A high-dimensional mediation model for a neuroimaging mediator: Integrating clinical,neuroimaging, and neurocognitive data to mitigate late effects in pediatric cancer

Pediatric cancer treatment, especially for brain tumors, can have profound and complicated late effects. With the survival rates increasing because of improved detection and treatment, a more comprehensive understanding of the impact of current treatments on neurocognitive function and brain structure is critically needed. A frontline medulloblastoma clinical trial (SJMB03) has collected data, including treatment, clinical, neuroimaging, and cognitive variables. Advanced methods for modeling and integrating these data are critically needed to understand the mediation pathway from the treatment through brain structure to neurocognitive outcomes. We propose an integrative Bayesian mediation analysis approach to model jointly a treatment exposure, a high-dimensional structural neuroimaging mediator, and a neurocognitive outcome and to uncover the mediation pathway. The high-dimensional imaging-related coefficients are modeled via a binary Ising–Gaussian Markov random field prior (BI-GMRF), addressing the sparsity, spatial dependency, and smoothness and increasing the power to detect brain regions with mediation effects. Numerical simulations demonstrate the estimation accuracy, power, and robustness. For the SJMB03 study, the BI-GMRF method has identified white matter microstructure that is damaged by cancer-directed treatment and impacts late neurocognitive outcomes. The results provide guidance on improving treatment planning to minimize long-term cognitive sequela for pediatric brain tumor patients.     

Generalized causal mediation analysis

The goal of mediation analysis is to assess direct and indirect effects of a treatment or exposure on an outcome. More generally, we may be interested in the context of a causal model as characterized by a directed acyclic graph (DAG), where mediation via a specific path from exposure to outcome may involve an arbitrary number of links (or "stages"). Methods for estimating mediation (or pathway) effects are available for a continuous outcome and a continuous mediator related via a linear model, while for a categorical outcome or categorical mediator, methods are usually limited to two-stage mediation. We present a method applicable to multiple stages of mediation and mixed variable types using generalized linear models. We define pathway effects using a potential outcomes framework and present a general formula that provides the effect of exposure through any specified pathway. Some pathway effects are nonidentifiable and their estimation requires an assumption regarding the correlation between counterfactuals. We provide a sensitivity analysis to assess the impact of this assumption. Confidence intervals for pathway effect estimates are obtained via a bootstrap method. The method is applied to a cohort study of dental caries in very low birth weight adolescents. A simulation study demonstrates low bias of pathway effect estimators and close-to-nominal coverage rates of confidence intervals. We also find low sensitivity to the counterfactual correlation in most scenarios.     

Bayesian mapping of quantitative trait loci for multiple complex traits with the use of variance components

Complex traits important for humans are often correlated phenotypically and genetically. Joint mapping of quantitative-trait loci (QTLs) for multiple correlated traits plays an important role in unraveling the genetic architecture of complex traits. Compared with single-trait analysis, joint mapping addresses more questions and has advantages for power of QTL detection and precision of parameter estimation. Some statistical methods have been developed to map QTLs underlying multiple traits, most of which are based on maximum-likelihood methods. We develop here a multivariate version of the Bayes methodology for joint mapping of QTLs, using the Markov chain-Monte Carlo (MCMC) algorithm. We adopt a variance-components method to model complex traits in outbred populations (e.g., humans). The method is robust, can deal with an arbitrary number of alleles with arbitrary patterns of gene actions (such as additive and dominant), and allows for multiple phenotype data of various types in the joint analysis (e.g., multiple continuous traits and mixtures of continuous traits and discrete traits). Under a Bayesian framework, parameters--including the number of QTLs--are estimated on the basis of their marginal posterior samples, which are generated through two samplers, the Gibbs sampler and the reversible-jump MCMC. In addition, we calculate the Bayes factor related to each identified QTL, to test coincident linkage versus pleiotropy. The performance of our method is evaluated in simulations with full-sib families. The results show that our proposed Bayesian joint-mapping method performs well for mapping multiple QTLs in situations of either bivariate continuous traits or mixed data types. Compared with the analysis for each trait separately, Bayesian joint mapping improves statistical power, provides stronger evidence of QTL detection, and increases precision in estimation of parameter and QTL position. We also applied the proposed method to a set of real data and detected a coincident linkage responsible for determining bone mineral density and areal bone size of wrist in humans.     

