Gene expression biomarkers differentiate overall survival of colorectal cancer upon targeted therapies.

While monoclonal antibody-based targeted therapies have substantially improved progression-free survival in cancer patients, the variability in individual responses poses a significant challenge in patient care. Therefore, identifying cancer subtypes and their associated biomarkers is required for assigning effective treatment. In this study, we integrated genotype and pre-treatment tissue RNA-seq data and identified biomarkers causally associated with the overall survival (OS) of colorectal cancer (CRC) patients treated with either cetuximab or bevacizumab. We performed enrichment analysis for specific consensus molecular subtypes (CMS) of colorectal cancer and evaluated differential expression of identified genes using paired tumor and normal tissue from an external cohort. In addition, we replicated the causal effect of these genes on OS using validation cohort and assessed their association with the Cancer Genome Atlas Program data as an external cohort. One of the replicated findings was WDR62, whose overexpression shortened OS of patients treated with cetuximab. Enrichment of its over expression in CMS1 and low expression in CMS4 suggests that patients with CMS4 subtype may drive greater benefit from cetuximab. In summary, this study highlights the importance of integrating different omics data for identifying promising biomarkers specific to a treatment or a cancer subtype.

In silico design and validation of a time-varying PID controller for an artificial pancreas with intraperitoneal insulin delivery and glucose sensing.

Type 1 diabetes (T1D) is a chronic autoimmune disease featured by the loss of beta cell function and the need for lifetime insulin replacement. Over the recent decade, the use of automated insulin delivery systems (AID) has shifted the paradigm of treatment: the availability of continuous subcutaneous (SC) glucose sensors to guide SC insulin delivery through a control algorithm has allowed, for the first time, to reduce the daily burden of the disease as well as to abate the risk for hypoglycemia. AID use is still limited by individual acceptance, local availability, coverage, and expertise. A major drawback of SC insulin delivery is the need for meal announcement and the peripheral hyperinsulinemia that, over time, contributes to macrovascular complications. Inpatient trials using intraperitoneal (IP) insulin pumps have demonstrated that glycemic control can be improved without meal announcement due to the faster insulin delivery through the peritoneal space. This calls for novel control algorithms able to account for the specificities of IP insulin kinetics. Recently, our group described a two-compartment model of IP insulin kinetics demonstrating that the peritoneal space acts as a virtual compartment and IP insulin delivery is virtually intraportal (intrahepatic), thus closely mimicking the physiology of insulin secretion. The FDA-accepted T1D simulator for SC insulin delivery and sensing has been updated for IP insulin delivery and sensing. Herein, we design and validate-in silico-a time-varying proportional integrative derivative controller to guide IP insulin delivery in a fully closed-loop mode without meal announcement.

Gene signatures derived from transcriptomic-causal networks stratified colorectal cancer patients for effective targeted therapy.

Predictive and prognostic gene signatures derived from interconnectivity among genes can tailor clinical care to patients in cancer treatment. We identified gene interconnectivity as the transcriptomic-causal network by integrating germline genotyping and tumor RNA-seq data from 1,165 patients with metastatic colorectal cancer (CRC). The patients were enrolled in a clinical trial with randomized treatment, either cetuximab or bevacizumab in combination with chemotherapy. We linked the network to overall survival (OS) and detected novel biomarkers by controlling for confounding genes. Our data-driven approach discerned sets of genes, each set collectively stratify patients based on OS. Two signatures under the cetuximab treatment were related to wound healing and macrophages. The signature under the bevacizumab treatment was related to cytotoxicity and we replicated its effect on OS using an external cohort. We also showed that the genes influencing OS within the signatures are downregulated in CRC tumor vs. normal tissue using another external cohort. Furthermore, the corresponding proteins encoded by the genes within the signatures interact each other and are functionally related. In conclusion, this study identified a group of genes that collectively stratified patients based on OS and uncovered promising novel prognostic biomarkers for personalized treatment of CRC using transcriptomic causal networks.

Closed-form expressions and nonparametric estimation of COVID-19 infection rate.

Quantitative assessment of the infection rate of a virus is key to monitor the evolution of an epidemic. However, such variable is not accessible to direct measurement and its estimation requires the solution of a difficult inverse problem. In particular, being the result not only of biological but also of social factors, the transmission dynamics can vary significantly in time. This makes questionable the use of parametric models which could be unable to capture their full complexity. In this paper we exploit compartmental models which include important COVID-19 peculiarities (like the presence of asymptomatic individuals) and allow the infection rate to assume any continuous-time profile. We show that these models are universal, i.e. capable to reproduce exactly any epidemic evolution, and extract from them closed-form expressions of the infection rate time-course. Building upon such expressions, we then design a regularized estimator able to reconstruct COVID-19 transmission dynamics in continuous-time. Using real data collected in Italy, our technique proves to be an useful tool to monitor COVID-19 transmission dynamics and to predict and assess the effect of lockdown restrictions.

