arXiv subjects

Mark A. van de Wiel

Publications and source records attributed to Mark A. van de Wiel.

34 records · Page 2Linked to original sources

arXiv2021

Fast marginal likelihood estimation of penalties for group-adaptive elastic net

Nowadays, clinical research routinely uses omics data, such as gene expression, for predicting clinical outcomes or selecting markers. Additionally, so-called co-data are often available, providing complementary information on the covariates, like p-values from previously published studies or groups of genes corresponding to pathways. Elastic net penalisation is widely used for prediction and covariate selection. Group-adaptive elastic net penalisation learns from co-data to improve the prediction and covariate selection, by penalising important groups of covariates less than other groups. Existing methods are, however, computationally expensive. Here we present a fast method for marginal likelihood estimation of group-adaptive elastic net penalties for generalised linear models. We first derive a low-dimensional representation of the Taylor approximation of the marginal likelihood and its first derivative for group-adaptive ridge penalties, to efficiently estimate these penalties. Then we show by using asymptotic normality of the linear predictors that the marginal likelihood for elastic net models may be approximated well by the marginal likelihood for ridge models. The ridge group penalties are then transformed to elastic net group penalties by using the variance function. The method allows for overlapping groups and unpenalised variables. We demonstrate the method in a model-based simulation study and an application to cancer genomics. The method substantially decreases computation time and outperforms or matches other methods by learning from co-data.

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arXiv2020

Flexible co-data learning for high-dimensional prediction

Clinical research often focuses on complex traits in which many variables play a role in mechanisms driving, or curing, diseases. Clinical prediction is hard when data is high-dimensional, but additional information, like domain knowledge and previously published studies, may be helpful to improve predictions. Such complementary data, or co-data, provide information on the covariates, such as genomic location or p-values from external studies. Our method enables exploiting multiple and various co-data sources to improve predictions. We use discrete or continuous co-data to define possibly overlapping or hierarchically structured groups of covariates. These are then used to estimate adaptive multi-group ridge penalties for generalised linear and Cox models. We combine empirical Bayes estimation of group penalty hyperparameters with an extra level of shrinkage. This renders a uniquely flexible framework as any type of shrinkage can be used on the group level. The hyperparameter shrinkage learns how relevant a specific co-data source is, counters overfitting of hyperparameters for many groups, and accounts for structured co-data. We describe various types of co-data and propose suitable forms of hypershrinkage. The method is very versatile, as it allows for integration and weighting of multiple co-data sets, inclusion of unpenalised covariates and posterior variable selection. We demonstrate it on two cancer genomics applications and show that it may improve the performance of other dense and parsimonious prognostic models substantially, and stabilises variable selection.

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arXiv2019

Stable prediction with radiomics data

Motivation: Radiomics refers to the high-throughput mining of quantitative features from radiographic images. It is a promising field in that it may provide a non-invasive solution for screening and classification. Standard machine learning classification and feature selection techniques, however, tend to display inferior performance in terms of (the stability of) predictive performance. This is due to the heavy multicollinearity present in radiomic data. We set out to provide an easy-to-use approach that deals with this problem. Results: We developed a four-step approach that projects the original high-dimensional feature space onto a lower-dimensional latent-feature space, while retaining most of the covariation in the data. It consists of (i) penalized maximum likelihood estimation of a redundancy filtered correlation matrix. The resulting matrix (ii) is the input for a maximum likelihood factor analysis procedure. This two-stage maximum-likelihood approach can be used to (iii) produce a compact set of stable features that (iv) can be directly used in any (regression-based) classifier or predictor. It outperforms other classification (and feature selection) techniques in both external and internal validation settings regarding survival in squamous cell cancers.

