The role of body mass index at diagnosis of colorectal cancer on Black-White disparities in survival: a density regression mediation approach.

The study of racial/ethnic inequalities in health is important to reduce the uneven burden of disease. In the case of colorectal cancer (CRC), disparities in survival among non-Hispanic Whites and Blacks are well documented, and mechanisms leading to these disparities need to be studied formally. It has also been established that body mass index (BMI) is a risk factor for developing CRC, and recent literature shows BMI at diagnosis of CRC is associated with survival. Since BMI varies by racial/ethnic group, a question that arises is whether differences in BMI are partially responsible for observed racial/ethnic disparities in survival for CRC patients. This article presents new methodology to quantify the impact of the hypothetical intervention that matches the BMI distribution in the Black population to a potentially complex distributional form observed in the White population on racial/ethnic disparities in survival. Our density mediation approach can be utilized to estimate natural direct and indirect effects in the general causal mediation setting under stronger assumptions. We perform a simulation study that shows our proposed Bayesian density regression approach performs as well as or better than current methodology allowing for a shift in the mean of the distribution only, and that standard practice of categorizing BMI leads to large biases when BMI is a mediator variable. When applied to motivating data from the Cancer Care Outcomes Research and Surveillance (CanCORS) Consortium, our approach suggests the proposed intervention is potentially beneficial for elderly and low-income Black patients, yet harmful for young or high-income Black populations.

The competition-compensation account of developmental language disorder.

Children with developmental language disorder (DLD) regularly use the bare form of verbs (e.g., dance) instead of inflected forms (e.g., danced). We propose an account of this behavior in which processing difficulties of children with DLD disproportionally affect processing novel inflected verbs in their input. Limited experience with inflection in novel contexts leads the inflection to face stronger competition from alternatives. Competition is resolved through a compensatory behavior that involves producing a more accessible alternative: in English, the bare form. We formalize this hypothesis within a probabilistic model that trades off context-dependent versus independent processing. Results show an over-reliance on preceding stem contexts when retrieving the inflection in a model that has difficulty with processing novel inflected forms. We further show that following the introduction of a bias to store and retrieve forms with preceding contexts, generalization in the typically developing (TD) models remains more or less stable, while the same bias in the DLD models exaggerates difficulties with generalization. Together, the results suggest that inconsistent use of inflectional morphemes by children with DLD could stem from inferences they make on the basis of data containing fewer novel inflected forms. Our account extends these findings to suggest that problems with detecting a form in novel contexts combined with a bias to rely on familiar contexts when retrieving a form could explain sequential planning difficulties in children with DLD. RESEARCH HIGHLIGHTS: Generalization difficulties with inflectional morphemes in children with Developmental Language Disorder arise from these children's limited experience with novel inflected forms. Limited experience with a form in novel contexts could lead to a storage bias where retrieving a form often requires relying on familiar preceding stems. While generalization in typically developing models remains stable across a range of model parameters, certain parameter values in the impaired models exaggerate difficulties with generalization. Children with DLD compensate for these retrieval difficulties through accessibility-driven language production: they produce the most accessible form among the alternatives.

TIGAR: An Improved Bayesian Tool for Transcriptomic Data Imputation Enhances Gene Mapping of Complex Traits.

The transcriptome-wide association studies (TWASs) that test for association between the study trait and the imputed gene expression levels from cis-acting expression quantitative trait loci (cis-eQTL) genotypes have successfully enhanced the discovery of genetic risk loci for complex traits. By using the gene expression imputation models fitted from reference datasets that have both genetic and transcriptomic data, TWASs facilitate gene-based tests with GWAS data while accounting for the reference transcriptomic data. The existing TWAS tools like PrediXcan and FUSION use parametric imputation models that have limitations for modeling the complex genetic architecture of transcriptomic data. Therefore, to improve on this, we employ a nonparametric Bayesian method that was originally proposed for genetic prediction of complex traits, which assumes a data-driven nonparametric prior for cis-eQTL effect sizes. The nonparametric Bayesian method is flexible and general because it includes both of the parametric imputation models used by PrediXcan and FUSION as special cases. Our simulation studies showed that the nonparametric Bayesian model improved both imputation R2 for transcriptomic data and the TWAS power over PrediXcan when ≥1% cis-SNPs co-regulate gene expression and gene expression heritability ≤0.2. In real applications, the nonparametric Bayesian method fitted transcriptomic imputation models for 57.8% more genes over PrediXcan, thus improving the power of follow-up TWASs. We implement both parametric PrediXcan and nonparametric Bayesian methods in a convenient software tool "TIGAR" (Transcriptome-Integrated Genetic Association Resource), which imputes transcriptomic data and performs subsequent TWASs using individual-level or summary-level GWAS data.