Iterative Bayesian Model Averaging: a method for the application of survival analysis to high-dimensional microarray data

Background  

Microarray technology is increasingly used to identify potential biomarkers for cancer prognostics and diagnostics. Previously, we have developed the iterative Bayesian Model Averaging (BMA) algorithm for use in classification. Here, we extend the iterative BMA algorithm for application to survival analysis on high-dimensional microarray data. The main goal in applying survival analysis to microarray data is to determine a highly predictive model of patients' time to event (such as death, relapse, or metastasis) using a small number of selected genes. Our multivariate procedure combines the effectiveness of multiple contending models by calculating the weighted average of their posterior probability distributions. Our results demonstrate that our iterative BMA algorithm for survival analysis achieves high prediction accuracy while consistently selecting a small and cost-effective number of predictor genes.     

Causal mediation analysis in nested case-control studies using conditional logistic regression

The paper proposes an approach to causal mediation analysis in nested case-control study designs, often incorporated with countermatching schemes using conditional likelihood, and we compare the method's performance to that of mediation analysis using the Cox model for the full cohort with a continuous or dichotomous mediator. Simulation studies are conducted to assess our proposed method and investigate the efficiency relative to the cohort. We illustrate the method using actual data from two studies of potential mediation of radiation risk conducted within the Adult Health Study cohort of atomic-bomb survivors. The performance becomes comparable to that based on the full cohort, illustrating the potential for valid mediation analysis based on the reduced data obtained through the nested case-control design.     

High dimensional mediation analysis with latent variables

We propose a model for high dimensional mediation analysis that includes latent variables. We describe our model in the context of an epidemiologic study for incident breast cancer with one exposure and a large number of biomarkers (i.e., potential mediators). We assume that the exposure directly influences a group of latent, or unmeasured, factors which are associated with both the outcome and a subset of the biomarkers. The biomarkers associated with the latent factors linking the exposure to the outcome are considered “mediators.” We derive the likelihood for this model and develop an expectation‐maximization algorithm to maximize an L1‐penalized version of this likelihood to limit the number of factors and associated biomarkers. We show that the resulting estimates are consistent and that the estimates of the nonzero parameters have an asymptotically normal distribution. In simulations, procedures based on this new model can have significantly higher power for detecting the mediating biomarkers compared with the simpler approaches. We apply our method to a study that evaluates the relationship between body mass index, 481 metabolic measurements, and estrogen‐receptor positive breast cancer.     

Cuckoo search epistasis: a new method for exploring significant genetic interactions

The advent of high-throughput sequencing technology has resulted in the ability to measure millions of single-nucleotide polymorphisms (SNPs) from thousands of individuals. Although these high-dimensional data have paved the way for better understanding of the genetic architecture of common diseases, they have also given rise to challenges in developing computational methods for learning epistatic relationships among genetic markers. We propose a new method, named cuckoo search epistasis (CSE) for identifying significant epistatic interactions in population-based association studies with a case–control design. This method combines a computationally efficient Bayesian scoring function with an evolutionary-based heuristic search algorithm, and can be efficiently applied to high-dimensional genome-wide SNP data. The experimental results from synthetic data sets show that CSE outperforms existing methods including multifactorial dimensionality reduction and Bayesian epistasis association mapping. In addition, on a real genome-wide data set related to Alzheimer''s disease, CSE identified SNPs that are consistent with previously reported results, and show the utility of CSE for application to genome-wide data.     

