A non-negative spike-and-slab lasso generalized linear stacking prediction modeling method for high-dimensional omics data
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ABSTRACT:
SUBMITTER: Shen J
PROVIDER: S-EPMC10953151 | biostudies-literature | 2024 Jan
REPOSITORIES: biostudies-literature
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Project description:MotivationLarge-scale molecular data have been increasingly used as an important resource for prognostic prediction of diseases and detection of associated genes. However, standard approaches for omics data analysis ignore the group structure among genes encoded in functional relationships or pathway information.ResultsWe propose new Bayesian hierarchical generalized linear models, called group spike-and-slab lasso GLMs, for predicting disease outcomes and detecting associated genes by incorporating large-scale molecular data and group structures. The proposed model employs a mixture double-exponential prior for coefficients that induces self-adaptive shrinkage amount on different coefficients. The group information is incorporated into the model by setting group-specific parameters. We have developed a fast and stable deterministic algorithm to fit the proposed hierarchal GLMs, which can perform variable selection within groups. We assess the performance of the proposed method on several simulated scenarios, by varying the overlap among groups, group size, number of non-null groups, and the correlation within group. Compared with existing methods, the proposed method provides not only more accurate estimates of the parameters but also better prediction. We further demonstrate the application of the proposed procedure on three cancer datasets by utilizing pathway structures of genes. Our results show that the proposed method generates powerful models for predicting disease outcomes and detecting associated genes.Availability and implementationThe methods have been implemented in a freely available R package BhGLM (http://www.ssg.uab.edu/bhglm/).Contactnyi@uab.edu.Supplementary informationSupplementary data are available at Bioinformatics online.
| S-EPMC5860634 | biostudies-literature
Project description:In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and extend them to a continuous spike-and-slab framework to allow self-adaptive shrinkage and model selection simultaneously. We develop an EM algorithm that performs fast and dynamic explorations of posterior modes. Our approach selects sparse models efficiently and automatically with substantially smaller bias than would be induced by alternative regularization procedures. The performance of the proposed methods are demonstrated through simulation and two real data examples.
| S-EPMC7845917 | biostudies-literature
Project description:MotivationThe use of human genome discoveries and other established factors to build an accurate risk prediction model is an essential step toward precision medicine. While multi-layer high-dimensional omics data provide unprecedented data resources for prediction studies, their corresponding analytical methods are much less developed.ResultsWe present a multi-kernel penalized linear mixed model with adaptive lasso (MKpLMM), a predictive modeling framework that extends the standard linear mixed models widely used in genomic risk prediction, for multi-omics data analysis. MKpLMM can capture not only the predictive effects from each layer of omics data but also their interactions via using multiple kernel functions. It adopts a data-driven approach to select predictive regions as well as predictive layers of omics data, and achieves robust selection performance. Through extensive simulation studies, the analyses of PET-imaging outcomes from the Alzheimer's Disease Neuroimaging Initiative study, and the analyses of 64 drug responses, we demonstrate that MKpLMM consistently outperforms competing methods in phenotype prediction.Availability and implementationThe R-package is available at https://github.com/YaluWen/OmicPred.Supplementary informationSupplementary data are available at Bioinformatics online.
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Project description:Spike-and-slab priors model predictors as arising from a mixture of distributions: those that should (slab) or should not (spike) remain in the model. The spike-and-slab lasso (SSL) is a mixture of double exponentials, extending the single lasso penalty by imposing different penalties on parameters based on their inclusion probabilities. The SSL was extended to Generalized Linear Models (GLM) for application in genetics/genomics, and can handle many highly correlated predictors of a scalar outcome, but does not incorporate these relationships into variable selection. When images/spatial data are used to model a scalar outcome, relevant parameters tend to cluster spatially, and model performance may benefit from incorporating spatial structure into variable selection. We propose to incorporate spatial information by assigning intrinsic autoregressive priors to the logit prior probabilities of inclusion, which results in more similar shrinkage penalties among spatially adjacent parameters. Using MCMC to fit Bayesian models can be computationally prohibitive for large-scale data, but we fit the model by adapting a computationally efficient coordinate-descent-based EM algorithm. A simulation study and an application to Alzheimer's Disease imaging data show that incorporating spatial information can improve model fitness.