Linear Model Identification for Personalized Prediction and Control in Diabetes.

OBJECTIVE: Type-1 diabetes (T1D) is a disease characterized by impaired blood glucose (BG) regulation, forcing patients to multiple daily therapeutic actions, including insulin administration. T1D management could considerably benefit of accurate BG predictions and automated insulin delivery. For both tasks, the large inter- and intra-individual variability in glucose response represents a major challenge. This work investigates different techniques to learn individualized linear models of glucose response to insulin and meal, suitable for model-based prediction and control. METHODS: We focus on data-driven techniques for linear model-learning and compare the state-of-art parametric pipeline with a novel non-parametric approach based on Gaussian regression and Stable-Spline kernel. On data collected by 11 T1D individuals, the effectiveness of different models was evaluated by measuring root mean squared error (RMSE), coefficient of determination (COD), and time gain associated with BG predictors. RESULTS: Among the tested approaches, the non-parametric technique results in the best prediction performance: median RMSE = 29.8 mg/dL, and median COD = 57.4%, for a prediction horizon (PH) of 60 min. With respect to the state-of-the-art parametric techniques, the non-parametric approach grants a COD improvement of about 2%, 7%, 21%, and 41% for PH = 30, 60, 90, and 120 min (paired-sample t-test p ≤ 0.001, p = 0.003, p = 0.03, and p = 0.07 respectively). CONCLUSION: Non-parametric linear model-learning grants statistically significant improvement with respect to the state-of-art parametric approach. The higher PH, the more pronounced the improvement. SIGNIFICANCE: The use of a linear non-parametric model-learning approach for model-based prediction and control could bring to a more prompt, safe and effective T1D management.

COVID-19 epidemic control using short-term lockdowns for collective gain.

While many efforts are currently devoted to vaccines development and administration, social distancing measures, including severe restrictions such as lockdowns, remain fundamental tools to contain the spread of COVID-19. A crucial point for any government is to understand, on the basis of the epidemic curve, the right temporal instant to set up a lockdown and then to remove it. Different strategies are being adopted with distinct shades of intensity. USA and Europe tend to introduce restrictions of considerable temporal length. They vary in time: a severe lockdown may be reached and then gradually relaxed. An interesting alternative is the Australian model where short and sharp responses have repeatedly tackled the virus and allowed people a return to near normalcy. After a few positive cases are detected, a lockdown is immediately set. In this paper we show that the Australian model can be generalized and given a rigorous mathematical analysis, casting strategies of the type short-term pain for collective gain in the context of sliding-mode control, an important branch of nonlinear control theory. This allows us to gain important insights regarding how to implement short-term lockdowns, obtaining a better understanding of their merits and possible limitations. Effects of vaccines administration in improving the control law's effectiveness are also illustrated. Our model predicts the duration of the severe lockdown to be set to maintain e.g. the number of people in intensive care under a certain threshold. After tuning our strategy exploiting data collected in Italy, it turns out that COVID-19 epidemic could be e.g. controlled by alternating one or two weeks of complete lockdown with one or two months of freedom, respectively. Control strategies of this kind, where the lockdown's duration is well circumscribed, could be important also to alleviate coronavirus impact on economy.

Distributed Multi-Agent Gaussian Regression via Finite-Dimensional Approximations.

We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with limited computational and communication capabilities and to gather $M$M noisy measurements in total on input locations independently drawn from a known common probability density. The optimal solution would require agents to exchange all the $M$M input locations and measurements and then invert an $M \times M$M×M matrix, a non-scalable task. Differently, we propose two suboptimal approaches using the first $E$E orthonormal eigenfunctions obtained from the Karhunen-Loève (KL) expansion of the chosen kernel, where typically $E\ll M$E≪M. The benefits are that the computation and communication complexities scale with $E$E and not with $M$M, and computing the required statistics can be performed via standard average consensus algorithms. We obtain probabilistic non-asymptotic bounds that determine a priori the desired level of estimation accuracy, and new distributed strategies relying on Stein's unbiased risk estimate (SURE) paradigms for tuning the regularization parameters and applicable to generic basis functions (thus not necessarily kernel eigenfunctions) and that can again be implemented via average consensus. The proposed estimators and bounds are finally tested on both synthetic and real field data.

Stable spline deconvolution for dynamic susceptibility contrast MRI.

