MOTIVATION: Researchers usually conduct statistical analyses based on models built on raw data collected from individual participants (individual-level data). There is a growing interest in enhancing inference efficiency by incorporating aggregated summary information from other sources, such as summary statistics on genetic markers' marginal associations with a given trait generated from genome-wide association studies. However, combining high-dimensional summary data with individual-level data using existing integrative procedures can be challenging due to various numeric issues in optimizing an objective function over a large number of unknown parameters. RESULTS: We develop a procedure to improve the fitting of a targeted statistical model by leveraging external summary data for more efficient statistical inference (both effect estimation and hypothesis testing). To make this procedure scalable to high-dimensional summary data, we propose a divide-and-conquer strategy by breaking the task into easier parallel jobs, each fitting the targeted model by integrating the individual-level data with a small proportion of summary data. We obtain the final estimates of model parameters by pooling results from multiple fitted models through the minimum distance estimation procedure. We improve the procedure for a general class of additive models commonly encountered in genetic studies. We further expand these two approaches to integrate individual-level and high-dimensional summary data from different study populations. We demonstrate the advantage of the proposed methods through simulations and an application to the study of the effect on pancreatic cancer risk by the polygenic risk score defined by BMI-associated genetic markers. AVAILABILITY AND IMPLEMENTATION: R package is available at https://github.com/fushengstat/MetaGIM.

Researchers are often interested in understanding the disease subtype heterogeneity by testing whether a risk exposure has the same level of effect on different disease subtypes. The polytomous logistic regression (PLR) model provides a flexible tool for such an evaluation. Disease subtype heterogeneity can also be investigated with a case-only study that uses a case-case comparison procedure to directly assess the difference between risk effects on two disease subtypes. Motivated by a large consortium project on the genetic basis of non-Hodgkin lymphoma (NHL) subtypes, we develop PolyGIM, a procedure to fit the PLR model by integrating individual-level data with summary data extracted from multiple studies under different designs. The summary data consist of coefficient estimates from working logistic regression models established by external studies. Examples of the working model include the case-case comparison model and the case-control comparison model, which compares the control group with a subtype group or a broad disease group formed by merging several subtypes. PolyGIM efficiently evaluates risk effects and provides a powerful test for disease subtype heterogeneity in situations when only summary data, instead of individual-level data, is available from external studies due to various informatics and privacy constraints. We investigate the theoretic properties of PolyGIM and use simulation studies to demonstrate its advantages. Using data from eight genome-wide association studies within the NHL consortium, we apply it to study the effect of the polygenic risk score defined by a lymphoid malignancy on the risks of four NHL subtypes. These results show that PolyGIM can be a valuable tool for pooling data from multiple sources for a more coherent evaluation of disease subtype heterogeneity.

MOTIVATION: Estimating haplotype frequencies from genotype data plays an important role in genetic analysis. In silico methods are usually computationally involved since phase information is not available. Due to tight linkage disequilibrium and low recombination rates, the number of haplotypes observed in human populations is far less than all the possibilities. This motivates us to solve the estimation problem by maximizing the sparsity of existing haplotypes. Here, we propose a new algorithm by applying the compressive sensing (CS) theory in the field of signal processing, compressive sensing haplotype inference (CSHAP), to solve the sparse representation of haplotype frequencies based on allele frequencies and between-allele co-variances. RESULTS: Our proposed approach can handle both individual genotype data and pooled DNA data with hundreds of loci. The CSHAP exhibits the same accuracy compared with the state-of-the-art methods, but runs several orders of magnitude faster. CSHAP can also handle with missing genotype data imputations efficiently. AVAILABILITY AND IMPLEMENTATION: The CSHAP is implemented in R, the source code and the testing datasets are available at http://home.ustc.edu.cn/∼zhouys/CSHAP/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

As meta-analysis results published by consortia of genome-wide association studies (GWASs) become increasingly available, many association summary statistics-based multi-locus tests have been developed to jointly evaluate multiple single-nucleotide polymorphisms (SNPs) to reveal novel genetic architectures of various complex traits. The validity of these approaches relies on the accurate estimate of z-score correlations at considered SNPs, which in turn requires knowledge on the set of SNPs assessed by each study participating in the meta-analysis. However, this exact SNP coverage information is usually unavailable from the meta-analysis results published by GWAS consortia. In the absence of the coverage information, researchers typically estimate the z-score correlations by making oversimplified coverage assumptions. We show through real studies that such a practice can generate highly inflated type I errors, and we demonstrate the proper way to incorporate correct coverage information into multi-locus analyses. We advocate that consortia should make SNP coverage information available when posting their meta-analysis results, and that investigators who develop analytic tools for joint analyses based on summary data should pay attention to the variation in SNP coverage and adjust for it appropriately.