Model Checking with Right Censored Data Using Relative Belief Ratio.

Model checking is a topic of special interest in statistics. When data are censored, the problem becomes more difficult. This paper employs the relative belief ratio and the beta-Stacy process to develop a method for model checking in the presence of right-censored data. The proposed method for the given model of interest compares the concentration of the posterior distribution to the concentration of the prior distribution using a relative belief ratio. We propose a computational algorithm for the method and then illustrate the method through several data analysis examples.

A semiparametric Bayesian approach to population finding with time-to-event and toxicity data in a randomized clinical trial.

A utility-based Bayesian population finding (BaPoFi) method was proposed by Morita and Müller to analyze data from a randomized clinical trial with the aim of identifying good predictive baseline covariates for optimizing the target population for a future study. The approach casts the population finding process as a formal decision problem together with a flexible probability model using a random forest to define a regression mean function. BaPoFi is constructed to handle a single continuous or binary outcome variable. In this paper, we develop BaPoFi-TTE as an extension of the earlier approach for clinically important cases of time-to-event (TTE) data with censoring, and also accounting for a toxicity outcome. We model the association of TTE data with baseline covariates using a semiparametric failure time model with a Pólya tree prior for an unknown error term and a random forest for a flexible regression mean function. We define a utility function that addresses a trade-off between efficacy and toxicity as one of the important clinical considerations for population finding. We examine the operating characteristics of the proposed method in extensive simulation studies. For illustration, we apply the proposed method to data from a randomized oncology clinical trial. Concerns in a preliminary analysis of the same data based on a parametric model motivated the proposed more general approach.

Data-driven experimental design and model development using Gaussian process with active learning.

Interest in computational modeling of cognition and behavior continues to grow. To be most productive, modelers should be equipped with tools that ensure optimal efficiency in data collection and in the integrity of inference about the phenomenon of interest. Traditionally, models in cognitive science have been parametric, which are particularly susceptible to model misspecification because their strong assumptions (e.g. parameterization, functional form) may introduce unjustified biases in data collection and inference. To address this issue, we propose a data-driven nonparametric framework for model development, one that also includes optimal experimental design as a goal. It combines Gaussian Processes, a stochastic process often used for regression and classification, with active learning, from machine learning, to iteratively fit the model and use it to optimize the design selection throughout the experiment. The approach, dubbed Gaussian process with active learning (GPAL), is an extension of the parametric, adaptive design optimization (ADO) framework (Cavagnaro, Myung, Pitt, & Kujala, 2010). We demonstrate the application and features of GPAL in a delay discounting task and compare its performance to ADO in two experiments. The results show that GPAL is a viable modeling framework that is noteworthy for its high sensitivity to individual differences, identifying novel patterns in the data that were missed by the model-constrained ADO. This investigation represents a first step towards the development of a data-driven cognitive modeling framework that serves as a middle ground between raw data, which can be difficult to interpret, and parametric models, which rely on strong assumptions.

A dependent Dirichlet process model for survival data with competing risks.

In this paper, we first propose a dependent Dirichlet process (DDP) model using a mixture of Weibull models with each mixture component resembling a Cox model for survival data. We then build a Dirichlet process mixture model for competing risks data without regression covariates. Next we extend this model to a DDP model for competing risks regression data by using a multiplicative covariate effect on subdistribution hazards in the mixture components. Though built on proportional hazards (or subdistribution hazards) models, the proposed nonparametric Bayesian regression models do not require the assumption of constant hazard (or subdistribution hazard) ratio. An external time-dependent covariate is also considered in the survival model. After describing the model, we discuss how both cause-specific and subdistribution hazard ratios can be estimated from the same nonparametric Bayesian model for competing risks regression. For use with the regression models proposed, we introduce an omnibus prior that is suitable when little external information is available about covariate effects. Finally we compare the models' performance with existing methods through simulations. We also illustrate the proposed competing risks regression model with data from a breast cancer study. An R package "DPWeibull" implementing all of the proposed methods is available at CRAN.

