OBJECTIVE: To develop a distributed algorithm to fit multi-center Cox regression models with time-varying coefficients to facilitate privacy-preserving data integration across multiple health systems. MATERIALS AND METHODS: The Cox model with time-varying coefficients relaxes the proportional hazards assumption of the usual Cox model and is particularly useful to model time-to-event outcomes. We proposed a One-shot Distributed Algorithm to fit multi-center Cox regression models with Time varying coefficients (ODACT). This algorithm constructed a surrogate likelihood function to approximate the Cox partial likelihood function, using patient-level data from a lead site and aggregated data from other sites. The performance of ODACT was demonstrated by simulation and a real-world study of opioid use disorder (OUD) using decentralized data from a large clinical research network across 5 sites with 69 163 subjects. RESULTS: The ODACT method precisely estimated the time-varying effects over time. In the simulation study, ODACT always achieved estimation close to that of the pooled analysis, while the meta-estimator showed considerable amount of bias. In the OUD study, the bias of the estimated hazard ratios by ODACT are smaller than those of the meta-estimator for all 7 risk factors at almost all of the time points from 0 to 2.5 years. The greatest bias of the meta-estimator was for the effects of age ≥65 years, and smoking. CONCLUSION: ODACT is a privacy-preserving and communication-efficient method for analyzing multi-center time-to-event data which allows the covariates' effects to be time-varying. ODACT provides estimates close to the pooled estimator and substantially outperforms the meta-analysis estimator. DISCUSSION: The proposed ODACT is a privacy-preserving distributed algorithm for fitting Cox models with time-varying coefficients. The limitations of ODACT include that privacy-preserving via aggregate data does rely on relatively large number of data at each individual site, and rigorous quantification of the risk of privacy leaks requires further investigation.

Data in large-scale genetic studies of complex human diseases, such as substance use disorders, are often incomplete. Despite great progress in genotype imputation, e.g., the IMPUTE2 method, considerably less progress has been made in inferring phenotypes. We designed a novel approach to integrate individuals' comorbid conditions with their genotype data to infer missing (unreported) diagnostic criteria of a disorder. The premise of our approach derives from correlations among symptoms and the shared biological bases of concurrent disorders such as co-dependence on cocaine and opioids. We describe a matrix completion method to construct a bi-linear model based on the interactions of genotypes and known symptoms of related disorders to infer unknown values of another set of symptoms or phenotypes. An efficient stochastic and parallel algorithm based on the linearized alternating direction method of multipliers was developed to solve the proposed optimization problem. Empirical evaluation of the approach in comparison with other advanced data matrix completion methods via a case study shows that it both significantly improves imputation accuracy and provides greater computational efficiency.

An important approach to reducing missing heritability and enhancing success of genome-wide association studies (GWAS) for complex diseases is the identification of traits that are highly heritable and homogeneous in their etiology. Many approaches have been proposed to define such traits based on either cluster analysis or pedigree-based heritable component analysis. None of the existing methods, however, exploit the dense genome-wide genotypic data that are now readily available from GWAS, and with exome and whole genome sequencing more data will be available in the future. Moreover, because a phenotype can vary with respect to a covariate, such as age or race. The fixed effect due to the covariates may lead to a spuriously elevated estimate of heritability. Existing heritable component analysis methods have not considered covariate effects. We propose an optimization approach to identify composite traits with high heritability as a function of multiple phenotypic variables where heritability is estimated from genome-wide single neucleotide polymorphisms (SNPs). Our approach can model the covariate effects within heritability analysis. The proposed optimization problem can be efficiently solved by a sequential quadratic programming algorithm. A case study demonstrates the effectiveness of the proposed approach for finding composite traits with high SNP-based heritability.

Background Many quantitative trait loci (QTL) influencing mouse model phenotypes for alcoholism have been mapped genetically. However, the gene(s) comprising the QTL (QTG) are largely unknown. In previous work, Bennett and colleagues created congenic strains carrying the DBA/2IBG (D2) region for alcohol preference (AP) on chromosome 2, on a C57BL/6IBG (B6) background [1]. Subsequently, interval specific congenic recombinant strains (ISCRS), in which the full D2 QTL region was broken into smaller, partially overlapping regions of introgression, were generated and tested. With information from two ISCRS, the QTL has been mapped onto mouse chromosome 2 (Chr2) in a region of 3.4Mb by using C57BL/6J (B6) x DBA/2J (D2) recombinant inbred (RI) strains as well as by using F2 populations. Several candidate genes, Gad1, Atp5g3, Atf2, Sp3 and Sp9, have been evaluated but none of them has been confirmed for a definitive role in the regulation of the QTL of AP on Chr2 [2,3].

