Reorienting Latent Variable Modeling for Supervised Learning.

Despite its potentials benefits, using prediction targets generated based on latent variable (LV) modeling is not a common practice in supervised learning, a dominating framework for developing prediction models. In supervised learning, it is typically assumed that the outcome to be predicted is clear and readily available, and therefore validating outcomes before predicting them is a foreign concept and an unnecessary step. The usual goal of LV modeling is inference, and therefore using it in supervised learning and in the prediction context requires a major conceptual shift. This study lays out methodological adjustments and conceptual shifts necessary for integrating LV modeling into supervised learning. It is shown that such integration is possible by combining the traditions of LV modeling, psychometrics, and supervised learning. In this interdisciplinary learning framework, generating practical outcomes using LV modeling and systematically validating them based on clinical validators are the two main strategies. In the example using the data from the Longitudinal Assessment of Manic Symptoms (LAMS) Study, a large pool of candidate outcomes is generated by flexible LV modeling. It is demonstrated that this exploratory situation can be used as an opportunity to tailor desirable prediction targets taking advantage of contemporary science and clinical insights.

Principal curve approaches for inferring 3D chromatin architecture.

Three-dimensional (3D) genome spatial organization is critical for numerous cellular processes, including transcription, while certain conformation-driven structural alterations are frequently oncogenic. Genome architecture had been notoriously difficult to elucidate, but the advent of the suite of chromatin conformation capture assays, notably Hi-C, has transformed understanding of chromatin structure and provided downstream biological insights. Although many findings have flowed from direct analysis of the pairwise proximity data produced by these assays, there is added value in generating corresponding 3D reconstructions deriving from superposing genomic features on the reconstruction. Accordingly, many methods for inferring 3D architecture from proximity data have been advanced. However, none of these approaches exploit the fact that single chromosome solutions constitute a one-dimensional (1D) curve in 3D. Rather, this aspect has either been addressed by imposition of constraints, which is both computationally burdensome and cell type specific, or ignored with contiguity imposed after the fact. Here, we target finding a 1D curve by extending principal curve methodology to the metric scaling problem. We illustrate how this approach yields a sequence of candidate solutions, indexed by an underlying smoothness or degrees-of-freedom parameter, and propose methods for selection from this sequence. We apply the methodology to Hi-C data obtained on IMR90 cells and so are positioned to evaluate reconstruction accuracy by referencing orthogonal imaging data. The results indicate the utility and reproducibility of our principal curve approach in the face of underlying structural variation.

Confounds in neuroimaging: A clear case of sex as a confound in brain-based prediction.

Muscle weakness is common in many neurological, neuromuscular, and musculoskeletal conditions. Muscle size only partially explains muscle strength as adaptions within the nervous system also contribute to strength. Brain-based biomarkers of neuromuscular function could provide diagnostic, prognostic, and predictive value in treating these disorders. Therefore, we sought to characterize and quantify the brain's contribution to strength by developing multimodal MRI pipelines to predict grip strength. However, the prediction of strength was not straightforward, and we present a case of sex being a clear confound in brain decoding analyses. While each MRI modality-structural MRI (i.e., gray matter morphometry), diffusion MRI (i.e., white matter fractional anisotropy), resting state functional MRI (i.e., functional connectivity), and task-evoked functional MRI (i.e., left or right hand motor task activation)-and a multimodal prediction pipeline demonstrated significant predictive power for strength (R 2 = 0.108-0.536, p ≤ 0.001), after correcting for sex, the predictive power was substantially reduced (R 2 = -0.038-0.075). Next, we flipped the analysis and demonstrated that each MRI modality and a multimodal prediction pipeline could significantly predict sex (accuracy = 68.0%-93.3%, AUC = 0.780-0.982, p < 0.001). However, correcting the brain features for strength reduced the accuracy for predicting sex (accuracy = 57.3%-69.3%, AUC = 0.615-0.780). Here we demonstrate the effects of sex-correlated confounds in brain-based predictive models across multiple brain MRI modalities for both regression and classification models. We discuss implications of confounds in predictive modeling and the development of brain-based MRI biomarkers, as well as possible strategies to overcome these barriers.

Multi-muscle deep learning segmentation to automate the quantification of muscle fat infiltration in cervical spine conditions.

