Bayesian Decision Theoretic Approach Research Articles

MEASURING PERFORMANCE FOR END-OF-LIFE CARE.

Although not without controversy, readmission is entrenched as a hospital quality metric with statistical analyses generally based on fitting a logistic-Normal generalized linear mixed model. Such analyses, however, ignore death as a competing risk, although doing so for clinical conditions with high mortality can have profound effects; a hospital's seemingly good performance for readmission may be an artifact of it having poor performance for mortality. in this paper we propose novel multivariate hospital-level performance measures for readmission and mortality that derive from framing the analysis as one of cluster-correlated semi-competing risks data. We also consider a number of profiling-related goals, including the identification of extreme performers and a bivariate classification of whether the hospital has higher-/lower-than-expected readmission and mortality rates via a Bayesian decision-theoretic approach that characterizes hospitals on the basis of minimizing the posterior expected loss for an appropriate loss function. in some settings, particularly if the number of hospitals is large, the computational burden may be prohibitive. To resolve this, we propose a series of analysis strategies that will be useful in practice. Throughout, the methods are illustrated with data from CMS on N = 17,685 patients diagnosed with pancreatic cancer between 2000-2012 at one of J = 264 hospitals in California.

Robust defect detection under uncertainties using spatially adaptive capacitive imaging

We develop a high-Q capacitive sensing based robust non-destructive evaluation (NDE) methodology that can be widely used in varied NDE applications. We show that the proposed method can detect defects in a host of robust regimes where uncertainties such as lift-off, probe tilt, fluctuations in sampling rates, and step sizes are inherent in the data collection process. We explicitly characterize the corruption in the capacitive sensing data due to various lift-off based uncertainties. We use a Bayesian decision theoretic approach to rigorously understand the impact of these corruptions on defect identification efficacy. Using an optimally tuned weighted classification loss, we prove that it is theoretically feasible to accurately detect defect location and sizes from capacitive sensing signals collected under the aforementioned uncertainties. The Bayesian decision theoretic study needs prior information for accurate detection that is not available in real NDE inspections. So, we develop a solely data driven algorithm that analyzes the capacitive sensing signals without any prior knowledge of defect or uncertainty types. The developed algorithm is non-parametric and uses spatially adaptive denoising to weed out uncertainty induced noises. By leveraging the spatial association in the capacitive sensing signals, our algorithm greatly improves on popular non-spatial approaches. Compared to popular thresholding methods and low-rank based denoising approaches, we demonstrate superior performance of the proposed method in terms of coverage and false positive metrics for defect identification. Using spatially adaptive denoising, we design a robust capacitive sensing method that can detect defects with high precision under various uncertainty regimes.

Properties of Fisher information gain for Bayesian design of experiments

The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and parameters). For most common utility functions, the expected utility is rarely available in closed form and requires a computationally expensive approximation which then needs to be maximised over the space of all possible designs. This hinders practical use of the Bayesian approach to find experimental designs. However, recently, a new utility called Fisher information gain has been proposed. The resulting expected Fisher information gain reduces to the prior expectation of the trace of the Fisher information matrix. Since the Fisher information is often available in closed form, this significantly simplifies approximation and subsequent identification of optimal designs. In this paper, it is shown that for exponential family models, maximising the expected Fisher information gain is equivalent to maximising an alternative objective function over a reduced-dimension space, simplifying even further the identification of optimal designs. However, if this function does not have enough global maxima, then designs that maximise the expected Fisher information gain lead to non-identifiability.

Logistic retainment interval dose exploration design for Phase I clinical trials of cytotoxic agents.

Phase I studies of a cytotoxic agent often aim to identify the dose that provides an investigator specified target dose-limiting toxicity (DLT) probability. In practice, an initial cohort receives a dose with a putative low DLT probability, and subsequent dosing follows by consecutively deciding whether to retain the current dose, escalate to the adjacent higher dose, or de-escalate to the adjacent lower dose. This article proposes a Phase I design derived using a Bayesian decision-theoretic approach to this sequential decision-making process. The design consecutively chooses the action that minimizes posterior expected loss where the loss reflects the distance on the log-odds scale between the target and the DLT probability of the dose that would be given to the next cohort under the corresponding action. A logistic model is assumed for the log odds of a DLT at the current dose with a weakly informative t-distribution prior centered at the target. The key design parameters are the pre-specified odds ratios for the DLT probabilities at the adjacent higher and lower doses. Dosing rules may be pre-tabulated, as these only depend on the outcomes at the current dose, which greatly facilitates implementation. The recommended default version of the proposed design improves dose selection relative to many established designs across a variety of scenarios.

