imPhy: Imputing Phylogenetic Trees with Missing Information Using Mathematical Programming.

Advances in modern genomics have allowed researchers to apply phylogenetic analyses on a genome-wide scale. While large volumes of genomic data can be generated cheaply and quickly, data missingness is a non-trivial and somewhat expected problem. Since the available information is often incomplete for a given set of genetic loci and individual organisms, a large proportion of trees that depict the evolutionary history of a single genetic locus, called gene trees, fail to contain all individuals. Data incompleteness causes difficulties in data collection, information extraction, and gene tree inference. Furthermore, identifying outlying gene trees, which can represent horizontal gene transfers, gene duplications, or hybridizations, is difficult when data is missing from the gene trees. The typical approach is to remove all individuals with missing data from the gene trees, and focus the analysis on individuals whose information is fully available - a huge loss of information. In this work, we propose and design an optimization-based imputation approach to infer the missing distances between leaves in a set of gene trees via a mixed integer non-linear programming model. We also present a new research pipeline, imPhy, that can (i) simulate a set of gene trees with leaves randomly missing in each tree, (ii) impute the missing pairwise distances in each gene tree, (iii) reconstruct the gene trees using the Neighbor Joining (NJ) and Unweighted Pair Group Method with Arithmetic Mean (UPGMA) methods, and (iv) analyze and report the efficiency of the reconstruction. To impute the missing leaves, we employ our newly proposed non-linear programming framework, and demonstrate its capability in reconstructing gene trees with incomplete information in both simulated and empirical datasets. In the empirical datasets apicomplexa and lungfish, our imputation has very small normalized mean square errors, even in the extreme case where 50 percent of the individuals in each gene tree are missing. Data, software, and user manuals can be found at https://github.com/yasuiniko/imPhy.

Association of LPA Variants With Aortic Stenosis: A Large-Scale Study Using Diagnostic and Procedural Codes From Electronic Health Records.

Importance: Elevated lipoprotein(a) levels are a risk factor for aortic stenosis (AS). However, a large-scale replication of associations between LPA variants and AS, their interactions with risk factors, and the effect of multiple risk alleles is not well established. Objective: To replicate the association between LPA variants with AS and identify subgroups who are at higher risk of developing AS. Design, Setting, and Participants: This case-control study of AS included 44 703 individuals (3469 cases) 55 years or older who were enrolled in the Genetic Epidemiology Research on Aging cohort and who were members of the Kaiser Permanente Northern California health care delivery system. The study leveraged the linkage of administrative health data, electronic medical records, genotypes, and self-reported questionnaire data. The 3469 AS cases were diagnosed between January 1996 and December 2015. Individuals with congential valvular heart disease were excluded. Exposures: Two single-nucleotide polymorphisms in the LPA locus, rs10455872 and rs3798220, that are known to associate with circulating plasma lipoprotein(a) levels and an LPA risk score. Main Outcomes and Measures: Aortic stenosis or aortic valve replacement. Results: The 44 703 participants were of European ancestry,of whom 22 019 (49.3%) were men. The mean (SD) age for the control group was 69.3 (8.3) years and the mean (SD) age for AS cases was 74.6 (8.5) years. Both LPA variants were associated with AS, with a per risk allele odds ratio of 1.34 (95% CI, 1.23-1.47; P = 1.7 × 10-10) for rs10455872 and 1.31 (95% CI, 1.09-1.58; P = 3.6 × 10-3) for rs3798220 after adjusting for age, age2, and sex. The results remained significant after adjusting for risk factors. The estimates were similar for an LPA risk score. Individuals with 2 risk alleles had a 2-fold or greater odds of AS compared with individuals with no risk alleles (for rs10455872, homozygous odds ratio, 2.05; 95% CI, 1.37-3.07; P = 5.3 × 10-4; for rs3798220, homozygous odds ratio, 3.74; 95% CI, 1.03-13.62; P = .05; and for compound heterygotes, odds ratio, 2.00; 95% CI, 1.17-3.44; P = .01). For rs10455872, the odds ratio for AS was greatest in individuals aged 55 to 64 years and declined with age (interaction P = .03). Each rs10455872 risk allele was also associated with AS that was diagnosed 0.71 years earlier (95% CI, -1.42 to 0; P = .05). Conclusions and Relevance: We provide a large-scale confirmation of the association between 2 LPA variants and AS, reaching genome-wide significance. In addition, individuals with 2 risk alleles have 2-fold or greater odds of developing AS. Age may modify these associations and identify subgroups who are at greater risk of developing AS.