Bayesian additive adaptive basis tensor product models for modeling high dimensional surfaces: an application to high-throughput toxicity testing.

Many modern datasets are sampled with error from complex high-dimensional surfaces. Methods such as tensor product splines or Gaussian processes are effective and well suited for characterizing a surface in two or three dimensions, but they may suffer from difficulties when representing higher dimensional surfaces. Motivated by high throughput toxicity testing where observed dose-response curves are cross sections of a surface defined by a chemical's structural properties, a model is developed to characterize this surface to predict untested chemicals' dose-responses. This manuscript proposes a novel approach that models the multidimensional surface as a sum of learned basis functions formed as the tensor product of lower dimensional functions, which are themselves representable by a basis expansion learned from the data. The model is described and a Gibbs sampling algorithm is proposed. The approach is investigated in a simulation study and through data taken from the US EPA's ToxCast high throughput toxicity testing platform.

Optimizing and evaluating biomarker combinations as trial-level general surrogates.

We extend the method proposed in a recent work by the Authors for trial-level general surrogate evaluation to allow combinations of biomarkers and provide a procedure for finding the "best" combination of biomarkers based on the absolute prediction error summary of surrogate quality. We use a nonparametric Bayesian model that allows us to select an optimal subset of biomarkers without having to consider a large number of explicit model specifications for that subset. This dramatically reduces the number of model comparisons needed. Given the model's flexibility, complex nonlinear relationships can be fit when enough data are available. We evaluate the operating characteristics of our proposed method in simulations designed to be similar to our motivating example. We use our method to compare and evaluate combinations of biomarkers as trial-level general surrogates for the pentavalent rotavirus vaccine RotaTeq™ (RV5) (Merck & Co, Inc, Kenilworth, New Jersey, USA), finding that the same single biomarker identified in our previously published analysis is likely the optimal subset.

A flexible mixed-effect negative binomial regression model for detecting unusual increases in MRI lesion counts in individual multiple sclerosis patients.

We develop a new modeling approach to enhance a recently proposed method to detect increases of contrast-enhancing lesions (CELs) on repeated magnetic resonance imaging, which have been used as an indicator for potential adverse events in multiple sclerosis clinical trials. The method signals patients with unusual increases in CEL activity by estimating the probability of observing CEL counts as large as those observed on a patient's recent scans conditional on the patient's CEL counts on previous scans. This conditional probability index (CPI), computed based on a mixed-effect negative binomial regression model, can vary substantially depending on the choice of distribution for the patient-specific random effects. Therefore, we relax this parametric assumption to model the random effects with an infinite mixture of beta distributions, using the Dirichlet process, which effectively allows any form of distribution. To our knowledge, no previous literature considers a mixed-effect regression for longitudinal count variables where the random effect is modeled with a Dirichlet process mixture. As our inference is in the Bayesian framework, we adopt a meta-analytic approach to develop an informative prior based on previous clinical trials. This is particularly helpful at the early stages of trials when less data are available. Our enhanced method is illustrated with CEL data from 10 previous multiple sclerosis clinical trials. Our simulation study shows that our procedure estimates the CPI more accurately than parametric alternatives when the patient-specific random effect distribution is misspecified and that an informative prior improves the accuracy of the CPI estimates.

Modeling a preference-based index for two condition-specific measures (asthma and overactive bladder) using a nonparametric Bayesian method.