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arXiv2019

Estimation of variance components, heritability and the ridge penalty in high-dimensional generalized linear models

For high-dimensional linear regression models, we review and compare several estimators of variances $τ^2$ and $σ^2$ of the random slopes and errors, respectively. These variances relate directly to ridge regression penalty $λ$ and heritability index $h^2$, often used in genetics. Direct and indirect estimators of these, either based on cross-validation (CV) or maximum marginal likelihood (MML), are also discussed. The comparisons include several cases of covariate matrix $\mathbf{X}_{n \times p}$, with $p \gg n$, such as multi-collinear covariates and data-derived ones. In addition, we study robustness against departures from the model such as sparse instead of dense effects and non-Gaussian errors. An example on weight gain data with genomic covariates confirms the good performance of MML compared to CV. Several extensions are presented. First, to the high-dimensional linear mixed effects model, with REML as an alternative to MML. Second, to the conjugate Bayesian setting, which proves to be a good alternative. Third, and most prominently, to generalized linear models for which we derive a computationally efficient MML estimator by re-writing the marginal likelihood as an $n$-dimensional integral. For Poisson and Binomial ridge regression, we demonstrate the superior accuracy of the resulting MML estimator of $λ$ as compared to CV. Software is provided to enable reproduction of all results presented here.

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arXiv2019

Incorporating prior information and borrowing information in high-dimensional sparse regression using the horseshoe and variational Bayes

We introduce a sparse high-dimensional regression approach that can incorporate prior information on the regression parameters and can borrow information across a set of similar datasets. Prior information may for instance come from previous studies or genomic databases, and information borrowed across a set of genes or genomic networks. The approach is based on prior modelling of the regression parameters using the horseshoe prior, with a prior on the sparsity index that depends on external information. Multiple datasets are integrated by applying an empirical Bayes strategy on hyperparameters. For computational efficiency we approximate the posterior distribution using a variational Bayes method. The proposed framework is useful for analysing large-scale data sets with complex dependence structures. We illustrate this by applications to the reconstruction of gene regulatory networks and to eQTL mapping.

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arXiv2018

Estimating Bayesian Optimal Treatment Regimes for Dichotomous Outcomes using Observational Data

Optimal treatment regimes (OTR) are individualised treatment assignment strategies that identify a medical treatment as optimal given all background information available on the individual. We discuss Bayes optimal treatment regimes estimated using a loss function defined on the bivariate distribution of dichotomous potential outcomes. The proposed approach allows considering more general objectives for the OTR than maximization of an expected outcome (e.g., survival probability) by taking into account, for example, unnecessary treatment burden. As a motivating example we consider the case of oropharynx cancer treatment where unnecessary burden due to chemotherapy is to be avoided while maximizing survival chances. Assuming ignorable treatment assignment we describe Bayesian inference about the OTR including a sensitivity analysis on the unobserved partial association of the potential outcomes. We evaluate the methodology by simulations that apply Bayesian parametric and more flexible non-parametric outcome models. The proposed OTR for oropharynx cancer reduces the frequency of the more burdensome chemotherapy assignment by approximately 75% without reducing the average survival probability. This regime thus offers a strong increase in expected quality of life of patients.

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arXiv2018

Detecting SNPs with interactive effects on a quantitative trait

Here we propose a test to detect effects of single nucleotide polymorphisms (SNPs) on a quantitative trait. Significant SNP-SNP interactions are more difficult to detect than significant SNPs, partly due to the massive amount of SNP-SNP combinations. We propose to move away from testing interaction terms, and move towards testing whether an individual SNP is involved in any interaction. This reduces the multiple testing burden to one test per SNP, and allows for interactions with unobserved factors. Analysing one SNP at a time, we split the individuals into two groups, based on the number of minor alleles. If the quantitative trait differs in mean between the two groups, the SNP has a main effect. If the quantitative trait differs in distribution between some individuals in one group and all other individuals, it possibly has an interactive effect. We propose a mixture test to detect both types of effects. Implicitly, the membership probabilities may suggest potential interacting variables. Analysing simulated and experimental data, we show that the proposed test is statistically powerful, maintains the type I error rate, and detects meaningful signals. The R package semisup is available from Bioconductor.

