Personalized treatment selection via product partition models with covariates.

Precision medicine is an approach for disease treatment that defines treatment strategies based on the individual characteristics of the patients. Motivated by an open problem in cancer genomics, we develop a novel model that flexibly clusters patients with similar predictive characteristics and similar treatment responses; this approach identifies, via predictive inference, which one among a set of treatments is better suited for a new patient. The proposed method is fully model based, avoiding uncertainty underestimation attained when treatment assignment is performed by adopting heuristic clustering procedures, and belongs to the class of product partition models with covariates, here extended to include the cohesion induced by the normalized generalized gamma process. The method performs particularly well in scenarios characterized by considerable heterogeneity of the predictive covariates in simulation studies. A cancer genomics case study illustrates the potential benefits in terms of treatment response yielded by the proposed approach. Finally, being model based, the approach allows estimating clusters' specific response probabilities and then identifying patients more likely to benefit from personalized treatment.

Bayesian graphical models for modern biological applications.

Graphical models are powerful tools that are regularly used to investigate complex dependence structures in high-throughput biomedical datasets. They allow for holistic, systems-level view of the various biological processes, for intuitive and rigorous understanding and interpretations. In the context of large networks, Bayesian approaches are particularly suitable because it encourages sparsity of the graphs, incorporate prior information, and most importantly account for uncertainty in the graph structure. These features are particularly important in applications with limited sample size, including genomics and imaging studies. In this paper, we review several recently developed techniques for the analysis of large networks under non-standard settings, including but not limited to, multiple graphs for data observed from multiple related subgroups, graphical regression approaches used for the analysis of networks that change with covariates, and other complex sampling and structural settings. We also illustrate the practical utility of some of these methods using examples in cancer genomics and neuroimaging.

Bayesian inference of networks across multiple sample groups and data types.

In this article, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to differing disease stage or subtype, is profiled across multiple platforms, such as metabolomics, proteomics, or transcriptomics data. Our proposed Bayesian hierarchical model first links the network structures within each platform using a Markov random field prior to relate edge selection across sample groups, and then links the network similarity parameters across platforms. This enables joint estimation in a flexible manner, as we make no assumptions on the directionality of influence across the data types or the extent of network similarity across the sample groups and platforms. In addition, our model formulation allows the number of variables and number of subjects to differ across the data types, and only requires that we have data for the same set of groups. We illustrate the proposed approach through both simulation studies and an application to gene expression levels and metabolite abundances on subjects with varying severity levels of chronic obstructive pulmonary disease. Bayesian inference; Chronic obstructive pulmonary disease (COPD); Data integration; Gaussian graphical model; Markov random field prior; Spike and slab prior.

Special issue on statistical analysis of networks: Preface by the guest editors.

The special issue on Statistical Analysis of Networks aspires to convey the breadth and depth of statistical learning with networks, ranging from networks that are observed to networks that are unobserved and learned from data. It includes ten select papers with methodological and theoretical advances, and demonstrates the usefulness of the network paradigm by applications to current problems.

Bayesian modeling of multiple structural connectivity networks during the progression of Alzheimer's disease.

Alzheimer's disease is the most common neurodegenerative disease. The aim of this study is to infer structural changes in brain connectivity resulting from disease progression using cortical thickness measurements from a cohort of participants who were either healthy control, or with mild cognitive impairment, or Alzheimer's disease patients. For this purpose, we develop a novel approach for inference of multiple networks with related edge values across groups. Specifically, we infer a Gaussian graphical model for each group within a joint framework, where we rely on Bayesian hierarchical priors to link the precision matrix entries across groups. Our proposal differs from existing approaches in that it flexibly learns which groups have the most similar edge values, and accounts for the strength of connection (rather than only edge presence or absence) when sharing information across groups. Our results identify key alterations in structural connectivity that may reflect disruptions to the healthy brain, such as decreased connectivity within the occipital lobe with increasing disease severity. We also illustrate the proposed method through simulations, where we demonstrate its performance in structure learning and precision matrix estimation with respect to alternative approaches.

