Regularized regression models are well studied and, under appropriate conditions, offer fast and statistically interpretable results. However, large data in many applications are heterogeneous in the sense of harboring distributional differences between latent groups. Then, the assumption that the conditional distribution of response $Y$ given features $X$ is the same for all samples may not hold. Furthermore, in scientific applications, the covariance structure of the features may contain important signals and its learning is also affected by latent group structure. We propose a class of mixture models for paired data $(X,Y)$ that couples together the distribution of $X$ (using sparse graphical models) and the conditional $Y \! \mid \! X$ (using sparse regression models). The regression and graphical models are specific to the latent groups and model parameters are estimated jointly. This allows signals in either or both of the feature distribution and regression model to inform learning of latent structure and provides automatic control of confounding by such structure. Estimation is handled via an expectation-maximization algorithm, whose convergence is established theoretically. We illustrate the key ideas via empirical examples. An R package is available at https://github.com/k-perrakis/regjmix.

Personalized longitudinal disease assessment is central to quickly diagnosing, appropriately managing, and optimally adapting the therapeutic strategy of multiple sclerosis (MS). It is also important for identifying idiosyncratic subject-specific disease profiles. Here, we design a novel longitudinal model to map individual disease trajectories in an automated way using smartphone sensor data that may contain missing values. First, we collect digital measurements related to gait and balance, and upper extremity functions using sensor-based assessments administered on a smartphone. Next, we treat missing data via imputation. We then discover potential markers of MS by employing a generalized estimation equation. Subsequently, parameters learned from multiple training datasets are ensembled to form a simple, unified longitudinal predictive model to forecast MS over time in previously unseen people with MS. To mitigate potential underestimation for individuals with severe disease scores, the final model incorporates additional subject-specific fine-tuning using data from the first day. The results show that the proposed model is promising to achieve personalized longitudinal MS assessment; they also suggest that features related to gait and balance as well as upper extremity function, remotely collected from sensor-based assessments, may be useful digital markers for predicting MS over time.

Cancer treatments can be highly toxic and frequently only a subset of the patient population will benefit from a given treatment. Tumour genetic makeup plays an important role in cancer drug sensitivity. We suspect that gene expression markers could be used as a decision aid for treatment selection or dosage tuning. Using in vitro cancer cell line dose-response and gene expression data from the Genomics of Drug Sensitivity in Cancer (GDSC) project, we build a dose-varying regression model. Unlike existing approaches, this allows us to estimate dosage-dependent associations with gene expression. We include the transcriptomic profiles as dose-invariant covariates into the regression model and assume that their effect varies smoothly over the dosage levels. A two-stage variable selection algorithm (variable screening followed by penalized regression) is used to identify genetic factors that are associated with drug response over the varying dosages. We evaluate the effectiveness of our method using simulation studies focusing on the choice of tuning parameters and cross-validation for predictive accuracy assessment. We further apply the model to data from five BRAF targeted compounds applied to different cancer cell lines under different dosage levels. We highlight the dosage-dependent dynamics of the associations between the selected genes and drug response, and we perform pathway enrichment analysis to show that the selected genes play an important role in pathways related to tumorigenesis and DNA damage response.

MOTIVATION: Molecular pathways and networks play a key role in basic and disease biology. An emerging notion is that networks encoding patterns of molecular interplay may themselves differ between contexts, such as cell type, tissue or disease (sub)type. However, while statistical testing of differences in mean expression levels has been extensively studied, testing of network differences remains challenging. Furthermore, since network differences could provide important and biologically interpretable information to identify molecular subgroups, there is a need to consider the unsupervised task of learning subgroups and networks that define them. This is a nontrivial clustering problem, with neither subgroups nor subgroup-specific networks known at the outset. RESULTS: We leverage recent ideas from high-dimensional statistics for testing and clustering in the network biology setting. The methods we describe can be applied directly to most continuous molecular measurements and networks do not need to be specified beforehand. We illustrate the ideas and methods in a case study using protein data from The Cancer Genome Atlas (TCGA). This provides evidence that patterns of interplay between signalling proteins differ significantly between cancer types. Furthermore, we show how the proposed approaches can be used to learn subtypes and the molecular networks that define them. AVAILABILITY AND IMPLEMENTATION: As the Bioconductor package nethet. CONTACT: [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Networks are widely used as structural summaries of biochemical systems. Statistical estimation of networks is usually based on linear or discrete models. However, the dynamics of biochemical systems are generally non-linear, suggesting that suitable non-linear formulations may offer gains with respect to causal network inference and aid in associated prediction problems. RESULTS: We present a general framework for network inference and dynamical prediction using time course data that is rooted in non-linear biochemical kinetics. This is achieved by considering a dynamical system based on a chemical reaction graph with associated kinetic parameters. Both the graph and kinetic parameters are treated as unknown; inference is carried out within a Bayesian framework. This allows prediction of dynamical behavior even when the underlying reaction graph itself is unknown or uncertain. Results, based on (i) data simulated from a mechanistic model of mitogen-activated protein kinase signaling and (ii) phosphoproteomic data from cancer cell lines, demonstrate that non-linear formulations can yield gains in causal network inference and permit dynamical prediction and uncertainty quantification in the challenging setting where the reaction graph is unknown. AVAILABILITY AND IMPLEMENTATION: MATLAB R2014a software is available to download from warwick.ac.uk/chrisoates. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Parameter inference in mechanistic models based on systems of coupled differential equations is a topical yet computationally challenging problem, due to the need to follow each parameter adaptation with a numerical integration of the differential equations. Techniques based on gradient matching, which aim to minimize the discrepancy between the slope of a data interpolant and the derivatives predicted from the differential equations, offer a computationally appealing shortcut to the inference problem. The present paper discusses a method based on nonparametric Bayesian statistics with Gaussian processes due to Calderhead et al. (2008), and shows how inference in this model can be substantially improved by consistently sampling from the joint distribution of the ODE parameters and GP hyperparameters. We demonstrate the efficiency of our adaptive gradient matching technique on three benchmark systems, and perform a detailed comparison with the method in Calderhead et al. (2008) and the explicit ODE integration approach, both in terms of parameter inference accuracy and in terms of computational efficiency.

Conventional dynamic Bayesian networks (DBNs) are based on the homogeneous Markov assumption, which is too restrictive in many practical applications. Various approaches to relax the homogeneity assumption have therefore been proposed in the last few years. The present paper aims to improve the flexibility of two recent versions of non-homogeneous DBNs, which either (i) suffer from the need for data discretization, or (ii) assume a time-invariant network structure. Allowing the network structure to be fully flexible leads to the risk of overfitting and inflated inference uncertainty though, especially in the highly topical field of systems biology, where independent measurements tend to be sparse. In the present paper we investigate three conceptually different regularization schemes based on inter-segment information sharing. We assess the performance in a comparative evaluation study based on simulated data. We compare the predicted segmentation of gene expression time series obtained during embryogenesis in Drosophila melanogaster with other state-of-the-art techniques. We conclude our evaluation with an application to synthetic biology, where the objective is to predict a known regulatory network of five genes in Saccharomyces cerevisiae.