Motivated by mobile devices that record data at a high frequency, we propose a new methodological framework for analyzing a semi-parametric regression model that allow us to study a nonlinear relationship between a scalar response and multiple functional predictors in the presence of scalar covariates. Utilizing functional principal component analysis (FPCA) and the least-squares kernel machine method (LSKM), we are able to substantially extend the framework of semi-parametric regression models of scalar responses on scalar predictors by allowing multiple functional predictors to enter the nonlinear model. Regularization is established for feature selection in the setting of reproducing kernel Hilbert spaces. Our method performs simultaneously model fitting and variable selection on functional features. For the implementation, we propose an effective algorithm to solve related optimization problems in that iterations take place between both linear mixed-effects models and a variable selection method (e.g., sparse group lasso). We show algorithmic convergence results and theoretical guarantees for the proposed methodology. We illustrate its performance through simulation experiments and an analysis of accelerometer data.
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Bayesian network-guided sparse regression with flexible varying effects
In this paper, we propose Varying Effects Regression with Graph Estimation (VERGE), a novel Bayesian method for feature selection in regression. Our model has key aspects that allow it to leverage the complex structure of data sets arising from genomics or imaging studies. We distinguish between the predictors, which are the features utilized in the outcome prediction model, and the subject-level covariates, which modulate the effects of the predictors on the outcome. We construct a varying coefficients modeling framework where we infer a network among the predictor variables and utilize this network information to encourage the selection of related predictors. We employ variable selection spike-and-slab priors that enable the selection of both network-linked predictor variables and covariates that modify the predictor effects. We demonstrate through simulation studies that our method outperforms existing alternative methods in terms of both feature selection and predictive accuracy. We illustrate VERGE with an application to characterizing the influence of gut microbiome features on obesity, where we identify a set of microbial taxa and their ecological dependence relations. We allow subject-level covariates, including sex and dietary intake variables to modify the coefficients of the microbiome predictors, providing additional insight into the interplay between these factors.
more » « less- PAR ID:
- 10547740
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 80
- Issue:
- 4
- ISSN:
- 0006-341X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract There is a growing need for flexible general frameworks that integrate individual-level data with external summary information for improved statistical inference. External information relevant for a risk prediction model may come in multiple forms, through regression coefficient estimates or predicted values of the outcome variable. Different external models may use different sets of predictors and the algorithm they used to predict the outcome Y given these predictors may or may not be known. The underlying populations corresponding to each external model may be different from each other and from the internal study population. Motivated by a prostate cancer risk prediction problem where novel biomarkers are measured only in the internal study, this paper proposes an imputation-based methodology, where the goal is to fit a target regression model with all available predictors in the internal study while utilizing summary information from external models that may have used only a subset of the predictors. The method allows for heterogeneity of covariate effects across the external populations. The proposed approach generates synthetic outcome data in each external population, uses stacked multiple imputation to create a long dataset with complete covariate information. The final analysis of the stacked imputed data is conducted by weighted regression. This flexible and unified approach can improve statistical efficiency of the estimated coefficients in the internal study, improve predictions by utilizing even partial information available from models that use a subset of the full set of covariates used in the internal study, and provide statistical inference for the external population with potentially different covariate effects from the internal population.
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Feature selection is an important initial step of exploratory analysis in biomedical studies. Its main objective is to eliminate the covariates that are uncorrelated with the outcome. For highly correlated covariates, traditional feature selection methods, such as the Lasso, tend to select one of them and eliminate the others, although some of the eliminated ones are still scientifically valuable. To alleviate this drawback, we propose a feature selection method based on covariate space decomposition, referred herein as the “Decomposition Feature Selection” (DFS), and show that this method can lead to scientifically meaningful results in studies with correlated high dimensional data. The DFS consists of two steps: (i) decomposing the covariate space into disjoint subsets such that each of the subsets contains only uncorrelated covariates and (ii) identifying significant predictors by traditional feature selection within each covariate subset. We demonstrate through simulation studies that the DFS has superior practical performance over the Lasso type methods when multiple highly correlated covariates need to be retained. Application of the DFS is demonstrated through a study of bipolar disorders with correlated biomarkers.
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To link a clinical outcome with compositional predictors in microbiome analysis, the linear log‐contrast model is a popular choice, and the inference procedure for assessing the significance of each covariate is also available. However, with the existence of multiple potentially interrelated outcomes and the information of the taxonomic hierarchy of bacteria, a multivariate analysis method that considers the group structure of compositional covariates and an accompanying group inference method are still lacking. Motivated by a study for identifying the microbes in the gut microbiome of preterm infants that impact their later neurobehavioral outcomes, we formulate a constrained integrative multi‐view regression. The neurobehavioral scores form multivariate responses, the log‐transformed sub‐compositional microbiome data form multi‐view feature matrices, and a set of linear constraints on their corresponding sub‐coefficient matrices ensures the sub‐compositional nature. We assume all the sub‐coefficient matrices are possible of low‐rank to enable joint selection and inference of sub‐compositions/views. We propose a scaled composite nuclear norm penalization approach for model estimation and develop a hypothesis testing procedure through de‐biasing to assess the significance of different views. Simulation studies confirm the effectiveness of the proposed procedure. We apply the method to the preterm infant study, and the identified microbes are mostly consistent with existing studies and biological understandings.
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null (Ed.)Abstract Background Drug sensitivity prediction and drug responsive biomarker selection on high-throughput genomic data is a critical step in drug discovery. Many computational methods have been developed to serve this purpose including several deep neural network models. However, the modular relations among genomic features have been largely ignored in these methods. To overcome this limitation, the role of the gene co-expression network on drug sensitivity prediction is investigated in this study. Methods In this paper, we first introduce a network-based method to identify representative features for drug response prediction by using the gene co-expression network. Then, two graph-based neural network models are proposed and both models integrate gene network information directly into neural network for outcome prediction. Next, we present a large-scale comparative study among the proposed network-based methods, canonical prediction algorithms (i.e., Elastic Net, Random Forest, Partial Least Squares Regression, and Support Vector Regression), and deep neural network models for drug sensitivity prediction. All the source code and processed datasets in this study are available at https://github.com/compbiolabucf/drug-sensitivity-prediction . Results In the comparison of different feature selection methods and prediction methods on a non-small cell lung cancer (NSCLC) cell line RNA-seq gene expression dataset with 50 different drug treatments, we found that (1) the network-based feature selection method improves the prediction performance compared to Pearson correlation coefficients; (2) Random Forest outperforms all the other canonical prediction algorithms and deep neural network models; (3) the proposed graph-based neural network models show better prediction performance compared to deep neural network model; (4) the prediction performance is drug dependent and it may relate to the drug’s mechanism of action. Conclusions Network-based feature selection method and prediction models improve the performance of the drug response prediction. The relations between the genomic features are more robust and stable compared to the correlation between each individual genomic feature and the drug response in high dimension and low sample size genomic datasets.more » « less
