Bayesian Nonparametric Inference - Why and How

A Personalized Dose-Finding Algorithm Based on Adaptive Gaussian Process Regression

Dose-finding studies play a crucial role in drug development by identifying the optimal dose(s) for later studies while considering tolerability. This not only saves time and effort in proceeding with Phase III trials but also improves efficacy. In an era of precision medicine, it is not ideal to assume patient homogeneity in dose-finding studies as patients may respond differently to the drug. To address this, we propose a personalized dose-finding algorithm that assigns patients to individualized optimal biological doses. Our design follows a two-stage approach. Initially, patients are enrolled under broad eligibility criteria. Based on the Stage 1 data, we fit a regression model of toxicity and efficacy outcomes on dose and biomarkers to characterize treatment-sensitive patients. In the second stage, we restrict the trial population to sensitive patients, apply a personalized dose allocation algorithm, and choose the recommended dose at the end of the trial. Simulation study shows that the proposed design reliably enriches the trial population, minimizes the number of failures, and yields superior operating characteristics compared to several existing dose-finding designs in terms of both the percentage of correct selection and the number of patients treated at target dose(s).

Bayesian graphical modeling for heterogeneous causal effects

There is a growing interest in current medical research to develop personalized treatments using a molecular-based approach. The broad goal is to implement a more precise and targeted decision-making process, relative to traditional treatments based primarily on clinical diagnoses. Specifically, we consider patients affected by Acute Myeloid Leukemia (AML), an hematological cancer characterized by uncontrolled proliferation of hematopoietic stem cells in the bone marrow. Because AML responds poorly to chemotherapeutic treatments, the development of targeted therapies is essential to improve patients' prospects. In particular, the dataset we analyze contains the levels of proteins involved in cell cycle regulation and linked to the progression of the disease. We evaluate treatment effects within a causal framework represented by a Directed Acyclic Graph (DAG) model, whose vertices are the protein levels in the network. A major obstacle in implementing the above program is represented by individual heterogeneity. We address this issue through a Dirichlet Process (DP) mixture of Gaussian DAG-models where both the graphical structure as well as the allied model parameters are regarded as uncertain. Our procedure determines a clustering structure of the units reflecting the underlying heterogeneity, and produces subject-specific estimates of causal effects based on Bayesian Model Averaging (BMA). With reference to the AML dataset, we identify different effects of protein regulation among individuals; moreover, our method clusters patients into groups that exhibit only mild similarities with traditional categories based on morphological features.

DNB: A Joint Learning Framework for Deep Bayesian Nonparametric Clustering

Clustering algorithms based on deep neural networks have been widely studied for image analysis. Most existing methods require partial knowledge of the true labels, namely, the number of clusters, which is usually not available in practice. In this article, we propose a Bayesian nonparametric framework, deep nonparametric Bayes (DNB), for jointly learning image clusters and deep representations in a doubly unsupervised manner. In doubly unsupervised learning, we are dealing with the problem of "unknown unknowns," where we estimate not only the unknown image labels but also the unknown number of labels as well. The proposed algorithm alternates between generating a potentially unbounded number of clusters in the forward pass and learning the deep networks in the backward pass. With the help of the Dirichlet process mixtures, the proposed method is able to partition the latent representations space without specifying the number of clusters a priori. An important feature of this work is that all the estimation is realized with an end-to-end solution, which is very different from the methods that rely on post hoc analysis to select the number of clusters. Another key idea in this article is to provide a principled solution to the problem of "trivial solution" for deep clustering, which has not been much studied in the current literature. With extensive experiments on benchmark datasets, we show that our doubly unsupervised method achieves good clustering performance and outperforms many other unsupervised image clustering methods.