Dissecting High-Dimensional Phenotypes with Bayesian Sparse Factor Analysis of Genetic Covariance Matrices

Quantitative genetic studies that model complex, multivariate phenotypes are important for both evolutionary prediction and artificial selection. For example, changes in gene expression can provide insight into developmental and physiological mechanisms that link genotype and phenotype. However, classical analytical techniques are poorly suited to quantitative genetic studies of gene expression where the number of traits assayed per individual can reach many thousand. Here, we derive a Bayesian genetic sparse factor model for estimating the genetic covariance matrix (G-matrix) of high-dimensional traits, such as gene expression, in a mixed-effects model. The key idea of our model is that we need consider only G-matrices that are biologically plausible. An organism’s entire phenotype is the result of processes that are modular and have limited complexity. This implies that the G-matrix will be highly structured. In particular, we assume that a limited number of intermediate traits (or factors, e.g., variations in development or physiology) control the variation in the high-dimensional phenotype, and that each of these intermediate traits is sparse – affecting only a few observed traits. The advantages of this approach are twofold. First, sparse factors are interpretable and provide biological insight into mechanisms underlying the genetic architecture. Second, enforcing sparsity helps prevent sampling errors from swamping out the true signal in high-dimensional data. We demonstrate the advantages of our model on simulated data and in an analysis of a published Drosophila melanogaster gene expression data set.     

Context Specific and Differential Gene Co-expression Networks via Bayesian Biclustering

Identifying latent structure in high-dimensional genomic data is essential for exploring biological processes. Here, we consider recovering gene co-expression networks from gene expression data, where each network encodes relationships between genes that are co-regulated by shared biological mechanisms. To do this, we develop a Bayesian statistical model for biclustering to infer subsets of co-regulated genes that covary in all of the samples or in only a subset of the samples. Our biclustering method, BicMix, allows overcomplete representations of the data, computational tractability, and joint modeling of unknown confounders and biological signals. Compared with related biclustering methods, BicMix recovers latent structure with higher precision across diverse simulation scenarios as compared to state-of-the-art biclustering methods. Further, we develop a principled method to recover context specific gene co-expression networks from the estimated sparse biclustering matrices. We apply BicMix to breast cancer gene expression data and to gene expression data from a cardiovascular study cohort, and we recover gene co-expression networks that are differential across ER+ and ER- samples and across male and female samples. We apply BicMix to the Genotype-Tissue Expression (GTEx) pilot data, and we find tissue specific gene networks. We validate these findings by using our tissue specific networks to identify trans-eQTLs specific to one of four primary tissues.     

Bayesian influence measures for joint models for longitudinal and survival data

Summary This article develops a variety of influence measures for carrying out perturbation (or sensitivity) analysis to joint models of longitudinal and survival data (JMLS) in Bayesian analysis. A perturbation model is introduced to characterize individual and global perturbations to the three components of a Bayesian model, including the data points, the prior distribution, and the sampling distribution. Local influence measures are proposed to quantify the degree of these perturbations to the JMLS. The proposed methods allow the detection of outliers or influential observations and the assessment of the sensitivity of inferences to various unverifiable assumptions on the Bayesian analysis of JMLS. Simulation studies and a real data set are used to highlight the broad spectrum of applications for our Bayesian influence methods.     

Bayesian joint mapping of quantitative trait loci for Gaussian and categorical characters in line crosses

Methodology for joint mapping of quantitative trait loci (QTL) affecting continuous and binary characters in experimental crosses is presented. The procedure consists of a Bayesian Gaussian-threshold model implemented via Markov chain Monte Carlo, which bypasses bottlenecks due to high-dimensional integrals required in maximum likelihood approaches. The method handles multiple binary traits and multiple QTL. Modeling of ordered categorical traits is discussed as well. Features of the method are illustrated using simulated datasets representing a backcross design, and the data are analyzed using mixed-trait and single-trait models. The mixed-trait analysis provides greater detection power of a QTL than a single-trait analysis when the QTL affects two or more traits. The number of QTL inferred in the mixed-trait analysis does not pertain to a specific trait, but the roles of each QTL on specific traits can be assessed from estimates of its effects. The impacts of varying incidence level and sample size on the mixed-trait QTL mapping analysis are investigated as well.     