PURPOSE: To present the stable spline (SS) deconvolution method for the quantification of the cerebral blood flow (CBF) from dynamic susceptibility contrast MRI. METHODS: The SS method was compared with both the block-circulant singular value decomposition (oSVD) and nonlinear stochastic regularization (NSR) methods. oSVD is one of the most popular deconvolution methods in dynamic susceptibility contrast MRI (DSC-MRI). NSR is an alternative approach that we proposed previously. The three methods were compared using simulated data and two clinical data sets. RESULTS: The SS method correctly reconstructed the dispersed residue function and its peak in presence of dispersion, regardless of the delay. In absence of dispersion, SS performs similarly to oSVD and does not correctly reconstruct the residue function and its peak. SS and NSR better differentiate healthy and pathologic CBF values compared with oSVD in all simulated conditions. Using acquired data, SS and NSR provide more clinically plausible and physiological estimates of the residue function and CBF maps compared with oSVD. CONCLUSION: The SS method overcomes some of the limitations of oSVD, such as unphysiological estimates of the residue function and NSR, the latter of which is too computationally expensive to be applied to large data sets. Thus, the SS method is a valuable alternative for CBF quantification using DSC-MRI data. Magn Reson Med 78:1801-1811, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

An index of parameter reproducibility accounting for estimation uncertainty: theory and case study on ß-cell responsivity and insulin sensitivity.

Parameter reproducibility is necessary to perform longitudinal studies where parameters are assessed to monitor disease progression or effect of therapy but are also useful in powering the study, i.e., to define how many subjects should be studied to observe a given effect. The assessment of parameter reproducibility is usually accomplished by methods that do not take into account the fact that these parameters are estimated with uncertainty. This is particularly relevant in physiological and clinical studies where usually reproducibility cannot be assessed by multiple testing and is usually assessed from a single replication of the test. Working in a suitable stochastic framework, here we propose a new index (S) to measure reproducibility that takes into account parameter uncertainty and is particularly suited to handle the normal testing conditions of physiological and clinical investigations. Simulation results prove that S, by properly taking into account parameter uncertainty, is more accurate and robust than the methods available in the literature. The new metric is applied to assess reproducibility of insulin sensitivity and ß-cell responsivity of a mixed-meal tolerance test from data obtained in the same subjects retested 1 wk apart. Results show that the indices of insulin sensitivity and ß-cell responsivity to glucose are well reproducible. We conclude that the oral minimal models provide useful indices that can be used safely in prospective studies or to assess the efficacy of a given therapy.

Estimation of arterial arrival time and cerebral blood flow from QUASAR arterial spin labeling using stable spline.

PURPOSE: QUASAR arterial spin labeling (ASL) permits the application of deconvolution approaches for the absolute quantification of cerebral perfusion. Currently, oscillation index regularized singular value decomposition (oSVD) combined with edge-detection (ED) is the most commonly used method. Its major drawbacks are nonphysiological oscillations in the impulse response function and underestimation of perfusion. The aim of this work is to introduce a novel method to overcome these limitations. METHODS: A system identification method, stable spline (SS), was extended to address ASL peculiarities such as the delay in arrival of the arterial blood in the tissue. The proposed framework was compared with oSVD + ED in both simulated and real data. SS was used to investigate the validity of using a voxel-wise tissue T1 value instead of using a single global value (of blood T1 ). RESULTS: SS outperformed oSVD + ED in 79.9% of simulations. When applied to real data, SS exhibited a physiologically realistic range for perfusion and a higher mean value with respect to oSVD + ED (55.5 ± 9.5 SS, 34.9 ± 5.2 oSVD + ED mL/100 g/min). CONCLUSION: SS can represent an alternative to oSVD + ED for the quantification of QUASAR ASL data. Analysis of the retrieved impulse response function revealed that using a voxel wise tissue T1 might be suboptimal.

The Connection Between Bayesian Estimation of a Gaussian Random Field and RKHS.

Reconstruction of a function from noisy data is key in machine learning and is often formulated as a regularized optimization problem over an infinite-dimensional reproducing kernel Hilbert space (RKHS). The solution suitably balances adherence to the observed data and the corresponding RKHS norm. When the data fit is measured using a quadratic loss, this estimator has a known statistical interpretation. Given the noisy measurements, the RKHS estimate represents the posterior mean (minimum variance estimate) of a Gaussian random field with covariance proportional to the kernel associated with the RKHS. In this brief, we provide a statistical interpretation when more general losses are used, such as absolute value, Vapnik or Huber. Specifically, for any finite set of sampling locations (that includes where the data were collected), the maximum a posteriori estimate for the signal samples is given by the RKHS estimate evaluated at the sampling locations. This connection establishes a firm statistical foundation for several stochastic approaches used to estimate unknown regularization parameters. To illustrate this, we develop a numerical scheme that implements a Bayesian estimator with an absolute value loss. This estimator is used to learn a function from measurements contaminated by outliers.

