In precision medicine, both predicting the disease susceptibility of an individual and forecasting its disease-free survival are areas of key research. Besides the classical epidemiological predictor variables, data from multiple (omic) platforms are increasingly available. To integrate this wealth of information, we propose new methodology to combine both cooperative learning, a recent approach to leverage the predictive power of several datasets, and polygenic hazard score models. Polygenic hazard score models provide a practitioner with a more differentiated view of the predicted disease-free survival than the one given by merely a point estimate, for instance computed with a polygenic risk score. Our aim is to leverage the advantages of cooperative learning for the computation of polygenic hazard score models via Cox's proportional hazard model, thereby improving the prediction of the disease-free survival. In our experimental study, we apply our methodology to forecast the disease-free survival for Alzheimer's disease (AD) using three layers of data. One layer contains epidemiological variables such as sex, APOE (apolipoprotein E, a genetic risk factor for AD) status and 10 leading principal components. Another layer contains selected genomic loci, and the last layer contains methylation data for selected CpG sites. We demonstrate that the survival curves computed via cooperative learning yield an AUC of around $0.7$, above the state-of-the-art performance of its competitors. Importantly, the proposed methodology returns (1) a linear score that can be easily interpreted (in contrast to machine learning approaches), and (2) a weighting of the predictive power of the involved data layers, allowing for an assessment of the importance of each omic (or other) platform. Similarly to polygenic hazard score models, our methodology also allows one to compute individual survival curves for each patient.

The computation of a similarity measure for genomic data is a standard tool in computational genetics. The principal components of such matrices are routinely used to correct for biases due to confounding by population stratification, for instance in linear regressions. However, the calculation of both a similarity matrix and its singular value decomposition (SVD) are computationally intensive. The contribution of this article is threefold. First, we demonstrate that the calculation of three matrices (called the covariance matrix, the weighted Jaccard matrix, and the genomic relationship matrix) can be reformulated in a unified way which allows for the application of a randomized SVD algorithm, which is faster than the traditional computation. The fast SVD algorithm we present is adapted from an existing randomized SVD algorithm and ensures that all computations are carried out in sparse matrix algebra. The algorithm only assumes that row-wise and column-wise subtraction and multiplication of a vector with a sparse matrix is available, an operation that is efficiently implemented in common sparse matrix packages. An exception is the so-called Jaccard matrix, which does not have a structure applicable for the fast SVD algorithm. Second, an approximate Jaccard matrix is introduced to which the fast SVD computation is applicable. Third, we establish guaranteed theoretical bounds on the accuracy (in [Formula: see text] norm and angle) between the principal components of the Jaccard matrix and the ones of our proposed approximation, thus putting the proposed Jaccard approximation on a solid mathematical foundation, and derive the theoretical runtime of our algorithm. We illustrate that the approximation error is low in practice and empirically verify the theoretical runtime scalings on both simulated data and data of the 1000 Genome Project.

Genetic similarity matrices are commonly used to assess population substructure (PS) in genetic studies. Through simulation studies and by the application to whole-genome sequencing (WGS) data, we evaluate the performance of three genetic similarity matrices: the unweighted and weighted Jaccard similarity matrices and the genetic relationship matrix. We describe different scenarios that can create numerical pitfalls and lead to incorrect conclusions in some instances. We consider scenarios in which PS is assessed based on loci that are located across the genome ('globally') and based on loci from a specific genomic region ('locally'). We also compare scenarios in which PS is evaluated based on loci from different minor allele frequency bins: common (>5%), low-frequency (5-0.5%) and rare (<0.5%) single-nucleotide variations (SNVs). Overall, we observe that all approaches provide the best clustering performance when computed based on rare SNVs. The performance of the similarity matrices is very similar for common and low-frequency variants, but for rare variants, the unweighted Jaccard matrix provides preferable clustering features. Based on visual inspection and in terms of standard clustering metrics, its clusters are the densest and the best separated in the principal component analysis of variants with rare SNVs compared with the other methods and different allele frequency cutoffs. In an application, we assessed the role of rare variants on local and global PS, using WGS data from multiethnic Alzheimer's disease data sets and European or East Asian populations from the 1000 Genome Project.

As of June 2022, the GISAID database contains more than 11 million SARS-CoV-2 genomes, including several thousand nucleotide sequences for the most common variants such as delta or omicron. These SARS-CoV-2 strains have been collected from patients around the world since the beginning of the pandemic. We start by assessing the similarity of all pairs of nucleotide sequences using the Jaccard index and principal component analysis. As shown previously in the literature, an unsupervised cluster analysis applied to the SARS-CoV-2 genomes results in clusters of sequences according to certain characteristics such as their strain or their clade. Importantly, we observe that nucleotide sequences of common variants are often outliers in clusters of sequences stemming from variants identified earlier on during the pandemic. Motivated by this finding, we are interested in applying outlier detection to nucleotide sequences. We demonstrate that nucleotide sequences of common variants (such as alpha, delta, or omicron) can be identified solely based on a statistical outlier criterion. We argue that outlier detection might be a useful surveillance tool to identify emerging variants in real time as the pandemic progresses.

MOTIVATION: Analysis of rare variants in family-based studies remains a challenge. Transmission-based approaches provide robustness against population stratification, but the evaluation of the significance of test statistics based on asymptotic theory can be imprecise. Also, power will depend heavily on the choice of the test statistic and on the underlying genetic architecture of the locus, which will be generally unknown. RESULTS: In our proposed framework, we utilize the FBAT haplotype algorithm to obtain the conditional offspring genotype distribution under the null hypothesis given the sufficient statistic. Based on this conditional offspring genotype distribution, the significance of virtually any association test statistic can be evaluated based on simulations or exact computations, without the need for asymptotic approximations. Besides standard linear burden-type statistics, this enables our approach to also evaluate other test statistics such as variance components statistics, higher criticism approaches, and maximum-single-variant-statistics, where asymptotic theory might be involved or does not provide accurate approximations for rare variant data. Based on these P-values, combined test statistics such as the aggregated Cauchy association test (ACAT) can also be utilized. In simulation studies, we show that our framework outperforms existing approaches for family-based studies in several scenarios. We also applied our methodology to a TOPMed whole-genome sequencing dataset with 897 asthmatic trios from Costa Rica. AVAILABILITY AND IMPLEMENTATION: FBAT software is available at https://sites.google.com/view/fbatwebpage. Simulation code is available at https://github.com/julianhecker/FBAT_rare_variant_test_simulations. Whole-genome sequencing data for 'NHLBI TOPMed: The Genetic Epidemiology of Asthma in Costa Rica' is available at https://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?study_id=phs000988.v4.p1. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Population stratification is one of the major sources of confounding in genetic association studies, potentially causing false-positive and false-negative results. Here, we present a novel approach for the identification of population substructure in high-density genotyping data/next generation sequencing data. The approach exploits the co-appearances of rare genetic variants in individuals. The method can be applied to all available genetic loci and is computationally fast. Using sequencing data from the 1000 Genomes Project, the features of the approach are illustrated and compared to existing methodology (i.e. EIGENSTRAT). We examine the effects of different cutoffs for the minor allele frequency on the performance of the approach. We find that our approach works particularly well for genetic loci with very small minor allele frequencies. The results suggest that the inclusion of rare-variant data/sequencing data in our approach provides a much higher resolution picture of population substructure than it can be obtained with existing methodology. Furthermore, in simulation studies, we find scenarios where our method was able to control the type 1 error more precisely and showed higher power. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.