Linking research of biomedical datasets

Biomedical data preprocessing and efficient computing can be as important as the statistical methods used to fit the data; data processing needs to consider application scenarios, data acquisition and individual rights and interests. We review common principles, knowledge and methods of integrated research according to the whole-pipeline processing mechanism diverse, coherent, sharing, auditable and ecological. First, neuromorphic and native algorithms integrate diverse datasets, providing linear scalability and high visualization. Second, the choice mechanism of different preprocessing, analysis and transaction methods from raw to neuromorphic was summarized on the node and coordinator platforms. Third, combination of node, network, cloud, edge, swarm and graph builds an ecosystem of cohort integrated research and clinical diagnosis and treatment. Looking forward, it is vital to simultaneously combine deep computing, mass data storage and massively parallel communication.

Utility-based Bayesian personalized treatment selection for advanced breast cancer

A Bayesian method is proposed for personalized treatment selection in settings where data are available from a randomized clinical trial with two or more outcomes. The motivating application is a randomized trial that compared letrozole plus bevacizimab to letrozole alone as first-line therapy for hormone receptor positive advanced breast cancer. The combination treatment arm had larger median progression-free survival time, but also a higher rate of severe toxicities. This suggests that the risk-benefit trade-off between these two outcomes should play a central role in selecting each patient's treatment, particularly since older patients are less likely to tolerate severe toxicities. To quantify the desirability of each possible outcome combination for an individual patient, we elicited from breast cancer oncologists a utility function that varied with age. The utility was used as an explicit criterion for quantifying risk-benefit trade-offs when making personalized treatment selections. A Bayesian nonparametric multivariate regression model with a dependent Dirichlet process prior was fit to the trial data. Under the fitted model, a new patient's treatment can be selected based on the posterior predictive utility distribution. For the breast cancer trial dataset, the optimal treatment depends on the patient's age, with the combination preferable for patients 70 years or younger and the single agent preferable for patients older than 70.

A Causal Framework for Making Individualized Treatment Decisions in Oncology

Simple Summary

Physicians routinely make individualized treatment decisions by accounting for the joint effects of patient prognostic covariates and treatments on clinical outcomes. Ideally, this is performed using historical randomized clinical trial (RCT) data. Randomization ensures that unbiased estimates of causal treatment effect parameters can be obtained from the historical RCT data and used to predict each new patient’s outcome based on the joint effect of their baseline covariates and each treatment being considered. However, this process becomes problematic if a patient seen in the clinic is very different from the patients who were enrolled in the RCT. That is, if a new patient does not satisfy the entry criteria of the RCT, then the patient does not belong to the population represented by the patients who were studied in the RCT. In such settings, it still may be possible to utilize the RCT data to help choose a new patient’s treatment. This may be achieved by combining the RCT data with data from other clinical trials, or possibly preclinical experiments, and using the combined dataset to predict the patient’s expected outcome for each treatment being considered. In such settings, combining data from multiple sources in a way that is statistically reliable is not entirely straightforward, and correctly identifying and estimating the effects of treatments and patient covariates on clinical outcomes can be complex. Causal diagrams provide a rational basis to guide this process. The first step is to construct a causal diagram that reflects the plausible relationships between treatment variables, patient covariates, and clinical outcomes. If the diagram is correct, it can be used to determine what additional data may be needed, how to combine data from multiple sources, how to formulate a statistical model for clinical outcomes as a function of treatment and covariates, and how to compute an unbiased treatment effect estimate for each new patient. We use adjuvant therapy of renal cell carcinoma to illustrate how causal diagrams may be used to guide these steps.

Abstract

We discuss how causal diagrams can be used by clinicians to make better individualized treatment decisions. Causal diagrams can distinguish between settings where clinical decisions can rely on a conventional additive regression model fit to data from a historical randomized clinical trial (RCT) to estimate treatment effects and settings where a different approach is needed. This may be because a new patient does not meet the RCT’s entry criteria, or a treatment’s effect is modified by biomarkers or other variables that act as mediators between treatment and outcome. In some settings, the problem can be addressed simply by including treatment–covariate interaction terms in the statistical regression model used to analyze the RCT dataset. However, if the RCT entry criteria exclude a new patient seen in the clinic, it may be necessary to combine the RCT data with external data from other RCTs, single-arm trials, or preclinical experiments evaluating biological treatment effects. For example, external data may show that treatment effects differ between histological subgroups not recorded in an RCT. A causal diagram may be used to decide whether external observational or experimental data should be obtained and combined with RCT data to compute statistical estimates for making individualized treatment decisions. We use adjuvant treatment of renal cell carcinoma as our motivating example to illustrate how to construct causal diagrams and apply them to guide clinical decisions.