Bayesian learning of multiple directed networks from observational data.

Graphical modeling represents an established methodology for identifying complex dependencies in biological networks, as exemplified in the study of co-expression, gene regulatory, and protein interaction networks. The available observations often exhibit an intrinsic heterogeneity, which impacts on the network structure through the modification of specific pathways for distinct groups, such as disease subtypes. We propose to infer the resulting multiple graphs jointly in order to benefit from potential similarities across groups; on the other hand our modeling framework is able to accommodate group idiosyncrasies. We consider directed acyclic graphs (DAGs) as network structures, and develop a Bayesian method for structural learning of multiple DAGs. We explicitly account for Markov equivalence of DAGs, and propose a suitable prior on the collection of graph spaces that induces selective borrowing strength across groups. The resulting inference allows in particular to compute the posterior probability of edge inclusion, a useful summary for representing flow directions within the network. Finally, we detail a simulation study addressing the comparative performance of our method, and present an analysis of two protein networks together with a substantive interpretation of our findings.

Calibration strategies for use of the nanoDot OSLD in CT applications.

Aluminum oxide based optically stimulated luminescent dosimeters (OSLD) have been recognized as a useful dosimeter for measuring CT dose, particularly for patient dose measurements. Despite the increasing use of this dosimeter, appropriate dosimeter calibration techniques have not been established in the literature; while the manufacturer offers a calibration procedure, it is known to have relatively large uncertainties. The purpose of this work was to evaluate two clinical approaches for calibrating these dosimeters for CT applications, and to determine the uncertainty associated with measurements using these techniques. Three unique calibration procedures were used to calculate dose for a range of CT conditions using a commercially available OSLD and reader. The three calibration procedures included calibration (a) using the vendor-provided method, (b) relative to a 120 kVp CT spectrum in air, and (c) relative to a megavoltage beam (implemented with 60 Co). The dose measured using each of these approaches was compared to dose measured using a calibrated farmer-type ion chamber. Finally, the uncertainty in the dose measured using each approach was determined. For the CT and megavoltage calibration methods, the dose measured using the OSLD nanoDot was within 5% of the dose measured using an ion chamber for a wide range of different CT scan parameters (80-140 kVp, and with measurements at a range of positions). When calibrated using the vendor-recommended protocol, the OSLD measured doses were on average 15.5% lower than ion chamber doses. Two clinical calibration techniques have been evaluated and are presented in this work as alternatives to the vendor-provided calibration approach. These techniques provide high precision for OSLD-based measurements in a CT environment.

Bayesian personalized treatment selection strategies that integrate predictive with prognostic determinants.

The evolution of "informatics" technologies has the potential to generate massive databases, but the extent to which personalized medicine may be effectuated depends on the extent to which these rich databases may be utilized to advance understanding of the disease molecular profiles and ultimately integrated for treatment selection, necessitating robust methodology for dimension reduction. Yet, statistical methods proposed to address challenges arising with the high-dimensionality of omics-type data predominately rely on linear models and emphasize associations deriving from prognostic biomarkers. Existing methods are often limited for discovering predictive biomarkers that interact with treatment and fail to elucidate the predictive power of their resultant selection rules. In this article, we present a Bayesian predictive method for personalized treatment selection that is devised to integrate both the treatment predictive and disease prognostic characteristics of a particular patient's disease. The method appropriately characterizes the structural constraints inherent to prognostic and predictive biomarkers, and hence properly utilizes these complementary sources of information for treatment selection. The methodology is illustrated through a case study of lower grade glioma. Theoretical considerations are explored to demonstrate the manner in which treatment selection is impacted by prognostic features. Additionally, simulations based on an actual leukemia study are provided to ascertain the method's performance with respect to selection rules derived from competing methods.