A multi-task learning approach for the extraction of single-trial evoked potentials.

Evoked potentials (EPs) are of great interest in neuroscience, but their measurement is difficult as they are embedded in background spontaneous electroencephalographic (EEG) activity which has a much larger amplitude. The widely used averaging technique requires the delivery of a large number of identical stimuli and yields only an "average" EP which does not allow the investigation of the possible variability of single-trial EPs. In the present paper, we propose the use of a multi-task learning method (MTL) for the simultaneous extraction of both the average and the N single-trial EPs from N recorded sweeps. The technique is developed within a Bayesian estimation framework and uses flexible stochastic models to describe the average response and the N shifts between the single-trial EPs and this average. Differently from other single-trial estimation approaches proposed in the literature, MTL can provide estimates of both the average and the N single-trial EPs in a single stage. In the present paper, MTL is successfully assessed on both synthetic (100 simulated recording sessions with N=20 sweeps) and real data (11 subjects with N=20 sweeps) relative to a cognitive task carried out for the investigation of the P300 component of the EP.

Finding potential support vectors in separable classification problems.

This paper considers the classification problem using support vector (SV) machines and investigates how to maximally reduce the size of the training set without losing information. Under separable data set assumptions, we derive the exact conditions stating which observations can be discarded without diminishing the overall information content. For this purpose, we introduce the concept of potential SVs, i.e., those data that can become SVs when future data become available. To complement this, we also characterize the set of discardable vectors (DVs), i.e., those data that, given the current data set, can never become SVs. Thus, these vectors are useless for future training purposes and can eventually be removed without loss of information. Then, we provide an efficient algorithm based on linear programming that returns the potential and DVs by constructing a simplex tableau. Finally, we compare it with alternative algorithms available in the literature on some synthetic data as well as on data sets from standard repositories.

Assessment of clinical data of nonlinear stochastic deconvolution versus block-circulant singular value decomposition for quantitative dynamic susceptibility contrast magnetic resonance imaging.

Dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI) allows the noninvasive assessment of brain hemodynamics alterations by quantifying, via deconvolution, the cerebral blood flow (CBF) and mean transit time (MTT). Singular value decomposition (SVD) and block-circulant SVD (cSVD) are the most widely adopted deconvolution method, although they bear some limitations, including unphysiological oscillations in the residue function and bias in the presence of delay and dispersion between the tissue and the arterial input function. A nonlinear stochastic regularization (NSR) has been proposed, which performs better than SVD and cSVD on simulated data both in the presence and absence of dispersion. Moreover, NSR allows to quantify the dispersion level. Here, cSVD and NSR are compared for the first time on a group of nine patients with severe atherosclerotic unilateral stenosis of internal carotid artery before and after carotid stenting to investigate the effect of arterial dispersion. According to region of interest-based analysis, NSR characterizes the pathologic tissue more accurately than cSVD, thus improving the quality of the information provided to physicians for diagnosis. In fact, in 7 (78%) of the 9 subjects, CBF and MTT maps provided by NSR allow to correctly identify the pathologic hemisphere to the physician. Moreover, by emphasizing the difference between pathologic and healthy tissues, NSR may be successfully used to monitor the subject's recovery after the treatment and/or surgery. NSR also generates dispersion level and non-dispersed CBF and MTT maps. The dispersion level provides information on CBF and MTT estimates reliability and may also be used as a clinical indicator of pathological tissue state complementary to CBF and MTT, thus increasing the clinical information provided by DSC-MRI analysis.

Client-server multitask learning from distributed datasets.

A client-server architecture to simultaneously solve multiple learning tasks from distributed datasets is described. In such architecture, each client corresponds to an individual learning task and the associated dataset of examples. The goal of the architecture is to perform information fusion from multiple datasets while preserving privacy of individual data. The role of the server is to collect data in real time from the clients and codify the information in a common database. Such information can be used by all the clients to solve their individual learning task, so that each client can exploit the information content of all the datasets without actually having access to private data of others. The proposed algorithmic framework, based on regularization and kernel methods, uses a suitable class of "mixed effect" kernels. The methodology is illustrated through a simulated recommendation system, as well as an experiment involving pharmacological data coming from a multicentric clinical trial.

Bayesian online multitask learning of Gaussian processes.