Muscle fat infiltration (MFI) has been widely reported across cervical spine disorders. The quantification of MFI requires time-consuming and rater-dependent manual segmentation techniques. A convolutional neural network (CNN) model was trained to segment seven cervical spine muscle groups (left and right muscles segmented separately, 14 muscles total) from Dixon MRI scans (n = 17, 17 scans < 2 weeks post motor vehicle collision (MVC), and 17 scans 12 months post MVC). The CNN MFI measures demonstrated high test reliability and accuracy in an independent testing dataset (n = 18, 9 scans < 2 weeks post MVC, and 9 scans 12 months post MVC). Using the CNN in 84 participants with scans < 2 weeks post MVC (61 females, 23 males, age = 34.2 ± 10.7 years) differences in MFI between the muscle groups and relationships between MFI and sex, age, and body mass index (BMI) were explored. Averaging across all muscles, females had significantly higher MFI than males (p = 0.026). The deep cervical muscles demonstrated significantly greater MFI than the more superficial muscles (p < 0.001), and only MFI within the deep cervical muscles was moderately correlated to age (r > 0.300, p ≤ 0.001). CNN's allow for the accurate and rapid, quantitative assessment of the composition of the architecturally complex muscles traversing the cervical spine. Acknowledging the wider reports of MFI in cervical spine disorders and the time required to manually segment the individual muscles, this CNN may have diagnostic, prognostic, and predictive value in disorders of the cervical spine.

Relating whole-brain functional connectivity to self-reported negative emotion in a large sample of young adults using group regularized canonical correlation analysis.

The goal of our study was to use functional connectivity to map brain function to self-reports of negative emotion. In a large dataset of healthy individuals derived from the Human Connectome Project (N = 652), first we quantified functional connectivity during a negative face-matching task to isolate patterns induced by emotional stimuli. Then, we did the same in a complementary task-free resting state condition. To identify the relationship between functional connectivity in these two conditions and self-reports of negative emotion, we introduce group regularized canonical correlation analysis (GRCCA), a novel algorithm extending canonical correlations analysis to model the shared common properties of functional connectivity within established brain networks. To minimize overfitting, we optimized the regularization parameters of GRCCA using cross-validation and tested the significance of our results in a held-out portion of the data set using permutations. GRCCA consistently outperformed plain regularized canonical correlation analysis. The only canonical correlation that generalized to the held-out test set was based on resting state data (r = 0.175, permutation test p = 0.021). This canonical correlation loaded primarily on Anger-aggression. It showed high loadings in the cingulate, orbitofrontal, superior parietal, auditory and visual cortices, as well as in the insula. Subcortically, we observed high loadings in the globus pallidus. Regarding brain networks, it loaded primarily on the primary visual, orbito-affective and ventral multimodal networks. Here, we present the first neuroimaging application of GRCCA, a novel algorithm for regularized canonical correlation analyses that takes into account grouping of the variables during the regularization scheme. Using GRCCA, we demonstrate that functional connections involving the visual, orbito-affective and multimodal networks are promising targets for investigating functional correlates of subjective anger and aggression. Crucially, our approach and findings also highlight the need of cross-validation, regularization and testing on held out data for correlational neuroimaging studies to avoid inflated effects.

Aortic growth and development of partial false lumen thrombosis are associated with late adverse events in type B aortic dissection.

BACKGROUND: Patients with medically treated type B aortic dissection (TBAD) remain at significant risk for late adverse events (LAEs). We hypothesize that not only initial morphological features, but also their change over time at follow-up are associated with LAEs. MATERIALS AND METHODS: Baseline and 188 follow-up computed tomography (CT) scans with a median follow-up time of 4 years (range, 10 days to 12.7 years) of 47 patients with acute uncomplicated TBAD were retrospectively reviewed. Morphological features (n = 8) were quantified at baseline and each follow-up. Medical records were reviewed for LAEs, which were defined according to current guidelines. To assess the effects of changes of morphological features over time, the linear mixed effects models were combined with Cox proportional hazards regression for the time-to-event outcome using a joint modeling approach. RESULTS: LAEs occurred in 21 of 47 patients at a median of 6.6 years (95% confidence interval [CI], 5.1-11.2 years). Among the 8 investigated morphological features, the following 3 features showed strong association with LAEs: increase in partial false lumen thrombosis area (hazard ratio [HR], 1.39; 95% CI, 1.18-1.66 per cm2 increase; P < .001), increase of major aortic diameter (HR, 1.24; 95% CI, 1.13-1.37 per mm increase; P < .001), and increase in the circumferential extent of false lumen (HR, 1.05; 95% CI, 1.01-1.10 per degree increase; P < .001). CONCLUSIONS: In medically treated TBAD, increases in aortic diameter, new or increased partial false lumen thrombosis area, and increases of circumferential extent of the false lumen are strongly associated with LAEs.