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arXiv2018

Adaptive group-regularized logistic elastic net regression

In high-dimensional data settings, additional information on the features is often available. Examples of such external information in omics research are: (a) p-values from a previous study, (b) a summary of prior information, and (c) omics annotation. The inclusion of this information in the analysis may enhance classification performance and feature selection, but is not straightforward in the standard regression setting. As a solution to this problem, we propose a group-regularized (logistic) elastic net regression method, where each penalty parameter corresponds to a group of features based on the external information. The method, termed gren, makes use of the Bayesian formulation of logistic elastic net regression to estimate both the model and penalty parameters in an approximate empirical-variational Bayes framework. Simulations and an application to a colon cancer microRNA study show that, if the partitioning of the features is informative, classification performance and feature selection are indeed enhanced.

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arXiv2018

Learning from a lot: Empirical Bayes in high-dimensional prediction settings

Empirical Bayes is a versatile approach to `learn from a lot' in two ways: first, from a large number of variables and second, from a potentially large amount of prior information, e.g. stored in public repositories. We review applications of a variety of empirical Bayes methods to several well-known model-based prediction methods including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss `formal' empirical Bayes methods which maximize the marginal likelihood, but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross-validation and full Bayes, and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and $p$, the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters which model a priori information on variables, termed `co-data'. In particular, we present two novel examples that allow for co-data. First, a Bayesian spike-and-slab setting that facilitates inclusion of multiple co-data sources and types; second, a hybrid empirical Bayes-full Bayes ridge regression approach for estimation of the posterior predictive interval.

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arXiv2017

Blood-based metabolic signatures in Alzheimer's disease

Introduction: Identification of blood-based metabolic changes might provide early and easy-to-obtain biomarkers. Methods: We included 127 AD patients and 121 controls with CSF-biomarker-confirmed diagnosis (cut-off tau/A$β_{42}$: 0.52). Mass spectrometry platforms determined the concentrations of 53 amine, 22 organic acid, 120 lipid, and 40 oxidative stress compounds. Multiple signatures were assessed: differential expression (nested linear models), classification (logistic regression), and regulatory (network extraction). Results: Twenty-six metabolites were differentially expressed. Metabolites improved the classification performance of clinical variables from 74% to 79%. Network models identified 5 hubs of metabolic dysregulation: Tyrosine, glycylglycine, glutamine, lysophosphatic acid C18:2 and platelet activating factor C16:0. The metabolite network for APOE $ε$4 negative AD patients was less cohesive compared to the network for APOE $ε$4 positive AD patients. Discussion: Multiple signatures point to various promising peripheral markers for further validation. The network differences in AD patients according to APOE genotype may reflect different pathways to AD.

q-bio.NC↗

arXiv2017

Improved high-dimensional prediction with Random Forests by the use of co-data

Prediction in high dimensional settings is difficult due to large by number of variables relative to the sample size. We demonstrate how auxiliary "co-data" can be used to improve the performance of a Random Forest in such a setting. Co-data are incorporated in the Random Forest by replacing the uniform sampling probabilities (used to draw candidate variables, the default for a Random Forest) by co-data moderated sampling probabilities. Co-data here is defined as any type information that is available on the variables of the primary data, but does not use its response labels. These moderated sampling probabilities are, inspired by empirical Bayes, learned from the data at hand. We demonstrate this co-data moderated Random Forest (CoRF) with one example. In the example we aim to predict a lymph node metastasis with gene expression data. We demonstrate how a set of external p-values, a gene signature, and the correlation between gene expression and DNA copy number can improve the predictive performance.

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arXiv2016

The Spectral Condition Number Plot for Regularization Parameter Determination

Many modern statistical applications ask for the estimation of a covariance (or precision) matrix in settings where the number of variables is larger than the number of observations. There exists a broad class of ridge-type estimators that employs regularization to cope with the subsequent singularity of the sample covariance matrix. These estimators depend on a penalty parameter and choosing its value can be hard, in terms of being computationally unfeasible or tenable only for a restricted set of ridge-type estimators. Here we introduce a simple graphical tool, the spectral condition number plot, for informed heuristic penalty parameter selection. The proposed tool is computationally friendly and can be employed for the full class of ridge-type covariance (precision) estimators.