BACKGROUND: Conventionally, parametric models were used for health state valuation data. Recently, researchers started to explore the use of nonparametric Bayesian methods in this area. OBJECTIVES: We present a nonparametric Bayesian model to estimate a preference-based index for two condition-specific five-dimensional health state classifications, one for asthma (five-dimensional Asthma Quality of Life Utility Index) and the other for overactive bladder (five-dimensional Overactive Bladder Quality of Life-Utility Index). METHODS: Samples of 307 and 311 members of the UK general population valued 99 health states selected from a total of 3125 health states defined by each of the measures using the time trade-off technique. The article presents the results of the nonparametric model and compares it with the original model estimated using a conventional parametric random-effects model. The different methods are compared theoretically and in terms of empirical performance across the two data sets. It also reports the effect of respondent characteristics on health state valuations. RESULTS: The nonparametric models were found to be better at predicting health state values within the estimation sample than without in terms of root mean square error and the patterns of standardized residuals. Some respondent characteristics were found to explain variation in health state values, but these did not have a significant effect on the health states values when estimates were adjusted for sample differences with the general population. CONCLUSIONS: The nonparametric Bayesian models are theoretically more appropriate than previously used parametric models and provide better utility estimates from the two condition-specific measures. Furthermore, the model is more flexible in estimating the effect of covariates.

A Bayesian nonparametric approach for handling item and examinee heterogeneity in assessment data.

We propose a novel nonparametric Bayesian item response theory model that estimates clusters at the question level, while simultaneously allowing for heterogeneity at the examinee level under each question cluster, characterized by a mixture of binomial distributions. The main contribution of this work is threefold. First, we present our new model and demonstrate that it is identifiable under a set of conditions. Second, we show that our model can correctly identify question-level clusters asymptotically, and the parameters of interest that measure the proficiency of examinees in solving certain questions can be estimated at a n rate (up to a log term). Third, we present a tractable sampling algorithm to obtain valid posterior samples from our proposed model. Compared to the existing methods, our model manages to reveal the multi-dimensionality of the examinees' proficiency level in handling different types of questions parsimoniously by imposing a nested clustering structure. The proposed model is evaluated via a series of simulations as well as apply it to an English proficiency assessment data set. This data analysis example nicely illustrates how our model can be used by test makers to distinguish different types of students and aid in the design of future tests.

Prioritizing Disease Diagnosis in Neonatal Cohorts through Multivariate Survival Analysis: A Nonparametric Bayesian Approach.

Understanding the intricate relationships between diseases is critical for both prevention and recovery. However, there is a lack of suitable methodologies for exploring the precedence relationships within multiple censored time-to-event data, resulting in decreased analytical accuracy. This study introduces the Censored Event Precedence Analysis (CEPA), which is a nonparametric Bayesian approach suitable for understanding the precedence relationships in censored multivariate events. CEPA aims to analyze the precedence relationships between events to predict subsequent occurrences effectively. We applied CEPA to neonatal data from the National Health Insurance Service, identifying the precedence relationships among the seven most commonly diagnosed diseases categorized by the International Classification of Diseases. This analysis revealed a typical diagnostic sequence, starting with respiratory diseases, followed by skin, infectious, digestive, ear, eye, and injury-related diseases. Furthermore, simulation studies were conducted to demonstrate CEPA suitability for censored multivariate datasets compared to traditional models. The performance accuracy reached 76% for uniform distribution and 65% for exponential distribution, showing superior performance in all four tested environments. Therefore, the statistical approach based on CEPA enhances our understanding of disease interrelationships beyond competitive methodologies. By identifying disease precedence with CEPA, we can preempt subsequent disease occurrences and propose a healthcare system based on these relationships.

Modeling SF-6D Hong Kong standard gamble health state preference data using a nonparametric Bayesian method.

OBJECTIVES: This article reports on the findings from applying a recently described approach to modeling health state valuation data and the impact of the respondent characteristics on health state valuations. The approach applies a nonparametric model to estimate a Bayesian six-dimensional health state short form (derived from short-form 36 health survey) health state valuation algorithm. METHODS: A sample of 197 states defined by the six-dimensional health state short form (derived from short-form 36 health survey)has been valued by a representative sample of the Hong Kong general population by using standard gamble. The article reports the application of the nonparametric model and compares it to the original model estimated by using a conventional parametric random effects model. The two models are compared theoretically and in terms of empirical performance. RESULTS: Advantages of the nonparametric model are that it can be used to predict scores in populations with different distributions of characteristics than observed in the survey sample and that it allows for the impact of respondent characteristics to vary by health state (while ensuring that full health passes through unity). The results suggest an important age effect with sex, having some effect, but the remaining covariates having no discernible effect. CONCLUSIONS: The nonparametric Bayesian model is argued to be more theoretically appropriate than previously used parametric models. Furthermore, it is more flexible to take into account the impact of covariates.