The human connectome project for disordered emotional states: Protocol and rationale for a research domain criteria study of brain connectivity in young adult anxiety and depression.

Through the Human Connectome Project (HCP) our understanding of the functional connectome of the healthy brain has been dramatically accelerated. Given the pressing public health need, we must increase our understanding of how connectome dysfunctions give rise to disordered mental states. Mental disorders arising from high levels of negative emotion or from the loss of positive emotional experience affect over 400 million people globally. Such states of disordered emotion cut across multiple diagnostic categories of mood and anxiety disorders and are compounded by accompanying disruptions in cognitive function. Not surprisingly, these forms of psychopathology are the leading cause of disability worldwide. The Research Domain Criteria (RDoC) initiative spearheaded by NIMH offers a framework for characterizing the relations among connectome dysfunctions, anchored in neural circuits and phenotypic profiles of behavior and self-reported symptoms. Here, we report on our Connectomes Related to Human Disease protocol for integrating an RDoC framework with HCP protocols to characterize connectome dysfunctions in disordered emotional states, and present quality control data from a representative sample of participants. We focus on three RDoC domains and constructs most relevant to depression and anxiety: 1) loss and acute threat within the Negative Valence System (NVS) domain; 2) reward valuation and responsiveness within the Positive Valence System (PVS) domain; and 3) working memory and cognitive control within the Cognitive System (CS) domain. For 29 healthy controls, we present preliminary imaging data: functional magnetic resonance imaging collected in the resting state and in tasks matching our constructs of interest ("Emotion", "Gambling" and "Continuous Performance" tasks), as well as diffusion-weighted imaging. All functional scans demonstrated good signal-to-noise ratio. Established neural networks were robustly identified in the resting state condition by independent component analysis. Processing of negative emotional faces significantly activated the bilateral dorsolateral prefrontal and occipital cortices, fusiform gyrus and amygdalae. Reward elicited a response in the bilateral dorsolateral prefrontal, parietal and occipital cortices, and in the striatum. Working memory was associated with activation in the dorsolateral prefrontal, parietal, motor, temporal and insular cortices, in the striatum and cerebellum. Diffusion tractography showed consistent profiles of fractional anisotropy along known white matter tracts. We also show that results are comparable to those in a matched sample from the HCP Healthy Young Adult data release. These preliminary data provide the foundation for acquisition of 250 subjects who are experiencing disordered emotional states. When complete, these data will be used to develop a neurobiological model that maps connectome dysfunctions to specific behaviors and symptoms.

Deep Learning Convolutional Neural Networks for the Automatic Quantification of Muscle Fat Infiltration Following Whiplash Injury.

Muscle fat infiltration (MFI) of the deep cervical spine extensors has been observed in cervical spine conditions using time-consuming and rater-dependent manual techniques. Deep learning convolutional neural network (CNN) models have demonstrated state-of-the-art performance in segmentation tasks. Here, we train and test a CNN for muscle segmentation and automatic MFI calculation using high-resolution fat-water images from 39 participants (26 female, average = 31.7 ± 9.3 years) 3 months post whiplash injury. First, we demonstrate high test reliability and accuracy of the CNN compared to manual segmentation. Then we explore the relationships between CNN muscle volume, CNN MFI, and clinical measures of pain and neck-related disability. Across all participants, we demonstrate that CNN muscle volume was negatively correlated to pain (R = -0.415, p = 0.006) and disability (R = -0.286, p = 0.045), while CNN MFI tended to be positively correlated to disability (R = 0.214, p = 0.105). Additionally, CNN MFI was higher in participants with persisting pain and disability (p = 0.049). Overall, CNN's may improve the efficiency and objectivity of muscle measures allowing for the quantitative monitoring of muscle properties in disorders of and beyond the cervical spine.

Automated Survival Prediction in Metastatic Cancer Patients Using High-Dimensional Electronic Medical Record Data.