Assessing the Impact of Precision Parameter Prior in Bayesian Non-parametric Growth Curve Modeling

Bayesian non-parametric (BNP) modeling has been developed and proven to be a powerful tool to analyze messy data with complex structures. Despite the increasing popularity of BNP modeling, it also faces challenges. One challenge is the estimation of the precision parameter in the Dirichlet process mixtures. In this study, we focus on a BNP growth curve model and investigate how non-informative prior, weakly informative prior, accurate informative prior, and inaccurate informative prior affect the model convergence, parameter estimation, and computation time. A simulation study has been conducted. We conclude that the non-informative prior for the precision parameter is less preferred because it yields a much lower convergence rate, and growth curve parameter estimates are not sensitive to informative priors.

Effect-Size Estimation Using Semiparametric Hierarchical Mixture Models in Disease-Association Studies with Neuroimaging Data

In disease-association studies using neuroimaging data, evaluating the biological or clinical significance of individual associations requires not only detection of disease-associated areas of the brain but also estimation of the magnitudes of the associations or effect sizes for individual brain areas. In this paper, we propose a model-based framework for voxel-based inferences under spatial dependency in neuroimaging data. Specifically, we employ hierarchical mixture models with a hidden Markov random field structure to incorporate the spatial dependency between voxels. A nonparametric specification is proposed for the effect size distribution to flexibly estimate the underlying effect size distribution. Simulation experiments demonstrate that compared with a naive estimation method, the proposed methods can substantially reduce the selection bias in the effect size estimates of the selected voxels with the greatest observed associations. An application to neuroimaging data from an Alzheimer's disease study is provided.

Bayesian cluster hierarchical model for subgroup borrowing in the design and analysis of basket trials with binary endpoints

Master protocol designs are often proposed to improve the efficiency of drug development with multiple subgroups. In the basket trial design, different subgroups can have similar biological pathogenesis pathways. Hence, a target therapy can result in similar responses. A good information sharing strategy between different subgroups can potentially improve the efficiency of evaluating treatment efficacy. In traditional hierarchical models, based on the exchangeability assumption, all subgroups are placed into the same sharing pool for cross subgroup information sharing. However, due to the heterogeneity between subgroups, there can be large differences in drug efficacy. Under such cases, strong borrowing across all subgroups is not suitable and no borrowing can be inefficient, because the treatment effect is analyzed in each subgroup separately. We propose a Bayesian cluster hierarchical model (BCHM) to improve the operating characteristics of estimating the treatment effect in multiple subgroups in basket trials. Bayesian nonparametric method is applied to dynamically calculate the number of clusters by conducting a multiple cluster classification based on subgroup outcomes. A hierarchical model is used to compute the posterior probability of the treatment effect, with the borrowing strength determined by the Bayesian nonparametric clustering and the similarities between subgroups. We apply the BCHM to clinical trials with binary endpoints. For treatment effect estimation, the BCHM yields lower mean squared error values, when compared to the independent analyses. In scenarios with a heterogeneous treatment effect, the BCHM provides lower mean squared error values compared to traditional hierarchical models. In addition, we can construct a loss function to optimize the design parameters. BCHM provides a balanced approach and smart borrowing, which yields better results in assessing the treatment effect in different scenarios compared to other conventional methods.