A Bayesian Decision-Theoretic Design for Simultaneous Biomarker-Based Subgroup Selection and Efficacy Evaluation

The success of drug development of targeted therapy often hinges on an appropriate selection of the sensitive patient population, mostly based on patients’ biomarker levels. At the planning stage of a Phase II study, although a potential biomarker may have been identified, a threshold value for defining sensitive patient population is often unavailable for adopting many existing biomarker-guided designs. To address this issue, we propose a two-stage design that allows for simultaneous biomarker threshold selection and efficacy evaluation while accommodating situations where the drug is efficacious in the entire patient population. The design uses a Bayesian decision-theoretic approach and incorporates the benefit and cost considerations of the study into a utility function. The operating characteristics of the proposed design under different scenarios are investigated via simulations. We also provide a discussion on the choice of the benefit and cost parameters in practice.

How to Do Things with Words: A Bayesian Approach


 
 
 Communication changes the beliefs of the listener and of the speaker. The value of a communicative act stems from the valuable belief states which result from this act. To model this we build on the Interactive POMDP (IPOMDP) framework, which extends POMDPs to allow agents to model others in multi-agent settings, and we include communication that can take place between the agents to formulate Communicative IPOMDPs (CIPOMDPs). We treat communication as a type of action and therefore, decisions regarding communicative acts are based on decision-theoretic planning using the Bellman optimality principle and value iteration, just as they are for all other rational actions. As in any form of planning, the results of actions need to be precisely specified. We use the Bayes’ theorem to derive how agents update their beliefs in CIPOMDPs; updates are due to agents’ actions, observations, messages they send to other agents, and messages they receive from others. The Bayesian decision-theoretic approach frees us from the commonly made assumption of cooperative discourse – we consider agents which are free to be dishonest while communicating and are guided only by their selfish rationality. We use a simple Tiger game to illustrate the belief update, and to show that the ability to rationally communicate allows agents to improve efficiency of their interactions.
 
 

How to do things with words: A Bayesian approach

Communication changes the beliefs of the listener and of the speaker. The value of a communicative act stems from the valuable belief states which result from this act. To model this we build on the Interactive POMDP (IPOMDP) framework, which extends POMDPs to allow agents to model others in multi-agent settings, and we include communication that can take place between the agents to formulate Communicative IPOMDPs (CIPOMDPs). We treat communication as a type of action and therefore, decisions regarding communicative acts are based on decision-theoretic planning using the Bellman optimality principle and value iteration, just as they are for all other rational actions. As in any form of planning, the results of actions need to be precisely specified. We use the Bayes’ theorem to derive how agents update their beliefs in CIPOMDPs; updates are due to agents’ actions, observations, messages they send to other agents, and messages they receive from others. The Bayesian decision-theoretic approach frees us from the commonly made assumption of cooperative discourse – we consider agents which are free to be dishonest while communicating and are guided only by their selfish rationality. We use a simple Tiger game to illustrate the belief update, and to show that the ability to rationally communicate allows agents to improve efficiency of their interactions.

Bayesian confidence intervals with more power to estimate the minimum effect and determine the sign

In this article, we propose two confidence intervals (CIs) for a single parameter, which can represent an effect in practice, through a Bayesian decision theoretic approach for different goals. One balances length and separating zero from a CI. The other one balances length and the ability of making direction decision of a CI. Two loss functions are constructed by adding suitable penalty terms into the traditional loss function. Then two CIs are obtained by minimizing the loss functions. When compared with the traditional Bayesian CI, the first CI has more chance to estimate the minimum effect; the second CI has more chance to make directional decision for the parameter. General steps for minimizing the loss functions to obtain the CIs are provided. A real data are analyzed through constructing the second CI.