Standard single-task kernel methods have recently been extended to the case of multitask learning in the context of regularization theory. There are experimental results, especially in biomedicine, showing the benefit of the multitask approach compared to the single-task one. However, a possible drawback is computational complexity. For instance, when regularization networks are used, complexity scales as the cube of the overall number of training data, which may be large when several tasks are involved. The aim of this paper is to derive an efficient computational scheme for an important class of multitask kernels. More precisely, a quadratic loss is assumed and each task consists of the sum of a common term and a task-specific one. Within a Bayesian setting, a recursive online algorithm is obtained, which updates both estimates and confidence intervals as new data become available. The algorithm is tested on two simulated problems and a real data set relative to xenobiotics administration in human patients.

Dynamic insulin sensitivity index: importance in diabetes.

The classical minimal model (MM) index of insulin sensitivity, S(I), does not account for how fast or slow insulin action takes place. In a recent work, we proposed a new dynamic insulin sensitivity index, S(I)(D), which is able to take into account the dynamics of insulin action as well. The new index is a function of two MM parameters, namely S(I) and p(2), the latter parameter governing the speed of rise and decay of insulin action. We have previously shown that in normal glucose tolerant subjects S(I)(D) provides a more comprehensive picture of insulin action on glucose metabolism than S(I). The aim of this study is to show that resorting to S(I)(D) rather S(I) is even more appropriate when studying diabetic patients who have a low and slow insulin action. We analyzed insulin-modified intravenous glucose tolerance test studies performed in 10 diabetic subjects and mixed meal glucose tolerance test studies exploiting the triple tracer technique in 14 diabetic subjects. We derived both S(I) and S(I)(D) resorting to Bayesian and Fisherian identification strategies. The results show that S(I)(D) is estimated more precisely than S(I) when using the Bayesian approach. In addition, the less labor-intensive Fisherian approach can still be used to obtain reliable point estimates of S(I)(D) but not of S(I). These results suggest that S(I)(D) yields a comprehensive, precise, and cost-effective assessment of insulin sensitivity in subjects with impaired insulin action like impaired glucose tolerant subjects or diabetic patients.

Nonlinear stochastic regularization to characterize tissue residue function in bolus-tracking MRI: assessment and comparison with SVD, block-circulant SVD, and Tikhonov.

An accurate characterization of tissue residue function R(t) in bolus-tracking magnetic resonance imaging is of crucial importance to quantify cerebral hemodynamics. R(t) estimation requires to solve a deconvolution problem. The most popular deconvolution method is singular value decomposition (SVD). However, SVD is known to bear some limitations, e.g., R(t) profiles exhibit nonphysiological oscillations and take on negative values. In addition, SVD estimates are biased in presence of bolus delay and dispersion. Recently, other deconvolution methods have been proposed, in particular block-circulant SVD (cSVD) and Tikhonov regularization (TIKH). Here we propose a new method based on nonlinear stochastic regularization (NSR). NSR is tested on simulated data and compared with SVD, cSVD, and TIKH in presence and absence of bolus dispersion. A clinical case in one patient has also been considered. NSR is shown to perform better than SVD, cSVD, and TIKH in reconstructing both the peak and the residue function, in particular when bolus dispersion is considered. In addition, differently from SVD, cSVD, and TIKH, NSR always provides positive and smooth R(t).

A new dynamic index of insulin sensitivity.

Insulin sensitivity is a crucial parameter of glucose metabolism. The standard measures of insulin sensitivity obtained by an euglycaemic hyperinsulinaemic clamp, Si(clamp), or by the minimal model (MM), SI, do not account for the dynamics of insulin action, i.e., how fast or slow insulin action reaches its plateau value. This is an important physiological information. In this paper we formally define a new insulin sensitivity index which also incorporates information on the dynamics of insulin action, SD(I), show its properties, and exemplify how it can be measured both with the clamp and the MM method. Then, by resorting to real and synthetic data, we show both in IVGTT MM and clamp studies why this new index SD(I) offers, in comparison with SI, a more comprehensive picture of the control of insulin on glucose.

Glucose production by deconvolution in intravenous and oral glucose tolerance tests: role of output variable.

Endogenous glucose production (EGP) after a glucose stimulus can be estimated by deconvolution of the endogenous component of glucose concentration, which is computed from noisy measurements. This study analyzes how measurement errors propagate to endogenous glucose and affect EGP reconstruction during intravenous (IVGTT) and oral (MEAL) glucose tolerance tests. Monte Carlo simulations show that the effect of errors on endogenous glucose and thus on EGP is more critical during IVGTT than during MEAL. A two regularization-parameter deconvolution technique for IVGTT is proposed, which successfully handles this added difficulty.