Bayesian credible subgroup identification for treatment effectiveness in time-to-event data

Due to differential treatment responses of patients to pharmacotherapy, drug development and practice in medicine are concerned with personalized medicine, which includes identifying subgroups of population that exhibit differential treatment effect. For time-to-event data, available methods only focus on detecting and testing treatment-by-covariate interactions and may not consider multiplicity. In this work, we introduce the Bayesian credible subgroups approach for time-to-event endpoints. It provides two bounding subgroups for the true benefiting subgroup: one which is likely to be contained by the benefiting subgroup and one which is likely to contain the benefiting subgroup. A personalized treatment effect is estimated by two common measures of survival time: the hazard ratio and restricted mean survival time. We apply the method to identify benefiting subgroups in a case study of prostate carcinoma patients and a simulated large clinical dataset.

A Bayesian nonparametric testing procedure for paired samples

We propose a Bayesian hypothesis testing procedure for comparing the distributions of paired samples. The procedure is based on a flexible model for the joint distribution of both samples. The flexibility is given by a mixture of Dirichlet processes. Our proposal uses a spike-slab prior specification for the base measure of the Dirichlet process and a particular parametrization for the kernel of the mixture in order to facilitate comparisons and posterior inference. The joint model allows us to derive the marginal distributions and test whether they differ or not. The procedure exploits the correlation between samples, relaxes the parametric assumptions, and detects possible differences throughout the entire distributions. A Monte Carlo simulation study comparing the performance of this strategy to other traditional alternatives is provided. Finally, we apply the proposed approach to spirometry data collected in the United States to investigate changes in pulmonary function in children and adolescents in response to air polluting factors.

Bayesian Nonparametrics and Biostatistics: The Case of PET Imaging

Biostatistic applications often require to collect and analyze a massive amount of data. Hence, it has become necessary to consider new statistical paradigms that perform well in characterizing complex data. Nonparametric Bayesian methods provide a widely used framework that offers the key advantages of a fully model-based probabilistic framework, while being highly flexible and adaptable. The goal of this paper is to provide a motivation of Bayesian nonparametrics (BNP) through a particular biomedical application, namely Positron Emission Tomography (PET) imaging reconstruction.

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.

Bayesian non-parametric survival regression for optimizing precision dosing of intravenous busulfan in allogeneic stem cell transplantation

Allogeneic stem cell transplantation (allo-SCT) is now part of standard of care for acute leukemia (AL). To reduce toxicity of the pre-transplant conditioning regimen, intravenous busulfan is usually used as a preparative regimen for AL patients undergoing allo-SCT. Systemic busulfan exposure, characterized by the area under the plasma concentration versus time curve (AUC), is strongly associated with clinical outcome. An AUC that is too high is associated with severe toxicities, while an AUC that is too low carries increased risks of disease recurrence and failure to engraft. Consequently, an optimal AUC interval needs to be determined for therapeutic use. To address the possibility that busulfan pharmacokinetics and pharmacodynamics vary significantly with patient characteristics, we propose a tailored approach to determine optimal covariate-specific AUC intervals. To estimate these personalized AUC intervals, we apply a flexible Bayesian nonparametric regression model based on a dependent Dirichlet process and Gaussian process, DDP-GP. Our analyses of a dataset of 151 patients identified optimal therapeutic intervals for AUC that varied substantively with age and whether the patient was in complete remission or had active disease at transplant. Extensive simulations to evaluate the DDP-GP model in similar settings showed that its performance compares favorably to alternative methods. We provide an R package, DDPGPSurv, that implements the DDP-GP model for a broad range of survival regression analyses.

Geometric Sensitivity Measures for Bayesian Nonparametric Density Estimation Models

We propose a geometric framework to assess global sensitivity in Bayesian nonparametric models for density estimation. We study sensitivity of nonparametric Bayesian models for density estimation, based on Dirichlet-type priors, to perturbations of either the precision parameter or the base probability measure. To quantify the different effects of the perturbations of the parameters and hyperparameters in these models on the posterior, we define three geometrically-motivated global sensitivity measures based on geodesic paths and distances computed under the nonparametric Fisher-Rao Riemannian metric on the space of densities, applied to posterior samples of densities: (1) the Fisher-Rao distance between density averages of posterior samples, (2) the log-ratio of Karcher variances of posterior samples, and (3) the norm of the difference of scaled cumulative eigenvalues of empirical covariance operators obtained from posterior samples. We validate our approach using multiple simulation studies, and consider the problem of sensitivity analysis for Bayesian density estimation models in the context of three real datasets that have previously been studied.