Transcriptomic analysis reveals inflammatory and metabolic pathways that are regulated by renal perfusion pressure in the outer medulla of Dahl-S rats.

Studies exploring the development of hypertension have traditionally been unable to distinguish which of the observed changes are underlying causes from those that are a consequence of elevated blood pressure. In this study, a custom-designed servo-control system was utilized to precisely control renal perfusion pressure to the left kidney continuously during the development of hypertension in Dahl salt-sensitive rats. In this way, we maintained the left kidney at control blood pressure while the right kidney was exposed to hypertensive pressures. As each kidney was exposed to the same circulating factors, differences between them represent changes induced by pressure alone. RNA sequencing analysis identified 1,613 differently expressed genes affected by renal perfusion pressure. Three pathway analysis methods were applied, one a novel approach incorporating arterial pressure as an input variable allowing a more direct connection between the expression of genes and pressure. The statistical analysis proposed several novel pathways by which pressure affects renal physiology. We confirmed the effects of pressure on p-Jnk regulation, in which the hypertensive medullas show increased p-Jnk/Jnk ratios relative to the left (0.79 ± 0.11 vs. 0.53 ± 0.10, P < 0.01, n = 8). We also confirmed pathway predictions of mitochondrial function, in which the respiratory control ratio of hypertensive vs. control mitochondria are significantly reduced (7.9 ± 1.2 vs. 10.4 ± 1.8, P < 0.01, n = 6) and metabolomic profile, in which 14 metabolites differed significantly between hypertensive and control medullas ( P < 0.05, n = 5). These findings demonstrate that subtle differences in the transcriptome can be used to predict functional changes of the kidney as a consequence of pressure elevation.

A Bayesian integrative approach for multi-platform genomic data: A kidney cancer case study.

Integration of genomic data from multiple platforms has the capability to increase precision, accuracy, and statistical power in the identification of prognostic biomarkers. A fundamental problem faced in many multi-platform studies is unbalanced sample sizes due to the inability to obtain measurements from all the platforms for all the patients in the study. We have developed a novel Bayesian approach that integrates multi-regression models to identify a small set of biomarkers that can accurately predict time-to-event outcomes. This method fully exploits the amount of available information across platforms and does not exclude any of the subjects from the analysis. Through simulations, we demonstrate the utility of our method and compare its performance to that of methods that do not borrow information across regression models. Motivated by The Cancer Genome Atlas kidney renal cell carcinoma dataset, our methodology provides novel insights missed by non-integrative models.

Reproducibility of patient setup in the seated treatment position: A novel treatment chair design.

Radiotherapy in a seated position may be indicated for patients who are unable to lie on the treatment couch for the duration of treatment, in scenarios where a seated treatment position provides superior anatomical positioning and dose distributions, or for a low-cost system designed using a fixed treatment beam and rotating seated patient. In this study, we report a novel treatment chair that was constructed to allow for three-dimensional imaging and treatment delivery while ensuring robust immobilization, providing reproducibility equivalent to that in the traditional supine position. Five patients undergoing radiation treatment for head-and-neck cancers were enrolled and were setup in the chair, with immobilization devices created, and then imaged with orthogonal X-rays in a scenario that mimicked radiation treatments (without treatment delivery). Six subregions of the acquired images were rigidly registered to evaluate intra- and interfraction displacement and chair construction. Displacements under conditions of simulated image guidance were acquired by first registering one subregion; the residual displacement of other subregions was then measured. Additionally, we administered a patient questionnaire to gain patient feedback and assess comparison to the supine position. Average inter- and intrafraction displacements of all subregions in the seated position were less than 2 and 3 mm, respectively. When image guidance was simulated, L-R and A-P interfraction displacements were reduced by an average of 1 mm, providing setup of comparable quality to supine setups. The enrolled patients, who had no indication for a seated treatment position, reported no preference in the seated or the supine position. The novel chair design provides acceptable inter- and intrafraction displacement, with reproducibility equivalent to that reported for patients in the supine position. Patient feedback will be incorporated in the refinement of the chair, facilitating treatment of head-and-neck cancer in patients who are unable to lie for the duration of treatment or for use in an economical fixed-beam setup.