Granger mediation analysis of multiple time series with an application to functional magnetic resonance imaging

This paper presents Granger mediation analysis, a new framework for causal mediation analysis of multiple time series. This framework is motivated by a functional magnetic resonance imaging (fMRI) experiment where we are interested in estimating the mediation effects between a randomized stimulus time series and brain activity time series from two brain regions. The independent observation assumption is thus unrealistic for this type of time‐series data. To address this challenge, our framework integrates two types of models: causal mediation analysis across the mediation variables, and vector autoregressive (VAR) models across the temporal observations. We use “Granger” to refer to VAR correlations modeled in this paper. We further extend this framework to handle multilevel data, in order to model individual variability and correlated errors between the mediator and the outcome variables. Using Rubin's potential outcome framework, we show that the causal mediation effects are identifiable under our time‐series model. We further develop computationally efficient algorithms to maximize our likelihood‐based estimation criteria. Simulation studies show that our method reduces the estimation bias and improves statistical power, compared with existing approaches. On a real fMRI data set, our approach quantifies the causal effects through a brain pathway, while capturing the dynamic dependence between two brain regions.     

Bayesian sensitivity analysis methods to evaluate bias due to misclassification and missing data using informative priors and external validation data

Background: Recent research suggests that the Bayesian paradigm may be useful for modeling biases in epidemiological studies, such as those due to misclassification and missing data. We used Bayesian methods to perform sensitivity analyses for assessing the robustness of study findings to the potential effect of these two important sources of bias. Methods: We used data from a study of the joint associations of radiotherapy and smoking with primary lung cancer among breast cancer survivors. We used Bayesian methods to provide an operational way to combine both validation data and expert opinion to account for misclassification of the two risk factors and missing data. For comparative purposes we considered a “full model” that allowed for both misclassification and missing data, along with alternative models that considered only misclassification or missing data, and the naïve model that ignored both sources of bias. Results: We identified noticeable differences between the four models with respect to the posterior distributions of the odds ratios that described the joint associations of radiotherapy and smoking with primary lung cancer. Despite those differences we found that the general conclusions regarding the pattern of associations were the same regardless of the model used. Overall our results indicate a nonsignificantly decreased lung cancer risk due to radiotherapy among nonsmokers, and a mildly increased risk among smokers. Conclusions: We described easy to implement Bayesian methods to perform sensitivity analyses for assessing the robustness of study findings to misclassification and missing data.     

A bayesian approach to improved estimation of causal effect predictiveness for a principal surrogate endpoint

Summary The literature on potential outcomes has shown that traditional methods for characterizing surrogate endpoints in clinical trials based only on observed quantities can fail to capture causal relationships between treatments, surrogates, and outcomes. Building on the potential-outcomes formulation of a principal surrogate, we introduce a Bayesian method to estimate the causal effect predictiveness (CEP) surface and quantify a candidate surrogate's utility for reliably predicting clinical outcomes. In considering the full joint distribution of all potentially observable quantities, our Bayesian approach has the following features. First, our approach illuminates implicit assumptions embedded in previously-used estimation strategies that have been shown to result in poor performance. Second, our approach provides tools for making explicit and scientifically-interpretable assumptions regarding associations about which observed data are not informative. Through simulations based on an HIV vaccine trial, we found that the Bayesian approach can produce estimates of the CEP surface with improved performance compared to previous methods. Third, our approach can extend principal-surrogate estimation beyond the previously considered setting of a vaccine trial where the candidate surrogate is constant in one arm of the study. We illustrate this extension through an application to an AIDS therapy trial where the candidate surrogate varies in both treatment arms.     

Joint inference of microsatellite mutation models, population history and genealogies using transdimensional Markov Chain Monte Carlo

We provide a framework for Bayesian coalescent inference from microsatellite data that enables inference of population history parameters averaged over microsatellite mutation models. To achieve this we first implemented a rich family of microsatellite mutation models and related components in the software package BEAST. BEAST is a powerful tool that performs Bayesian MCMC analysis on molecular data to make coalescent and evolutionary inferences. Our implementation permits the application of existing nonparametric methods to microsatellite data. The implemented microsatellite models are based on the replication slippage mechanism and focus on three properties of microsatellite mutation: length dependency of mutation rate, mutational bias toward expansion or contraction, and number of repeat units changed in a single mutation event. We develop a new model that facilitates microsatellite model averaging and Bayesian model selection by transdimensional MCMC. With Bayesian model averaging, the posterior distributions of population history parameters are integrated across a set of microsatellite models and thus account for model uncertainty. Simulated data are used to evaluate our method in terms of accuracy and precision of estimation and also identification of the true mutation model. Finally we apply our method to a red colobus monkey data set as an example.     