Fully Bayesian analysis of RNA-seq counts for the detection of gene expression heterosis

Heterosis, or hybrid vigor, is the enhancement of the phenotype of hybrid progeny relative to their inbred parents. Heterosis is extensively used in agriculture, and the underlying mechanisms are unclear. To investigate the molecular basis of phenotypic heterosis, researchers search tens of thousands of genes for heterosis with respect to expression in the transcriptome. Difficulty arises in the assessment of heterosis due to composite null hypotheses and non-uniform distributions for p-values under these null hypotheses. Thus, we develop a general hierarchical model for count data and a fully Bayesian analysis in which an efficient parallelized Markov chain Monte Carlo algorithm ameliorates the computational burden. We use our method to detect gene expression heterosis in a two-hybrid plant-breeding scenario, both in a real RNA-seq maize dataset and in simulation studies. In the simulation studies, we show our method has well-calibrated posterior probabilities and credible intervals when the model assumed in analysis matches the model used to simulate the data. Although model misspecification can adversely affect calibration, the methodology is still able to accurately rank genes. Finally, we show that hyperparameter posteriors are extremely narrow and an empirical Bayes (eBayes) approach based on posterior means from the fully Bayesian analysis provides virtually equivalent posterior probabilities, credible intervals, and gene rankings relative to the fully Bayesian solution. This evidence of equivalence provides support for the use of eBayes procedures in RNA-seq data analysis if accurate hyperparameter estimates can be obtained.

From here to infinity: sparse finite versus Dirichlet process mixtures in model-based clustering

In model-based clustering mixture models are used to group data points into clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli et al. (Stat Comput 26:303-324, 2016) are sparse finite mixtures, where the prior distribution on the weight distribution of a mixture with K components is chosen in such a way that a priori the number of clusters in the data is random and is allowed to be smaller than K with high probability. The number of clusters is then inferred a posteriori from the data. The present paper makes the following contributions in the context of sparse finite mixture modelling. First, it is illustrated that the concept of sparse finite mixture is very generic and easily extended to cluster various types of non-Gaussian data, in particular discrete data and continuous multivariate data arising from non-Gaussian clusters. Second, sparse finite mixtures are compared to Dirichlet process mixtures with respect to their ability to identify the number of clusters. For both model classes, a random hyper prior is considered for the parameters determining the weight distribution. By suitable matching of these priors, it is shown that the choice of this hyper prior is far more influential on the cluster solution than whether a sparse finite mixture or a Dirichlet process mixture is taken into consideration.

Multiplicity-adjusted semiparametric benefiting subgroup identification in clinical trials

Background A recent focus in the health sciences has been the development of personalized medicine, which includes determining the population for which a given treatment is effective. Due to limited data, identifying the true benefiting population is a challenging task. To tackle this difficulty, the credible subgroups approach provides a pair of bounding subgroups for the true benefiting subgroup, constructed so that one is contained by the benefiting subgroup while the other contains the benefiting subgroup with high probability. However, the method has so far only been developed for parametric linear models. Methods In this article, we develop the details required to follow the credible subgroups approach in more realistic settings by considering nonlinear and semiparametric regression models, supported for regulatory science by conditional power simulations. We also present an improved multiple testing approach using a step-down procedure. We evaluate our approach via simulations and apply it to data from four trials of Alzheimer's disease treatments carried out by AbbVie. Results Semiparametric modeling yields credible subgroups that are more robust to violations of linear treatment effect assumptions, and careful choice of the population of interest as well as the step-down multiple testing procedure result in a higher rate of detection of benefiting types of patients. The approach allows us to identify types of patients that benefit from treatment in the Alzheimer's disease trials. Conclusion Attempts to identify benefiting subgroups of patients in clinical trials are often met with skepticism due to a lack of multiplicity control and unrealistically restrictive assumptions. Our proposed approach merges two techniques, credible subgroups, and semiparametric regression, which avoids these problems and makes benefiting subgroup identification practical and reliable.