Genetic association analysis of complex diseases has been limited by heterogeneity in their clinical manifestations and genetic etiology. Research has made it possible to differentiate homogeneous subtypes of the disease phenotype. Currently, the most sophisticated subtyping methods perform unsupervised cluster analysis using only clinical features of a disorder, resulting in subtypes for which genetic association may be limited. In this study, we seek to derive a novel multiview data analytic method that integrates two views of the data: the clinical features and the genetic markers of the same set of patients. Our method is based on multiobjective programming that is capable of clinically categorizing a disease phenotype so as to discover genetically different subtypes.We optimize two objectives jointly: 1) in cluster analysis, the derived clusters should differ significantly in clinical features; 2) these clusters can be well separated using genetic markers by constructed classifiers. Extensive computational experiments with two substance-use disorders using two populations show that the proposed algorithm is superior to existing subtyping methods.

Complex disorders exhibit great heterogeneity in both clinical manifestation and genetic etiology. This heterogeneity substantially limits the identification of geneotype-phenotype associations. Differentiating homogeneous subtypes of a complex phenotype will enable the detection of genetic variants contributing to the effect of subtypes that cannot be detected by the non-differentiated phenotype. However, the most sophisticated subtyping methods available so far perform unsupervised cluster analysis or latent class analysis on only phenotypic features. Without guidance from the genetic dimension, the resultant subtypes can be suboptimal and genetic associations may fail. We propose a multi-view biclustering approach that integrates phenotypic features and genetic markers to detect confirming evidence in the two views for a disease subtype. This approach groups subjects in clusters that are consistent between the phenotypic and genetic views, and simultaneously identifies the phenotypic features that are used to define a subtype and the genotypes that are associated with the subtype. Our simulation study validates this approach, and our extensive comparison with several biclustering and multi-view data analytics on real-life disease data demonstrates the superior performance of the proposed approach.

Identifying genetic variation underlying a complex disease is important. Many complex diseases have heterogeneous phenotypes and are products of a variety of genetic and environmental factors acting in concert. Deriving highly heritable quantitative traits of a complex disease can improve the identification of genetic risk of the disease. The most sophisticated methods so far perform unsupervised cluster analysis on phenotypic features; and then a quantitative trait is derived based on each resultant cluster. Heritability is estimated to assess the validity of the derived quantitative traits. However, none of these methods explicitly maximize the heritability of the derived traits. We propose a quadratic optimization approach that directly utilizes heritability as an objective during the derivation of quantitative traits of a disease. This method maximizes an objective function that is formulated by decomposing the traditional maximum likelihood method for estimating heritability of a quantitative trait. We demonstrate the effectiveness of the proposed method on both synthetic data and real-world problems. We apply our algorithm to identify highly heritable traits of complex human-behavior disorders including opioid and cocaine use disorders, and highly heritable traits of dairy cattle that are economically important. Our approach outperforms standard cluster analysis and several previous methods.

Identifying genetic variations that underlie human disease is very important to advance our understanding of the disease's pathophysiology and promote its personalized treatment. However, many disease phenotypes have complex clinical manifestations and a complicated etiology. Gene finding efforts for complex diseases have had limited success to date. Research results suggest that one way to enhance these efforts is to differentiate subtypes of a complex multifactorial disease phenotype. Existing subtyping methods rely on cluster analysis using only clinical features of a disorder without guidance from genetic data, resulting in subtypes for which genotype association may be limited. In this work, we seek to derive a novel computational method based on multi-objective programming that is capable of clinically categorizing a disease phenotype so as to discover genetically different subtypes. Our approach optimizes two objectives: (1) the cluster-derived subtypes should differ significantly on clinical features; (2) these subtypes can be well separated using candidate genes. This work has been motivated by clinical studies of opioid dependence, a serious, prevalent disorder that is heterogeneous phenotypically. Analyses on a sample of 1,470 European American subjects aggregated from multiple genetic studies of opioid dependence show that the proposed algorithm is superior to existing subtyping methods.

SUMMARY: Genotype calling from high-throughput platforms such as Illumina and Affymetrix is a critical step in data processing, so that accurate information on genetic variants can be obtained for phenotype-genotype association studies. A number of algorithms have been developed to infer genotypes from data generated through the Illumina BeadStation platform, including GenCall, GenoSNP, Illuminus and CRLMM. Most of these algorithms are built on population-based statistical models to genotype every SNP in turn, such as GenCall with the GenTrain clustering algorithm, and require a large reference population to perform well. These approaches may not work well for rare variants where only a small proportion of the individuals carry the variant. A fundamentally different approach, implemented in GenoSNP, adopts a single nucleotide polymorphism (SNP)-based model to infer genotypes of all the SNPs in one individual, making it an appealing alternative to call rare variants. However, compared to the population-based strategies, more SNPs in GenoSNP may fail the Hardy-Weinberg Equilibrium test. To take advantage of both strategies, we propose a two-stage SNP calling procedure, named the modified mixture model (M(3)), to improve call accuracy for both common and rare variants. The effectiveness of our approach is demonstrated through applications to genotype calling on a set of HapMap samples used for quality control purpose in a large case-control study of cocaine dependence. The increase in power with M(3) is greater for rare variants than for common variants depending on the model. AVAILABILITY: M(3) algorithm: http://bioinformatics.med.yale.edu/group. CONTACT: [email protected]; [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.