Novel algorithmic approach predicts tumor mutation load and correlates with immunotherapy clinical outcomes using a defined gene mutation set.

BACKGROUND: While clinical outcomes following immunotherapy have shown an association with tumor mutation load using whole exome sequencing (WES), its clinical applicability is currently limited by cost and bioinformatics requirements. METHODS: We developed a method to accurately derive the predicted total mutation load (PTML) within individual tumors from a small set of genes that can be used in clinical next generation sequencing (NGS) panels. PTML was derived from the actual total mutation load (ATML) of 575 distinct melanoma and lung cancer samples and validated using independent melanoma (n = 312) and lung cancer (n = 217) cohorts. The correlation of PTML status with clinical outcome, following distinct immunotherapies, was assessed using the Kaplan-Meier method. RESULTS: PTML (derived from 170 genes) was highly correlated with ATML in cutaneous melanoma and lung adenocarcinoma validation cohorts (R2 = 0.73 and R2 = 0.82, respectively). PTML was strongly associated with clinical outcome to ipilimumab (anti-CTLA-4, three cohorts) and adoptive T-cell therapy (1 cohort) clinical outcome in melanoma. Clinical benefit from pembrolizumab (anti-PD-1) in lung cancer was also shown to significantly correlate with PTML status (log rank P value < 0.05 in all cohorts). CONCLUSIONS: The approach of using small NGS gene panels, already applied to guide employment of targeted therapies, may have utility in the personalized use of immunotherapy in cancer.

Atypical chronic myeloid leukemia is clinically distinct from unclassifiable myelodysplastic/myeloproliferative neoplasms.

Atypical chronic myeloid leukemia (aCML) is a rare subtype of myelodysplastic/myeloproliferative neoplasm (MDS/MPN) largely defined morphologically. It is, unclear, however, whether aCML-associated features are distinctive enough to allow its separation from unclassifiable MDS/MPN (MDS/MPN-U). To study these 2 rare entities, 134 patient archives were collected from 7 large medical centers, of which 65 (49%) cases were further classified as aCML and the remaining 69 (51%) as MDS/MPN-U. Distinctively, aCML was associated with many adverse features and an inferior overall survival (12.4 vs 21.8 months, P = .004) and AML-free survival (11.2 vs 18.9 months, P = .003). The aCML defining features of leukocytosis and circulating myeloid precursors, but not dysgranulopoiesis, were independent negative predictors. Other factors, such as lactate dehydrogenase, circulating myeloblasts, platelets, and cytogenetics could further stratify MDS/MPN-U but not aCML patient risks. aCML appeared to have more mutated RAS (7/20 [35%] vs 4/29 [14%]) and less JAK2p.V617F (3/42 [7%] vs 10/52 [19%]), but was not statistically significant. Somatic CSF3R T618I (0/54) and CALR (0/30) mutations were not detected either in aCML or MDS/MPN-U. In conclusion, within MDS/MPN, the World Health Organization 2008 criteria for aCML identify a subgroup of patients with features clearly distinct from MDS/MPN-U. The MDS/MPN-U category is heterogeneous, and patient risk can be further stratified by a number of clinicopathological parameters.

Bayesian predictive modeling for genomic based personalized treatment selection.