Bayesian nonparametric statistics: A new toolkit for discovery in cancer research

Many commonly used statistical methods for data analysis or clinical trial design rely on incorrect assumptions or assume an over-simplified framework that ignores important information. Such statistical practices may lead to incorrect conclusions about treatment effects or clinical trial designs that are impractical or that do not accurately reflect the investigator's goals. Bayesian nonparametric (BNP) models and methods are a very flexible new class of statistical tools that can overcome such limitations. This is because BNP models can accurately approximate any distribution or function and can accommodate a broad range of statistical problems, including density estimation, regression, survival analysis, graphical modeling, neural networks, classification, clustering, population models, forecasting and prediction, spatiotemporal models, and causal inference. This paper describes 3 illustrative applications of BNP methods, including a randomized clinical trial to compare treatments for intraoperative air leaks after pulmonary resection, estimating survival time with different multi-stage chemotherapy regimes for acute leukemia, and evaluating joint effects of targeted treatment and an intermediate biological outcome on progression-free survival time in prostate cancer.

Flexible modeling of the hazard rate and treatment effects in long-term survival studies

The effects of predictors on time to failure may be difficult to assess in cancer studies with longer follow-up, as the commonly used assumption of proportionality of hazards holding over an extended period is often questionable. Motivated by a long-term prostate cancer clinical trial, we contrast and compare four powerful methods for estimation of the hazard rate. These four methods allow for varying degrees of smoothness as well as covariates with effects that vary over time. We pay particular attention to an extended multiresolution hazard estimator, which is a flexible, semi-parametric, Bayesian method for joint estimation of predictor effects and the hazard rate. We compare the results of the extended multiresolution hazard model to three other commonly used, comparable models: Aalen's additive model, Kooperberg's hazard regression model, and an extended Cox model. Through simulations and the analysis of a large-scale randomized prostate cancer clinical trial, we use the different methods to examine patterns of biochemical failure and to estimate the time-varying effects of androgen deprivation therapy treatment and other covariates.

Non-parametric genetic prediction of complex traits with latent Dirichlet process regression models

Using genotype data to perform accurate genetic prediction of complex traits can facilitate genomic selection in animal and plant breeding programs, and can aid in the development of personalized medicine in humans. Because most complex traits have a polygenic architecture, accurate genetic prediction often requires modeling all genetic variants together via polygenic methods. Here, we develop such a polygenic method, which we refer to as the latent Dirichlet process regression model. Dirichlet process regression is non-parametric in nature, relies on the Dirichlet process to flexibly and adaptively model the effect size distribution, and thus enjoys robust prediction performance across a broad spectrum of genetic architectures. We compare Dirichlet process regression with several commonly used prediction methods with simulations. We further apply Dirichlet process regression to predict gene expressions, to conduct PrediXcan based gene set test, to perform genomic selection of four traits in two species, and to predict eight complex traits in a human cohort.Genetic prediction of complex traits with polygenic architecture has wide application from animal breeding to disease prevention. Here, Zeng and Zhou develop a non-parametric genetic prediction method based on latent Dirichlet Process regression models.

Identifying Mixtures of Mixtures Using Bayesian Estimation

The use of a finite mixture of normal distributions in model-based clustering allows us to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by imposing constraints on the model or by using post-processing procedures. Within the Bayesian framework, we propose a different approach based on sparse finite mixtures to achieve identifiability. We specify a hierarchical prior, where the hyperparameters are carefully selected such that they are reflective of the cluster structure aimed at. In addition, this prior allows us to estimate the model using standard MCMC sampling methods. In combination with a post-processing approach which resolves the label switching issue and results in an identified model, our approach allows us to simultaneously (1) determine the number of clusters, (2) flexibly approximate the cluster distributions in a semiparametric way using finite mixtures of normals and (3) identify cluster-specific parameters and classify observations. The proposed approach is illustrated in two simulation studies and on benchmark datasets. Supplementary materials for this article are available online.