MOTIVATION: Multivariate tests derived from the logistic regression model are widely used to assess the joint effect of multiple predictors on a disease outcome in case-control studies. These tests become less optimal if the joint effect cannot be approximated adequately by the additive model. The tree-structure model is an attractive alternative, as it is more apt to capture non-additive effects. However, the tree model is used most commonly for prediction and seldom for hypothesis testing, mainly because of the computational burden associated with the resampling-based procedure required for estimating the significance level. RESULTS: We designed a fast algorithm for building the tree-structure model and proposed a robust TREe-based Association Test (TREAT) that incorporates an adaptive model selection procedure to identify the optimal tree model representing the joint effect. We applied TREAT as a multilocus association test on >20 000 genes/regions in a study of esophageal squamous cell carcinoma (ESCC) and detected a highly significant novel association between the gene CDKN2B and ESCC ([Formula: see text]). We also demonstrated, through simulation studies, the power advantage of TREAT over other commonly used tests. AVAILABILITY AND IMPLEMENTATION: The package TREAT is freely available for download at http://www.hanzhang.name/softwares/treat, implemented in C++ and R and supported on 64-bit Linux and 64-bit MS Windows. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The multifactor-dimensionality reduction (MDR) method has been widely used in multi-locus interaction analysis. It reduces dimensionality by partitioning the multi-locus genotypes into a high-risk group and a low-risk group according to whether the genotype-specific risk ratio exceeds a fixed threshold or not. Alternatively, one can maximize the chi(2) value exhaustively over all possible ways of partitioning the multi-locus genotypes into two groups, and we aim to show that this is computationally feasible. METHODS: We advocate finding the optimal MDR (OMDR) that would have resulted from an exhaustive search over all possible ways of partitioning the multi-locus genotypes into two groups. It is shown that this optimal MDR can be obtained efficiently using an ordered combinatorial partitioning (OCP) method, which differs from the existing MDR method in the use of a data-driven rather than fixed threshold. The generalized extreme value distribution (GEVD) theory is applied to find the optimal order of gene combination and assess statistical significance of interactions. RESULTS: The computational complexity of OCP strategy is linear in the number of multi-locus genotypes in contrast with an exponential order for the naive exhaustive search strategy. Simulation studies show that OMDR can be more powerful than MDR with substantial power gain possible when the partitioning of OMDR is different from that of MDR. The analysis results of a breast cancer dataset show that the use of GEVD accelerates the determination of interaction order and reduces the time cost for P-value calculation by more than 10-fold. AVAILABILITY: C++ program is available at http://home.ustc.edu.cn/~zhanghan/ocp/ocp.html

MOTIVATION: Pooling large number of DNA samples is a common practice in association study, especially for initial screening. However, the use of expectation-maximization (EM)-type algorithms in estimating haplotype distributions for even moderate pool sizes is hampered by the computational complexity involved. A novel constrained EM algorithm called PoooL has been proposed recently to bypass the difficulty via the use of asymptotic normality of the pooled allele frequencies. The resulting estimates are, however, not maximum likelihood estimates and hence not optimal. Furthermore, the assumption of Hardy-Weinberg equilibrium (HWE) made may not be realistic in practice. METHODS: Rather than carrying out constrained maximization as in PoooL, we revert to the usual EM algorithm but make it computationally feasible by using normal approximations. The resulting algorithm is much simpler to implement than PoooL because there is no need to invoke sophisticated iterative scaling methods as in PoooL. We also develop an estimating equation analogue of the EM algorithm for the case of Hardy-Weinberg disequilibrium (HWD) by conditioning on the haplotypes of both chromosomes of the same individual. Incorporated into the method is a way of estimating the inbreeding coefficient by relating it to overdispersion. RESULTS: Simulation study assuming HWE shows that our simplified implementation of the EM algorithm leads to estimates with substantially smaller SDs than PoooL estimates. Further simulations show that ignoring HWD will induce biases in the estimates. Our extended method with estimation of inbreeding coefficient incorporated is able to reduce the bias leading to estimates with substantially smaller mean square errors. We also present results to suggest that our method can cope with a certain degree of locus-specific inbreeding as well as additional overdispersion not caused by inbreeding. AVAILABILITY: http://staff.ustc.edu.cn/ approximately ynyang/aem-aes

MOTIVATION: Pooling DNA is a cost-effective alternative to individual genotyping method. It is often used for initial screening in genome-wide association analysis. In some studies, large pools with sizes up to several hundreds were applied in order to significantly reduce genotyping cost. However, method for estimating haplotype frequencies from large DNA pools has not been available due to computational complexity involved. METHODS: We propose a novel constrained EM algorithm, PoooL, to estimate frequencies of single-nucleotide polymorphism (SNP) haplotypes from DNA pools. A quantity called importance factor is introduced to measure the contribution of a haplotype to the likelihood. Under the assumption of asymptotic normality of the estimated allele frequencies and a system of linear constraints on haplotype frequencies the importance factor remains a constant in the iterative maximization process. The maximization problem in the EM algorithm is then formulated into a constrained maximum entropy model and solved by the improved iterative scaling method. RESULTS: Simulation study shows that our algorithm can efficiently estimate haplotype frequencies from DNA pools with arbitrarily large sizes. The algorithm works equally well for large pools with sizes up to hundreds or thousands and for pools with sizes as small as one or two individuals. The computational complexity of the PoooL algorithm is independent of pool sizes, and the computational efficiency for large pools is thus substantially improved over existing estimating methods. Simulation results also show that the proposed method is robust to genotype errors and population admixture.