| S-EPMC10004347 | biostudies-literature
Project description:MotivationLarge-scale molecular profiling data have offered extraordinary opportunities to improve survival prediction of cancers and other diseases and to detect disease associated genes. However, there are considerable challenges in analyzing large-scale molecular data.ResultsWe propose new Bayesian hierarchical Cox proportional hazards models, called the spike-and-slab lasso Cox, for predicting survival outcomes and detecting associated genes. We also develop an efficient algorithm to fit the proposed models by incorporating Expectation-Maximization steps into the extremely fast cyclic coordinate descent algorithm. The performance of the proposed method is assessed via extensive simulations and compared with the lasso Cox regression. We demonstrate the proposed procedure on two cancer datasets with censored survival outcomes and thousands of molecular features. Our analyses suggest that the proposed procedure can generate powerful prognostic models for predicting cancer survival and can detect associated genes.Availability and implementationThe methods have been implemented in a freely available R package BhGLM ( http://www.ssg.uab.edu/bhglm/ ).Contactnyi@uab.edu.Supplementary informationSupplementary data are available at Bioinformatics online.
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Project description:There are proposals that extend the classical generalized additive models (GAMs) to accommodate high-dimensional data ( p≫n$$ p\gg n $$ ) using group sparse regularization. However, the sparse regularization may induce excess shrinkage when estimating smooth functions, damaging predictive performance. Moreover, most of these GAMs consider an "all-in-all-out" approach for functional selection, rendering them difficult to answer if nonlinear effects are necessary. While some Bayesian models can address these shortcomings, using Markov chain Monte Carlo algorithms for model fitting creates a new challenge, scalability. Hence, we propose Bayesian hierarchical generalized additive models as a solution: we consider the smoothing penalty for proper shrinkage of curve interpolation via reparameterization. A novel two-part spike-and-slab LASSO prior for smooth functions is developed to address the sparsity of signals while providing extra flexibility to select the linear or nonlinear components of smooth functions. A scalable and deterministic algorithm, EM-Coordinate Descent, is implemented in an open-source R package BHAM. Simulation studies and metabolomics data analyses demonstrate improved predictive and computational performance against state-of-the-art models. Functional selection performance suggests trade-offs exist regarding the effect hierarchy assumption.
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Project description:In observational studies, estimation of a causal effect of a treatment on an outcome relies on proper adjustment for confounding. If the number of the potential confounders (p) is larger than the number of observations (n), then direct control for all potential confounders is infeasible. Existing approaches for dimension reduction and penalization are generally aimed at predicting the outcome, and are less suited for estimation of causal effects. Under standard penalization approaches (e.g. Lasso), if a variable Xj is strongly associated with the treatment T but weakly with the outcome Y, the coefficient βj will be shrunk towards zero thus leading to confounding bias. Under the assumption of a linear model for the outcome and sparsity, we propose continuous spike and slab priors on the regression coefficients βj corresponding to the potential confounders Xj . Specifically, we introduce a prior distribution that does not heavily shrink to zero the coefficients (βj s) of the Xj s that are strongly associated with T but weakly associated with Y. We compare our proposed approach to several state of the art methods proposed in the literature. Our proposed approach has the following features: 1) it reduces confounding bias in high dimensional settings; 2) it shrinks towards zero coefficients of instrumental variables; and 3) it achieves good coverages even in small sample sizes. We apply our approach to the National Health and Nutrition Examination Survey (NHANES) data to estimate the causal effects of persistent pesticide exposure on triglyceride levels.
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Project description:This paper is concerned with testing linear hypotheses in high-dimensional generalized linear models. To deal with linear hypotheses, we first propose constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are χ2 distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow non-central χ2 distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to ∞ at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.
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Project description:Modeling and drawing inference on the joint associations between single-nucleotide polymorphisms and a disease has sparked interest in genome-wide associations studies. In the motivating Boston Lung Cancer Survival Cohort (BLCSC) data, the presence of a large number of single nucleotide polymorphisms of interest, though smaller than the sample size, challenges inference on their joint associations with the disease outcome. In similar settings, we find that neither the debiased lasso approach (van de Geer et al., 2014), which assumes sparsity on the inverse information matrix, nor the standard maximum likelihood method can yield confidence intervals with satisfactory coverage probabilities for generalized linear models. Under this "large n, diverging p" scenario, we propose an alternative debiased lasso approach by directly inverting the Hessian matrix without imposing the matrix sparsity assumption, which further reduces bias compared to the original debiased lasso and ensures valid confidence intervals with nominal coverage probabilities. We establish the asymptotic distributions of any linear combinations of the parameter estimates, which lays the theoretical ground for drawing inference. Simulations show that the proposed refined debiased estimating method performs well in removing bias and yields honest confidence interval coverage. We use the proposed method to analyze the aforementioned BLCSC data, a large-scale hospital-based epidemiology cohort study investigating the joint effects of genetic variants on lung cancer risks.
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