Bayesian Nonparametric Estimation for Dynamic Treatment Regimes with Sequential Transition Times

We analyze a dataset arising from a clinical trial involving multi-stage chemotherapy regimes for acute leukemia. The trial design was a 2 × 2 factorial for frontline therapies only. Motivated by the idea that subsequent salvage treatments affect survival time, we model therapy as a dynamic treatment regime (DTR), that is, an alternating sequence of adaptive treatments or other actions and transition times between disease states. These sequences may vary substantially between patients, depending on how the regime plays out. To evaluate the regimes, mean overall survival time is expressed as a weighted average of the means of all possible sums of successive transitions times. We assume a Bayesian nonparametric survival regression model for each transition time, with a dependent Dirichlet process prior and Gaussian process base measure (DDP-GP). Posterior simulation is implemented by Markov chain Monte Carlo (MCMC) sampling. We provide general guidelines for constructing a prior using empirical Bayes methods. The proposed approach is compared with inverse probability of treatment weighting, including a doubly robust augmented version of this approach, for both single-stage and multi-stage regimes with treatment assignment depending on baseline covariates. The simulations show that the proposed nonparametric Bayesian approach can substantially improve inference compared to existing methods. An R program for implementing the DDP-GP-based Bayesian nonparametric analysis is freely available at https://www.ma.utexas.edu/users/yxu/.

Bayesian inference for the distribution of grams of marijuana in a joint

BACKGROUND

The average amount of marijuana in a joint is unknown, yet this figure is a critical quantity for creating credible measures of marijuana consumption. It is essential for projecting tax revenues post-legalization, estimating the size of illicit marijuana markets, and learning about how much marijuana users are consuming in order to understand health and behavioral consequences.

METHODS

Arrestee Drug Abuse Monitoring data collected between 2000 and 2010 contain relevant information on 10,628 marijuana transactions, joints and loose marijuana purchases, including the city in which the purchase occurred and the price paid for the marijuana. Using the Brown-Silverman drug pricing model to link marijuana price and weight, we are able to infer the distribution of grams of marijuana in a joint and provide a Bayesian posterior distribution for the mean weight of marijuana in a joint.

RESULTS

We estimate that the mean weight of marijuana in a joint is 0.32g (95% Bayesian posterior interval: 0.30-0.35).

CONCLUSIONS

Our estimate of the mean weight of marijuana in a joint is lower than figures commonly used to make estimates of marijuana consumption. These estimates can be incorporated into drug policy discussions to produce better understanding about illicit marijuana markets, the size of potential legalized marijuana markets, and health and behavior outcomes.

Flexible Bayesian survival modeling with semiparametric time-dependent and shape-restricted covariate effects

Presently, there are few options with available software to perform a fully Bayesian analysis of time-to-event data wherein the hazard is estimated semi- or non-parametrically. One option is the piecewise exponential model, which requires an often unrealistic assumption that the hazard is piecewise constant over time. The primary aim of this paper is to construct a tractable semiparametric alternative to the piecewise exponential model that assumes the hazard is continuous, and to provide modifiable, user-friendly software that allows the use of these methods in a variety of settings. To accomplish this aim, we use a novel model formulation for the log-hazard based on a low-rank thin plate linear spline that readily facilitates adjustment for covariates with time-dependent and proportional hazards effects, possibly subject to shape restrictions. We investigate the performance of our model choices via simulation. We then analyze colorectal cancer data from a clinical trial comparing the effectiveness of two novel treatment regimes relative to the standard of care for overall survival. We estimate a time-dependent hazard ratio for each novel regime relative to the standard of care while adjusting for the effect of aspartate transaminase, a biomarker of liver function, that is subject to a non-decreasing shape restriction.