BACKGROUND: Oncologists use patients' life expectancy to guide decisions and may benefit from a tool that accurately predicts prognosis. Existing prognostic models generally use only a few predictor variables. We used an electronic medical record dataset to train a prognostic model for patients with metastatic cancer. METHODS: The model was trained and tested using 12 588 patients treated for metastatic cancer in the Stanford Health Care system from 2008 to 2017. Data sources included provider note text, labs, vital signs, procedures, medication orders, and diagnosis codes. Patients were divided randomly into a training set used to fit the model coefficients and a test set used to evaluate model performance (80%/20% split). A regularized Cox model with 4126 predictor variables was used. A landmarking approach was used due to the multiple observations per patient, with t0 set to the time of metastatic cancer diagnosis. Performance was also evaluated using 399 palliative radiation courses in test set patients. RESULTS: The C-index for overall survival was 0.786 in the test set (averaged across landmark times). For palliative radiation courses, the C-index was 0.745 (95% confidence interval [CI] = 0.715 to 0.775) compared with 0.635 (95% CI = 0.601 to 0.669) for a published model using performance status, primary tumor site, and treated site (two-sided P < .001). Our model's predictions were well-calibrated. CONCLUSIONS: The model showed high predictive performance, which will need to be validated using external data. Because it is fully automated, the model can be used to examine providers' practice patterns and could be deployed in a decision support tool to help improve quality of care.

Machine learning in human movement biomechanics: Best practices, common pitfalls, and new opportunities.

Traditional laboratory experiments, rehabilitation clinics, and wearable sensors offer biomechanists a wealth of data on healthy and pathological movement. To harness the power of these data and make research more efficient, modern machine learning techniques are starting to complement traditional statistical tools. This survey summarizes the current usage of machine learning methods in human movement biomechanics and highlights best practices that will enable critical evaluation of the literature. We carried out a PubMed/Medline database search for original research articles that used machine learning to study movement biomechanics in patients with musculoskeletal and neuromuscular diseases. Most studies that met our inclusion criteria focused on classifying pathological movement, predicting risk of developing a disease, estimating the effect of an intervention, or automatically recognizing activities to facilitate out-of-clinic patient monitoring. We found that research studies build and evaluate models inconsistently, which motivated our discussion of best practices. We provide recommendations for training and evaluating machine learning models and discuss the potential of several underutilized approaches, such as deep learning, to generate new knowledge about human movement. We believe that cross-training biomechanists in data science and a cultural shift toward sharing of data and tools are essential to maximize the impact of biomechanics research.

Construction of longitudinal prediction targets using semisupervised learning.

In establishing prognostic models, often aided by machine learning methods, much effort is concentrated in identifying good predictors. However, the same level of rigor is often absent in improving the outcome side of the models. In this study, we focus on this rather neglected aspect of model development. We are particularly interested in the use of longitudinal information as a way of improving the outcome side of prognostic models. This involves optimally characterizing individuals' outcome status, classifying them, and validating the formulated prediction targets. None of these tasks are straightforward, which may explain why longitudinal prediction targets are not commonly used in practice despite their compelling benefits. As a way of improving this situation, we explore the joint use of empirical model fitting, clinical insights, and cross-validation based on how well formulated targets are predicted by clinically relevant baseline characteristics (antecedent validators). The idea here is that all these methods are imperfect but can be used together to triangulate valid prediction targets. The proposed approach is illustrated using data from the longitudinal assessment of manic symptoms study.

FIRE: functional inference of genetic variants that regulate gene expression.

MOTIVATION: Interpreting genetic variation in noncoding regions of the genome is an important challenge for personal genome analysis. One mechanism by which noncoding single nucleotide variants (SNVs) influence downstream phenotypes is through the regulation of gene expression. Methods to predict whether or not individual SNVs are likely to regulate gene expression would aid interpretation of variants of unknown significance identified in whole-genome sequencing studies. RESULTS: We developed FIRE (Functional Inference of Regulators of Expression), a tool to score both noncoding and coding SNVs based on their potential to regulate the expression levels of nearby genes. FIRE consists of 23 random forests trained to recognize SNVs in cis-expression quantitative trait loci (cis-eQTLs) using a set of 92 genomic annotations as predictive features. FIRE scores discriminate cis-eQTL SNVs from non-eQTL SNVs in the training set with a cross-validated area under the receiver operating characteristic curve (AUC) of 0.807, and discriminate cis-eQTL SNVs shared across six populations of different ancestry from non-eQTL SNVs with an AUC of 0.939. FIRE scores are also predictive of cis-eQTL SNVs across a variety of tissue types. AVAILABILITY AND IMPLEMENTATION: FIRE scores for genome-wide SNVs in hg19/GRCh37 are available for download at https://sites.google.com/site/fireregulatoryvariation/. CONTACT: nilah@stanford.edu. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Combinatorial Extracellular Matrix Microenvironments for Probing Endothelial Differentiation of Human Pluripotent Stem Cells.