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arXiv2016

An empirical Bayes approach to network recovery using external knowledge

Reconstruction of a high-dimensional network may benefit substantially from the inclusion of prior knowledge on the network topology. In the case of gene interaction networks such knowledge may come for instance from pathway repositories like KEGG, or be inferred from data of a pilot study. The Bayesian framework provides a natural means of including such prior knowledge. Based on a Bayesian Simultaneous Equation Model, we develop an appealing empirical Bayes procedure which automatically assesses the relevance of the used prior knowledge. We use variational Bayes method for posterior densities approximation and compare its accuracy with that of Gibbs sampling strategy. Our method is computationally fast, and can outperform known competitors. In a simulation study we show that accurate prior data can greatly improve the reconstruction of the network, but need not harm the reconstruction if wrong. We demonstrate the benefits of the method in an analysis of gene expression data from GEO. In particular, the edges of the recovered network have superior reproducibility (compared to that of competitors) over resampled versions of the data.

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arXiv2015

Better prediction by use of co-data: Adaptive group-regularized ridge regression

For many high-dimensional studies, additional information on the variables, like (genomic) annotation or external p-values, is available. In the context of binary and continuous prediction, we develop a method for adaptive group-regularized (logistic) ridge regression, which makes structural use of such 'co-data'. Here, 'groups' refer to a partition of the variables according to the co-data. We derive empirical Bayes estimates of group-specific penalties, which possess several nice properties: i) they are analytical; ii) they adapt to the informativeness of the co-data for the data at hand; iii) only one global penalty parameter requires tuning by cross-validation. In addition, the method allows use of multiple types of co-data at little extra computational effort. We show that the group-specific penalties may lead to a larger distinction between `near-zero' and relatively large regression parameters, which facilitates post-hoc variable selection. The method, termed GRridge, is implemented in an easy-to-use R-package. It is demonstrated on two cancer genomics studies, which both concern the discrimination of precancerous cervical lesions from normal cervix tissues using methylation microarray data. For both examples, GRridge clearly improves the predictive performances of ordinary logistic ridge regression and the group lasso. In addition, we show that for the second study the relatively good predictive performance is maintained when selecting only 42 variables.

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arXiv2013

Modeling association between DNA copy number and gene expression with constrained piecewise linear regression splines

DNA copy number and mRNA expression are widely used data types in cancer studies, which combined provide more insight than separately. Whereas in existing literature the form of the relationship between these two types of markers is fixed a priori, in this paper we model their association. We employ piecewise linear regression splines (PLRS), which combine good interpretation with sufficient flexibility to identify any plausible type of relationship. The specification of the model leads to estimation and model selection in a constrained, nonstandard setting. We provide methodology for testing the effect of DNA on mRNA and choosing the appropriate model. Furthermore, we present a novel approach to obtain reliable confidence bands for constrained PLRS, which incorporates model uncertainty. The procedures are applied to colorectal and breast cancer data. Common assumptions are found to be potentially misleading for biologically relevant genes. More flexible models may bring more insight in the interaction between the two markers.

stat.AP↗

arXiv2008

A nonparametric control chart based on the Mann-Whitney statistic

Nonparametric or distribution-free charts can be useful in statistical process control problems when there is limited or lack of knowledge about the underlying process distribution. In this paper, a phase II Shewhart-type chart is considered for location, based on reference data from phase I analysis and the well-known Mann-Whitney statistic. Control limits are computed using Lugannani-Rice-saddlepoint, Edgeworth, and other approximations along with Monte Carlo estimation. The derivations take account of estimation and the dependence from the use of a reference sample. An illustrative numerical example is presented. The in-control performance of the proposed chart is shown to be much superior to the classical Shewhart $\bar{X}$ chart. Further comparisons on the basis of some percentiles of the out-of-control conditional run length distribution and the unconditional out-of-control ARL show that the proposed chart is almost as good as the Shewhart $\bar{X}$ chart for the normal distribution, but is more powerful for a heavy-tailed distribution such as the Laplace, or for a skewed distribution such as the Gamma. Interactive software, enabling a complete implementation of the chart, is made available on a website.

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