A Bayesian Nonparametric Approach for Functional Data Classification with Application to Hepatic Tissue Characterization

Computed tomography perfusion (CTp) is an emerging functional imaging technology that provides a quantitative assessment of the passage of fluid through blood vessels. Tissue perfusion plays a critical role in oncology due to the proliferation of networks of new blood vessels typical of cancer angiogenesis, which triggers modifications to the vasculature of the surrounding host tissue. In this article, we consider a Bayesian semiparametric model for the analysis of functional data. This method is applied to a study of four interdependent hepatic perfusion CT characteristics that were acquired under the administration of contrast using a sequence of repeated scans over a period of 590 seconds. More specifically, our modeling framework facilitates borrowing of information across patients and tissues. Additionally, the approach enables flexible estimation of temporal correlation structures exhibited by mappings of the correlated perfusion biomarkers and thus accounts for the heteroskedasticity typically observed in those measurements, by incorporating change-points in the covariance estimation. This method is applied to measurements obtained from regions of liver surrounding malignant and benign tissues, for each perfusion biomarker. We demonstrate how to cluster the liver regions on the basis of their CTp profiles, which can be used in a prediction context to classify regions of interest provided by future patients, and thereby assist in discriminating malignant from healthy tissue regions in diagnostic settings.

Using indirect comparisons to compare interventions within a Cochrane review: a tool for comparative effectiveness research

AIM

Assessing relative performance among competing interventions is an important part of comparative effectiveness research. Bayesian indirect comparisons add information to existing Cochrane reviews, such as which intervention is likely to perform best. However, heterogeneity variance priors may influence results and, potentially, clinical guidance.

METHODS

We highlight the features of Bayesian indirect comparisons using a case study of a Cochrane review update in asthma care. The probability that one self-management educational intervention outperforms others is estimated. Simulation studies investigate the effect of heterogeneity variance prior distributions.

RESULTS

Results suggest a 55% probability that individual education is best, followed by combination (39%) and group (6%). The intervention with few trials was sensitive to prior distributions.

CONCLUSION

Bayesian indirect comparisons updates of Cochrane reviews are valuable comparative effectiveness research tools.

Robust meta-analytic-predictive priors in clinical trials with historical control information

Historical information is always relevant for clinical trial design. Additionally, if incorporated in the analysis of a new trial, historical data allow to reduce the number of subjects. This decreases costs and trial duration, facilitates recruitment, and may be more ethical. Yet, under prior-data conflict, a too optimistic use of historical data may be inappropriate. We address this challenge by deriving a Bayesian meta-analytic-predictive prior from historical data, which is then combined with the new data. This prospective approach is equivalent to a meta-analytic-combined analysis of historical and new data if parameters are exchangeable across trials. The prospective Bayesian version requires a good approximation of the meta-analytic-predictive prior, which is not available analytically. We propose two- or three-component mixtures of standard priors, which allow for good approximations and, for the one-parameter exponential family, straightforward posterior calculations. Moreover, since one of the mixture components is usually vague, mixture priors will often be heavy-tailed and therefore robust. Further robustness and a more rapid reaction to prior-data conflicts can be achieved by adding an extra weakly-informative mixture component. Use of historical prior information is particularly attractive for adaptive trials, as the randomization ratio can then be changed in case of prior-data conflict. Both frequentist operating characteristics and posterior summaries for various data scenarios show that these designs have desirable properties. We illustrate the methodology for a phase II proof-of-concept trial with historical controls from four studies. Robust meta-analytic-predictive priors alleviate prior-data conflicts ' they should encourage better and more frequent use of historical data in clinical trials.

Survival Analysis with Electronic Health Record Data: Experiments with Chronic Kidney Disease

This paper presents a detailed survival analysis for chronic kidney disease (CKD). The analysis is based on the EHR data comprising almost two decades of clinical observations collected at New York-Presbyterian, a large hospital in New York City with one of the oldest electronic health records in the United States. Our survival analysis approach centers around Bayesian multiresolution hazard modeling, with an objective to capture the changing hazard of CKD over time, adjusted for patient clinical covariates and kidney-related laboratory tests. Special attention is paid to statistical issues common to all EHR data, such as cohort definition, missing data and censoring, variable selection, and potential for joint survival and longitudinal modeling, all of which are discussed alone and within the EHR CKD context.