Frequentist Properties of Bayesian Multiplicity Control for Multiple Testing of Normal Means

We consider the standard problem of multiple testing of normal means, obtaining Bayesian multiplicity control by assuming that the prior inclusion probability (the assumed equal prior probability that each mean is nonzero) is unknown and assigned a prior distribution. The asymptotic frequentist behavior of the Bayesian procedure is studied, as the number of tests grows. Studied quantities include the false positive probability, which is shown to go to zero asymptotically. The asymptotics of a Bayesian decision-theoretic approach are also presented.

Bayesian Approaches to Subgroup Analysis and Related Adaptive Clinical Trial Designs.

We review Bayesian and Bayesian decision theoretic approaches to subgroup analysis and applications to subgroup-based adaptive clinical trial designs. Subgroup analysis refers to inference about subpopulations with significantly distinct treatment effects. The discussion mainly focuses on inference for a benefiting subpopulation, that is, a characterization of a group of patients who benefit from the treatment under consideration more than the overall population. We introduce alternative approaches and demonstrate them with a small simulation study. Then, we turn to clinical trial designs. When the selection of the interesting subpopulation is carried out as the trial proceeds, the design becomes an adaptive clinical trial design, using subgroup analysis to inform the randomization and assignment of treatments to patients. We briefly review some related designs. There are a variety of approaches to Bayesian subgroup analysis. Practitioners should consider the type of subpopulations in which they are interested and choose their methods accordingly. We demonstrate how subgroup analysis can be carried out by different Bayesian methods and discuss how they identify slightly different subpopulations.

Optimized adaptive enrichment designs.

Based on a Bayesian decision theoretic approach, we optimize frequentist single- and adaptive two-stage trial designs for the development of targeted therapies, where in addition to an overall population, a pre-defined subgroup is investigated. In such settings, the losses and gains of decisions can be quantified by utility functions that account for the preferences of different stakeholders. In particular, we optimize expected utilities from the perspectives both of a commercial sponsor, maximizing the net present value, and also of the society, maximizing cost-adjusted expected health benefits of a new treatment for a specific population. We consider single-stage and adaptive two-stage designs with partial enrichment, where the proportion of patients recruited from the subgroup is a design parameter. For the adaptive designs, we use a dynamic programming approach to derive optimal adaptation rules. The proposed designs are compared to trials which are non-enriched (i.e. the proportion of patients in the subgroup corresponds to the prevalence in the underlying population). We show that partial enrichment designs can substantially improve the expected utilities. Furthermore, adaptive partial enrichment designs are more robust than single-stage designs and retain high expected utilities even if the expected utilities are evaluated under a different prior than the one used in the optimization. In addition, we find that trials optimized for the sponsor utility function have smaller sample sizes compared to trials optimized under the societal view and may include the overall population (with patients from the complement of the subgroup) even if there is substantial evidence that the therapy is only effective in the subgroup.

Regret-Based Selection for Sparse Dynamic Portfolios

This paper considers passive fund selection from an individual investor’s perspective. The growth of the passive fund market over the past decade is staggering. Individual investors who wish to buy these funds for their retirement and brokerage accounts have many options and are faced with a difficult selection problem. Which funds do they invest in, and in what proportions? We develop a novel statistical methodology to address this problem. A Bayesian decision-theoretic approach is presented to construct optimal sparse portfolios for individual investors over time.