Endothelial cells derived from human pluripotent stem cells are a promising cell type for enhancing angiogenesis in ischemic cardiovascular tissues. However, our understanding of microenvironmental factors that modulate the process of endothelial differentiation is limited. We examined the role of combinatorial extracellular matrix (ECM) proteins on endothelial differentiation systematically using an arrayed microscale platform. Human pluripotent stem cells were differentiated on the arrayed ECM microenvironments for 5 days. Combinatorial ECMs composed of collagen IV + heparan sulfate + laminin (CHL) or collagen IV + gelatin + heparan sulfate (CGH) demonstrated significantly higher expression of CD31, compared to single-factor ECMs. These results were corroborated by fluorescence activated cell sorting showing a 48% yield of CD31+/VE-cadherin+ cells on CHL, compared to 27% on matrigel. To elucidate the signaling mechanism, a gene expression time course revealed that VE-cadherin and FLK1 were upregulated in a dynamically similar manner as integrin subunit ß3 (>50 fold). To demonstrate the functional importance of integrin ß3 in promoting endothelial differentiation, the addition of neutralization antibody inhibited endothelial differentiation on CHL-modified dishes by >50%. These data suggest that optimal combinatorial ECMs enhance endothelial differentiation, compared to many single-factor ECMs, in part through an integrin ß3-mediated pathway.

Prognostic significance of early aortic remodeling in acute uncomplicated type B aortic dissection and intramural hematoma.

BACKGROUND: Patients with Stanford type B aortic dissections (ADs) are at risk of long-term disease progression and late complications. The aim of this study was to evaluate the natural course and evolution of acute type B AD and intramural hematomas (IMHs) in patients who presented without complications during their initial hospital admission and who were treated with optimal medical management (MM). METHODS: Databases from 2 aortic centers in Europe and the United States were used to identify 136 patients with acute type B AD (n = 92) and acute type B IMH (n = 44) who presented without complications during their index admission and were treated with MM. Computed tomography angiography scans were available at onset (≤14 days) and during follow-up for those patients. Relevant data, including evidence of adverse events during follow-up (AE; defined according to current guidelines), were retrieved from medical records and by reviewing computed tomography scan images. Aortic diameters were measured with dedicated 3-dimensional software. RESULTS: The 1-, 2-, and 5-year event-free survival rates of patients with type B AD were 84.3% (95% confidence interval [CI], 74.4-90.6), 75.4% (95% CI, 64.0-83.7), and 62.6% (95% CI, 68.9-73.6), respectively. Corresponding estimates for IMH were 76.5% (95% CI, 57.8-87.8), 76.5% (95% CI, 57.8-87.8), and 68.9% (95% CI, 45.2-83.9), respectively. In patients with type B AD, risk of an AE increased with aortic growth within the first 6 months after onset. A diameter increase of 5 mm in the first half year was associated with a relative risk for AE of 2.29 (95% CI, 1.70-3.09) compared with the median 6 months' growth of 2.4 mm. In approximately 60% of patients with IMH, the abnormality resolved within 12 months and in the patients with nonresolving IMH, risk of an adverse event was greatest in the first year after onset and remained stable thereafter. CONCLUSIONS: More than one third of patients with initially uncomplicated type B AD suffer an AE under MM within 5 years of initial diagnosis. In patients with nonresolving IMH, most adverse events are observed in the first year after onset. In patients with type B AD an early aortic growth is associated with a greater risk of AE.

Targeted use of growth mixture modeling: a learning perspective.

From the statistical learning perspective, this paper shows a new direction for the use of growth mixture modeling (GMM), a method of identifying latent subpopulations that manifest heterogeneous outcome trajectories. In the proposed approach, we utilize the benefits of the conventional use of GMM for the purpose of generating potential candidate models based on empirical model fitting, which can be viewed as unsupervised learning. We then evaluate candidate GMM models on the basis of a direct measure of success; how well the trajectory types are predicted by clinically and demographically relevant baseline features, which can be viewed as supervised learning. We examine the proposed approach focusing on a particular utility of latent trajectory classes, as outcomes that can be used as valid prediction targets in clinical prognostic models. Our approach is illustrated using data from the Longitudinal Assessment of Manic Symptoms study. Copyright © 2016 John Wiley & Sons, Ltd.

Combinatorial extracellular matrix microenvironments promote survival and phenotype of human induced pluripotent stem cell-derived endothelial cells in hypoxia.

