2021. ; https://doi.org/10.1101/2021.04.01.21254711doi: medRxiv preprint \n\n20 of 20\n(GWAS) on bilirubin concentrations in subjects with metabolic syndrome: Sex-specific gwas analysis and gene-diet interactions\nin a mediterranean population. Nutrients 2019, 11. doi:10.3390/nu11010090.\n78. Bielinski, S.J.; Chai, H.S.; Pathak, J.; Talwalkar, J.A.; Limburg, P .J.; Gullerud, R.E.; Sicotte, H.; Klee, E.W.; Ross, J.L.; Kocher, J.P .A.;\nKullo, I.J.; Heit, J.A.; Petersen, G.M.; De Andrade, M.; Chute, C.G. Mayo genome consortia: A genotype-phenotype resource for\ngenome-wide association studies with an application to the analysis of circulating bilirubin levels. Mayo Clinic Proceedings 2011,\n86. doi:10.4065/mcp.2011.0178.\n79. Kathiresan, S.; Manning, A.K.; Demissie, S.; D’Agostino, R.B.; Surti, A.; Guiducci, C.; Gianniny, L.; Burtt, N.P .; Melander, O.;\nOrho-Melander, M.; Arnett, D.K.; Peloso, G.M.; Ordovas, J.M.; Cupples, L.A. A genome-wide association study for blood lipid\nphenotypes in the Framingham Heart Study. BMC Medical Genetics 2007, 8. doi:10.1186/1471-2350-8-S1-S17.\n80. Martin, A.R.; Kanai, M.; Kamatani, Y.; Okada, Y.; Neale, B.M.; Daly, M.J. Clinical use of current polygenic risk scores may\nexacerbate health disparities. Nature genetics 2019, 51, 584. PMC6563838.\n81. Loos, R.J.; Yeo, G.S. The bigger picture of FTO—the first GWAS-identified obesity gene. Nature Reviews Endocrinology 2014,\n10, 51–61.\n82. Vattikuti, S.; Lee, J.J.; Chang, C.C.; Hsu, S.D.; Chow, C.C. Applying compressed sensing to genome-wide association studies.\nGigaScience 2014, 3, 2047–217X.\n83. Van Rossum, G.; Drake, F.L. Python 3 Reference Manual; CreateSpace: Scotts Valley, CA, 2009.\n84. Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V .; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P .; Weiss, R.; Dubourg, V .;\nVanderplas, J.; Passos, A.; Cournapeau, D.; Brucher, M.; Perrot, M.; Duchesnay, E. Scikit-learn: Machine Learning in Python.\nJournal of Machine Learning Research 2011, 12, 2825–2830.\n85. Chang, C.C.; Chow, C.C.; Tellier, L.C.; Vattikuti, S.; Purcell, S.M.; Lee, J.J. Second-generation PLINK: rising to the challenge of\nlarger and richer datasets. Gigascience 2015, 4, s13742–015. PMC4342193.\n86. Horta, D. Pandas-Plink. Available online: https://pypi.org/project/pandas-plink/ (accessed on 29-03-2021).\n87. Kadie, C.M. PySNPTools. Available online: https://pypi.org/project/pysnptools/ (accessed on 30-03-2021).\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 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