A Bayesian Approach to Pathway Analysis by Integrating Gene–Gene Functional Directions and Microarray Data

Many statistical methods have been developed to screen for differentially expressed genes associated with specific phenotypes in the microarray data. However, it remains a major challenge to synthesize the observed expression patterns with abundant biological knowledge for more complete understanding of the biological functions among genes. Various methods including clustering analysis on genes, neural network, Bayesian network and pathway analysis have been developed toward this goal. In most of these procedures, the activation and inhibition relationships among genes have hardly been utilized in the modeling steps. We propose two novel Bayesian models to integrate the microarray data with the putative pathway structures obtained from the KEGG database and the directional gene–gene interactions in the medical literature. We define the symmetric Kullback–Leibler divergence of a pathway, and use it to identify the pathway(s) most supported by the microarray data. Monte Carlo Markov Chain sampling algorithm is given for posterior computation in the hierarchical model. The proposed method is shown to select the most supported pathway in an illustrative example. Finally, we apply the methodology to a real microarray data set to understand the gene expression profile of osteoblast lineage at defined stages of differentiation. We observe that our method correctly identifies the pathways that are reported to play essential roles in modulating bone mass.     

缺失数据和贝叶斯系统发育分析精确度之探索

The effect of missing data on phylogenetic methods is a potentially important issue in our attempts to reconstruct the Tree of Life. If missing data are truly problematic, then it may be unwise to include species in an analysis that lack data for some characters (incomplete taxa) or to include characters that lack data for some species. Given the difficulty of obtaining data from all characters for all taxa (e.g., fossils), missing data might seriously impede efforts to reconstruct a comprehensive phylogeny that includes all species. Fortunately, recent simulations and empirical analyses suggest that missing data cells are not themselves problematic, and that incomplete taxa can be accurately placed as long as the overall number of characters in the analysis is large. However, these studies have so far only been conducted on parsimony, likelihood, and neighbor-joining methods. Although Bayesian phylogenetic methods have become widely used in recent years, the effects of missing data on Bayesian analysis have not been adequately studied. Here, we conduct simulations to test whether Bayesian analyses can accurately place incomplete taxa despite extensive missing data. In agreement with previous studies of other methods, we find that Bayesian analyses can accurately reconstruct the position of highly incomplete taxa (i.e., 95% missing data), as long as the overall number of characters in the analysis is large. These results suggest that highly incomplete taxa can be safely included in many Bayesian phylogenetic analyses.     

Mining Pure,Strict Epistatic Interactions from High-Dimensional Datasets: Ameliorating the Curse of Dimensionality

Background

The interaction between loci to affect phenotype is called epistasis. It is strict epistasis if no proper subset of the interacting loci exhibits a marginal effect. For many diseases, it is likely that unknown epistatic interactions affect disease susceptibility. A difficulty when mining epistatic interactions from high-dimensional datasets concerns the curse of dimensionality. There are too many combinations of SNPs to perform an exhaustive search. A method that could locate strict epistasis without an exhaustive search can be considered the brass ring of methods for analyzing high-dimensional datasets.

Methodology/Findings

A SNP pattern is a Bayesian network representing SNP-disease relationships. The Bayesian score for a SNP pattern is the probability of the data given the pattern, and has been used to learn SNP patterns. We identified a bound for the score of a SNP pattern. The bound provides an upper limit on the Bayesian score of any pattern that could be obtained by expanding a given pattern. We felt that the bound might enable the data to say something about the promise of expanding a 1-SNP pattern even when there are no marginal effects. We tested the bound using simulated datasets and semi-synthetic high-dimensional datasets obtained from GWAS datasets. We found that the bound was able to dramatically reduce the search time for strict epistasis. Using an Alzheimer''s dataset, we showed that it is possible to discover an interaction involving the APOE gene based on its score because of its large marginal effect, but that the bound is most effective at discovering interactions without marginal effects.

Conclusions/Significance

We conclude that the bound appears to ameliorate the curse of dimensionality in high-dimensional datasets. This is a very consequential result and could be pivotal in our efforts to reveal the dark matter of genetic disease risk from high-dimensional datasets.