Complex Disease Individual Molecular Characterization Using Infinite Sparse Graphical Independent Component Analysis.

Identifying individual mechanisms involved in complex diseases, such as cancer, is essential for precision medicine. Their characterization is particularly challenging due to the unknown relationships of high-dimensional omics data and their inter-patient heterogeneity. We propose to model individual gene expression as a combination of unobserved molecular mechanisms (molecular components) that may differ between the individuals. Considering a baseline molecular profile common to all individuals, these molecular components may represent molecular pathways differing from the population background. We defined an infinite sparse graphical independent component analysis (isgICA) to identify these molecular components. This model relies on double sparseness: the source matrix sparseness defines the subset of genes involved in each molecular component, whereas the weight matrix sparseness identifies the subset of molecular components associated with each patient. As the number of molecular components is unknown but likely high, we simultaneously inferred it and the weight matrix sparseness using the beta-Bernoulli process (BBP). We simulated data from a double sparse ICA with 10/30 components with specific sparseness structures for 100/500 individuals and 500/1000/5000 genes with different noise variance levels to evaluate the reconstruction of the latent structures by our model. For all simulations, the isgICA was able to reconstruct with higher accuracy than 2 state-of-the-art methods (ica and fastICA) the number of components, the weight and source matrix sparsenesses (correlation simulated/estimated >.8). Applying our model to the expression of 1063 genes of 614 breast cancer patients, the isgICA identified 22 components. According to the source matrix, 7 of these 22 components seemed to be specifically related to 3 known molecular pathways with a prognostic effect in early breast cancer (immune system, proliferation, and stroma invasion). This proposed algorithm provides an insight into individual molecular heterogeneity to better understand complex disease mechanisms.

A Bayesian Nonparametric Approach for Modeling SF-6D Health State Utility Scores.

OBJECTIVES: Typically, models that were used for health state valuation data have been parametric. Recently, many researchers have explored the use of nonparametric Bayesian methods in this field. In this article, we report on the results from using a nonparametric model to predict a Bayesian short-form 6-dimension (SF-6D) health state valuation algorithm along with estimating the effect of the individual characteristics on health state valuations. METHODS: A sample of 126 Lebanese members from the American University of Beirut valued 49 SF-6D health states using the standard gamble technique. Results from applying the nonparametric model were reported and compared with those obtained using a standard parametric model. The covariates' effect on health state valuations was also reported. RESULTS: The nonparametric Bayesian model was found to perform better than the parametric model at (1) predicting health state values within the full estimation data and in an out-of-sample validation in terms of mean predictions, root mean squared error, and the patterns of standardized residuals and (2) allowing for the covariates' effect to vary by health state. The findings also suggest a potential age effect with some gender effect. CONCLUSIONS: The nonparametric model is theoretically more flexible and produces better utility predictions from the SF-6D than previously used classical parametric model. In addition, the Bayesian model is more appropriate to account the covariates' effect. Further research is encouraged.

TIGAR-V2: Efficient TWAS tool with nonparametric Bayesian eQTL weights of 49 tissue types from GTEx V8.

Standard transcriptome-wide association study (TWAS) methods first train gene expression prediction models using reference transcriptomic data and then test the association between the predicted genetically regulated gene expression and phenotype of interest. Most existing TWAS tools require cumbersome preparation of genotype input files and extra coding to enable parallel computation. To improve the efficiency of TWAS tools, we developed Transcriptome-Integrated Genetic Association Resource V2 (TIGAR-V2), which directly reads Variant Call Format (VCF) files, enables parallel computation, and reduces up to 90% of computation cost (mainly due to loading genotype data) compared to the original version. TIGAR-V2 can train gene expression imputation models using either nonparametric Bayesian Dirichlet process regression (DPR) or Elastic-Net (as used by PrediXcan), perform TWASs using either individual-level or summary-level genome-wide association study (GWAS) data, and implement both burden and variance-component statistics for gene-based association tests. We trained gene expression prediction models by DPR for 49 tissues using Genotype-Tissue Expression (GTEx) V8 by TIGAR-V2 and illustrated the usefulness of these Bayesian cis-expression quantitative trait locus (eQTL) weights through TWASs of breast and ovarian cancer utilizing public GWAS summary statistics. We identified 88 and 37 risk genes, respectively, for breast and ovarian cancer, most of which are either known or near previously identified GWAS (∼95%) or TWAS (∼40%) risk genes and three novel independent TWAS risk genes with known functions in carcinogenesis. These findings suggest that TWASs can provide biological insight into the transcriptional regulation of complex diseases. The TIGAR-V2 tool, trained Bayesian cis-eQTL weights, and linkage disequilibrium (LD) information from GTEx V8 are publicly available, providing a useful resource for mapping risk genes of complex diseases.