Efforts to personalize medicine in oncology have been limited by reductive characterizations of the intrinsically complex underlying biological phenomena. Future advances in personalized medicine will rely on molecular signatures that derive from synthesis of multifarious interdependent molecular quantities requiring robust quantitative methods. However, highly parameterized statistical models when applied in these settings often require a prohibitively large database and are sensitive to proper characterizations of the treatment-by-covariate interactions, which in practice are difficult to specify and may be limited by generalized linear models. In this article, we present a Bayesian predictive framework that enables the integration of a high-dimensional set of genomic features with clinical responses and treatment histories of historical patients, providing a probabilistic basis for using the clinical and molecular information to personalize therapy for future patients. Our work represents one of the first attempts to define personalized treatment assignment rules based on large-scale genomic data. We use actual gene expression data acquired from The Cancer Genome Atlas in the settings of leukemia and glioma to explore the statistical properties of our proposed Bayesian approach for personalizing treatment selection. The method is shown to yield considerable improvements in predictive accuracy when compared to penalized regression approaches.

Joint Bayesian variable and graph selection for regression models with network-structured predictors.

In this work, we develop a Bayesian approach to perform selection of predictors that are linked within a network. We achieve this by combining a sparse regression model relating the predictors to a response variable with a graphical model describing conditional dependencies among the predictors. The proposed method is well-suited for genomic applications because it allows the identification of pathways of functionally related genes or proteins that impact an outcome of interest. In contrast to previous approaches for network-guided variable selection, we infer the network among predictors using a Gaussian graphical model and do not assume that network information is available a priori. We demonstrate that our method outperforms existing methods in identifying network-structured predictors in simulation settings and illustrate our proposed model with an application to inference of proteins relevant to glioblastoma survival.

Bayesian nonlinear model selection for gene regulatory networks.

Gene regulatory networks represent the regulatory relationships between genes and their products and are important for exploring and defining the underlying biological processes of cellular systems. We develop a novel framework to recover the structure of nonlinear gene regulatory networks using semiparametric spline-based directed acyclic graphical models. Our use of splines allows the model to have both flexibility in capturing nonlinear dependencies as well as control of overfitting via shrinkage, using mixed model representations of penalized splines. We propose a novel discrete mixture prior on the smoothing parameter of the splines that allows for simultaneous selection of both linear and nonlinear functional relationships as well as inducing sparsity in the edge selection. Using simulation studies, we demonstrate the superior performance of our methods in comparison with several existing approaches in terms of network reconstruction and functional selection. We apply our methods to a gene expression dataset in glioblastoma multiforme, which reveals several interesting and biologically relevant nonlinear relationships.

miRNA-target gene regulatory networks: A Bayesian integrative approach to biomarker selection with application to kidney cancer.

The availability of cross-platform, large-scale genomic data has enabled the investigation of complex biological relationships for many cancers. Identification of reliable cancer-related biomarkers requires the characterization of multiple interactions across complex genetic networks. MicroRNAs are small non-coding RNAs that regulate gene expression; however, the direct relationship between a microRNA and its target gene is difficult to measure. We propose a novel Bayesian model to identify microRNAs and their target genes that are associated with survival time by incorporating the microRNA regulatory network through prior distributions. We assume that biomarkers involved in regulatory networks are likely associated with survival time. We employ non-local prior distributions and a stochastic search method for the selection of biomarkers associated with the survival outcome. We use KEGG pathway information to incorporate correlated gene effects within regulatory networks. Using simulation studies, we assess the performance of our method, and apply it to experimental data of kidney renal cell carcinoma (KIRC) obtained from The Cancer Genome Atlas. Our novel method validates previously identified cancer biomarkers and identifies biomarkers specific to KIRC progression that were not previously discovered. Using the KIRC data, we confirm that biomarkers involved in regulatory networks are more likely to be associated with survival time, showing connections in one regulatory network for five out of six such genes we identified.

Characterization of biological pathways associated with a 1.37 Mbp genomic region protective of hypertension in Dahl S rats.