UNLABELLED: Recent developments in cell therapy using human induced pluripotent stem cell-derived endothelial cells (iPSC-ECs) hold great promise for treating ischemic cardiovascular tissues. However, poor post-transplantation viability largely limits the potential of stem cell therapy. Although the extracellular matrix (ECM) has become increasingly recognized as an important cell survival factor, conventional approaches primarily rely on single ECMs for in vivo co-delivery with cells, even though the endothelial basement membrane is comprised of a milieu of different ECMs. To address this limitation, we developed a combinatorial ECM microarray platform to simultaneously interrogate hundreds of micro-scale multi-component chemical compositions of ECMs on iPSC-EC response. After seeding iPSC-ECs onto ECM microarrays, we performed high-throughput analysis of the effects of combinatorial ECMs on iPSC-EC survival, endothelial phenotype, and nitric oxide production under conditions of hypoxia (1% O2) and reduced nutrients (1% fetal bovine serum), as is present in ischemic injury sites. Using automated image acquisition and analysis, we identified combinatorial ECMs such as collagen IV+gelatin+heparan sulfate+laminin and collagen IV+fibronectin+gelatin+heparan sulfate+laminin that significantly improved cell survival, nitric oxide production, and CD31 phenotypic expression, in comparison to single-component ECMs. These results were further validated in conventional cell culture platforms and within three-dimensional scaffolds. Furthermore, this approach revealed complex ECM interactions and non-intuitive cell behavior that otherwise could not be easily determined using conventional cell culture platforms. Together these data suggested that iPSC-EC delivery within optimal combinatorial ECMs may improve their survival and function under the condition of hypoxia with reduced nutrients. STATEMENT OF SIGNIFICANCE: Human endothelial cells (ECs) derived from induced pluripotent stem cells (iPSC-ECs) are promising for treating diseases associated with reduced nutrient and oxygen supply like heart failure. However, diminished iPSC-EC survival after implantation into diseased environments limits their therapeutic potential. Since native ECs interact with numerous extracellular matrix (ECM) proteins for functional maintenance, we hypothesized that combinatorial ECMs may improve cell survival and function under conditions of reduced oxygen and nutrients. We developed a high-throughput system for simultaneous screening of iPSC-ECs cultured on multi-component ECM combinations under the condition of hypoxia and reduced serum. Using automated image acquisition and analytical algorithms, we identified combinatorial ECMs that significantly improved cell survival and function, in comparison to single ECMs. Furthermore, this approach revealed complex ECM interactions and non-intuitive cell behavior that otherwise could not be easily determined.

Learning the Structure of Mixed Graphical Models.

We consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to structure learning. In previous work, authors have considered structure learning of Gaussian graphical models and structure learning of discrete models. Our approach is a natural generalization of these two lines of work to the mixed case. The penalization scheme involves a novel symmetric use of the group-lasso norm and follows naturally from a particular parametrization of the model. Supplementary materials for this paper are available online.

Effective degrees of freedom: a flawed metaphor.

To most applied statisticians, a fitting procedure's degrees of freedom is synonymous with its model complexity, or its capacity for overfitting to data. In particular, it is often used to parameterize the bias-variance tradeoff in model selection. We argue that, on the contrary, model complexity and degrees of freedom may correspond very poorly. We exhibit and theoretically explore various fitting procedures for which degrees of freedom is not monotonic in the model complexity parameter, and can exceed the total dimension of the ambient space even in very simple settings. We show that the degrees of freedom for any non-convex projection method can be unbounded.

Network-based elucidation of human disease similarities reveals common functional modules enriched for pluripotent drug targets.

Current work in elucidating relationships between diseases has largely been based on pre-existing knowledge of disease genes. Consequently, these studies are limited in their discovery of new and unknown disease relationships. We present the first quantitative framework to compare and contrast diseases by an integrated analysis of disease-related mRNA expression data and the human protein interaction network. We identified 4,620 functional modules in the human protein network and provided a quantitative metric to record their responses in 54 diseases leading to 138 significant similarities between diseases. Fourteen of the significant disease correlations also shared common drugs, supporting the hypothesis that similar diseases can be treated by the same drugs, allowing us to make predictions for new uses of existing drugs. Finally, we also identified 59 modules that were dysregulated in at least half of the diseases, representing a common disease-state "signature". These modules were significantly enriched for genes that are known to be drug targets. Interestingly, drugs known to target these genes/proteins are already known to treat significantly more diseases than drugs targeting other genes/proteins, highlighting the importance of these core modules as prime therapeutic opportunities.