InfPolyn, a Nonparametric Bayesian Characterization for Composition-Dependent Interdiffusion Coefficients.

Composition-dependent interdiffusion coefficients are key parameters in many physical processes. However, finding such coefficients for a system with few components is challenging due to the underdetermination of the governing diffusion equations, the lack of data in practice, and the unknown parametric form of the interdiffusion coefficients. In this work, we propose InfPolyn, Infinite Polynomial, a novel statistical framework to characterize the component-dependent interdiffusion coefficients. Our model is a generalization of the commonly used polynomial fitting method with extended model capacity and flexibility and it is combined with the numerical inversion-based Boltzmann-Matano method for the interdiffusion coefficient estimations. We assess InfPolyn on ternary and quaternary systems with predefined polynomial, exponential, and sinusoidal interdiffusion coefficients. The experiments show that InfPolyn outperforms the competitors, the SOTA numerical inversion-based Boltzmann-Matano methods, with a large margin in terms of relative error (10× more accurate). Its performance is also consistent and stable, whereas the number of samples required remains small.

Modeling SF-6D Health Utilities: Is Bayesian Approach Appropriate?

BACKGROUND: Valuation studies of preference-based health measures like SF6D have been conducted in many countries. However, the cost of conducting such studies in countries with small populations or low- and middle-income countries (LMICs) can be prohibitive. There is potential to use results from readily available countries' valuations to produce better valuation estimates. METHODS: Data from Lebanon and UK SF-6D value sets were analyzed, where values for 49 and 249 health states were extracted from samples of Lebanon and UK populations, respectively, using standard gamble techniques. A nonparametric Bayesian model was used to estimate a Lebanon value set using the UK data as informative priors. The resulting estimates were then compared to a Lebanon value set obtained using Lebanon data by itself via various prediction criterions. RESULTS: The findings permit the UK evidence to contribute potential prior information to the Lebanon analysis by producing more precise valuation estimates than analyzing Lebanon data only under all criterions used. CONCLUSIONS: The positive findings suggest that existing valuation studies can be merged with a small valuation set in another country to produce value sets, thereby making own country value sets more attainable for LMICs.

Bayesian modeling of health state preferences: could borrowing strength from existing countries' valuations produce better estimates.

BACKGROUND: Valuations of preference-based measure such as EQ-5D and/or SF6D have been conducted in different countries. There is potential to borrow strength from existing countries' valuations to generate better representative utility estimates. This is explored using two case studies modelling UK data alongside Japan samples to generate Japan estimates. METHODS: Data from two SF-6D valuation studies were analyzed, where using similar standard gamble protocols, values for 241 and 249 states were devised from representative samples of Japan and UK general adult populations, respectively. Two nonparametric Bayesian models were applied to estimate a Japan value set, where the UK results were used as informative priors in the first model and subsets of the Japan data set for 25 and 50 health states were modelled alongside the full UK data set in the second. Generated estimates were compared to a Japan value set estimated using Japan values alone using different prediction criterion. RESULTS: The results allowed the UK data to provide significant prior information to the Japan analysis by generating better estimates than using Japan data alone. Also, using Japan data elicited for 50 health states alongside the existing UK data produces roughly similar predicted valuations as the Japan data by itself. CONCLUSION: The promising results suggest that the existing preference data could be combined with data from a valuation study in a new country to generate preference weights, thus making own country value sets more achievable for low-middle income countries. Further research and application to other countries and preference-based measures are encouraged.