The goal of the present study was to narrow a region of chromosome 13 to only several genes and then apply unbiased statistical approaches to identify molecular networks and biological pathways relevant to blood-pressure salt sensitivity in Dahl salt-sensitive (SS) rats. The analysis of 13 overlapping subcongenic strains identified a 1.37 Mbp region on chromosome 13 that influenced the mean arterial blood pressure by at least 25 mmHg in SS rats fed a high-salt diet. DNA sequencing and analysis filled genomic gaps and provided identification of five genes in this region, Rfwd2, Fam5b, Astn1, Pappa2, and Tnr. A cross-platform normalization of transcriptome data sets obtained from our previously published Affymetrix GeneChip dataset and newly acquired RNA-seq data from renal outer medullary tissue provided 90 observations for each gene. Two Bayesian methods were used to analyze the data: 1) a linear model analysis to assess 243 biological pathways for their likelihood to discriminate blood pressure levels across experimental groups and 2) a Bayesian graphical modeling of pathways to discover genes with potential relationships to the candidate genes in this region. As none of these five genes are known to be involved in hypertension, this unbiased approach has provided useful clues to be experimentally explored. Of these five genes, Rfwd2, the gene most strongly expressed in the renal outer medulla, was notably associated with pathways that can affect blood pressure via renal transcellular Na(+) and K(+) electrochemical gradients and tubular Na(+) transport, mitochondrial TCA cycle and cell energetics, and circadian rhythms.

Reproducibility in patient-specific IMRT QA.

The purpose of this study was to determine the reproducibility of patient-specific, intensity-modulated radiation therapy (IMRT) quality assurance (QA) results in a clinical setting. Six clinical patient plans were delivered to a variety of devices and analyses, including 1) radiographic film; 2) ion chamber; 3) 2D diode array delivered and analyzed in three different configurations (AP delivery with field-by-field analysis, AP delivery with composite analysis, and planned gantry angle delivery); 4) helical diode array; and 5) in-house-designed multiple ion chamber phantom. The six clinical plans were selected from a range of treatment sites and were of various levels of complexity. Of note, three of the plans had failed at least preliminary evaluation with our in-house IMRT QA; the other three plans had passed QA. These plans were delivered three times sequentially without changing the setup, and then delivered two more times after breaking down and rebuilding the setup between each. This allowed for an investigation of reproducibility (in terms of dose, dose difference or percent of pixels passing gamma) of both the delivery and the physical setup. This study showed that the variability introduced from the setup was generally higher than the variability from redelivering the plan. Radiographic film showed the poorest reproducibility of the dosimeters investigated. In conclusion, the various IMRT QA systems demonstrated varying abilities to reproduce QA results consistently. All dosimetric devices demonstrated a reproducibility (coefficient of variation) of less than 4% in their QA results for all plans, with an average reproducibility of less than 2%. This work provides some quantification for the variability that may be seen for IMRT QA dosimeters.

Variable selection for discriminant analysis with Markov random field priors for the analysis of microarray data.

MOTIVATION: Discriminant analysis is an effective tool for the classification of experimental units into groups. Here, we consider the typical problem of classifying subjects according to phenotypes via gene expression data and propose a method that incorporates variable selection into the inferential procedure, for the identification of the important biomarkers. To achieve this goal, we build upon a conjugate normal discriminant model, both linear and quadratic, and include a stochastic search variable selection procedure via an MCMC algorithm. Furthermore, we incorporate into the model prior information on the relationships among the genes as described by a gene-gene network. We use a Markov random field (MRF) prior to map the network connections among genes. Our prior model assumes that neighboring genes in the network are more likely to have a joint effect on the relevant biological processes. RESULTS: We use simulated data to assess performances of our method. In particular, we compare the MRF prior to a situation where independent Bernoulli priors are chosen for the individual predictors. We also illustrate the method on benchmark datasets for gene expression. Our simulation studies show that employing the MRF prior improves on selection accuracy. In real data applications, in addition to identifying markers and improving prediction accuracy, we show how the integration of existing biological knowledge into the prior model results in an increased ability to identify genes with strong discriminatory power and also aids the interpretation of the results.