Special issue in honor of Kathryn Chaloner

We are honored to be guest editors for this special issue of Applied Stochastic Models in Business and Industry, dedicated to Kathryn Chaloner's life and achievements. Contributions from her colleagues and friends in this volume are devoted to Kathryn's early research interest in Bayesian optimal design. She was a pioneer in this field and had a broad impact on the subsequent literature on experimental design. Kathryn was internationally known for her research in Bayesian Statistics, which included design of experiments, outlier detection, prior elicitation, and clinical trials, and for her advancements in the study of HIV/AIDS. She was an accomplished researcher, teacher, and mentor. She actively encouraged women and under-represented minority students to join the field of biostatistics and provided mentorship, support, and encouragement. The special issue contains seven papers. The first three papers present some of the recent work in Bayesian optimal designs for nonlinear models, binary responses, and experiments with adversarial components. This is followed by two articles on Bayesian designs in clinical trials. The last two articles of the special issue involve engineering design problems. The paper by Giovagnoli considers the binary response models of Chaloner and Larntz (1989, Journal of Statistical Planning and Inference, 21:191–208) and develops an adaptive version of A-optimal Bayesian designs that are revised as additional data become available during the experiment. Adaptive Bayesian compound designs is also discussed as another extension. Konstantinou and Dette develop approximate Bayesian D-optimal designs for nonlinear regression models that involve covariates that cannot be observed directly. Applications to specific nonlinear models including the exponential regression model are considered and characterizations of the D-optimal saturated designs are presented. Optimal sample size selection for experiments is considered by De Santis and Gubbiotti in an adversarial setting where the decision makers have different prior opinions while having common utility functions and data. Using a Bayesian decision approach with a quadratic loss function, the authors present results for the one-parameter exponential family and investigate effect of the priors on the optimal sample size. Müller, Xu, and Thall discuss advantages and limitations of Bayesian decision theoretic approach in design of clinical trials. In doing so, the authors present a specific case study and point out the limitations such as the computational difficulties involved in solving sequential problems as well as selection of utility functions capturing different stakeholder interests. The article by Ventz, Parmigiani, and Trippa also consider limitations of the Bayesian framework in design of clinical trials and propose a strategy to alleviate these. The proposed strategy involves combining Bayesian designs with frequentist metrics such as error rates, confidence intervals, etc. that are commonly used by medical community and regulatory agencies. The authors show that this can be achieved by an inclusion of frequentist constraints into the Bayesian formulation. The constrained decision theoretic framework is illustrated via several applications and computational algorithms are presented for implementing the proposed approach. Nakamura, Seepaul, Kadane, and Reeja-Jayan discuss design of experiments in materials science. The authors consider use of a batch-sequential experiment and a regression model to determine optimal levels of input variables for synthesis of ceramic materials. It is illustrated that the optimal settings produce more reliable results than other experiments. The final article by Polson and Soyer considers Bayesian design of accelerated life tests for reliability assessment. An augmented probability simulation (APS) approach using Lindley's (1976, Annals of Statistics, 4:1–10) conjugate utility functions is proposed to compute optimal designs in an efficient manner. The proposed approach is illustrated using single and multiple point designs. Use of particle based methods for APS is also discussed as an alternative to Markov chain Monte Carlo methods.

Subgroup finding via Bayesian additive regression trees.

We provide a Bayesian decision theoretic approach to finding subgroups that have elevated treatment effects. Our approach separates the modeling of the response variable from the task of subgroup finding and allows a flexible modeling of the response variable irrespective of potential subgroups of interest. We use Bayesian additive regression trees to model the response variable and use a utility function defined in terms of a candidate subgroup and the predicted response for that subgroup. Subgroups are identified by maximizing the expected utility where the expectation is taken with respect to the posterior predictive distribution of the response, and the maximization is carried out over an a priori specified set of candidate subgroups. Our approach allows subgroups based on both quantitative and categorical covariates. We illustrate the approach using simulated data set study and a real data set. Copyright © 2017 John Wiley & Sons, Ltd.

Semiparametric Bayesian optimal replacement policies: application to railroad tracks

We present a Bayesian decision theoretic approach for developing replacement strategies. In so doing, we consider a semiparametric model to describe the failure characteristics of systems by specifying a nonparametric form for cumulative intensity function and by taking into account effect of covariates by a parametric form. Use of a gamma process prior for the cumulative intensity function complicates the Bayesian analysis when the updating is based on failure count data. We develop a Bayesian analysis of the model using Markov chain Monte Carlo methods and determine replacement strategies. Adoption of Markov chain Monte Carlo methods involves a data augmentation algorithm. We show the implementation of our approach using actual data from railroad tracks. Copyright © 2016 John Wiley & Sons, Ltd.

A Bayesian Decision-Theoretic Approach to Logically-Consistent Hypothesis Testing

This work addresses an important issue regarding the performance of simultaneous test procedures: the construction of multiple tests that at the same time are optimal from a statistical perspective and that also yield logically-consistent results that are easy to communicate to practitioners of statistical methods. For instance, if hypothesis A implies hypothesis B, is it possible to create optimal testing procedures that reject A whenever they reject B? Unfortunately, several standard testing procedures fail in having such logical consistency. Although this has been deeply investigated under a frequentist perspective, the literature lacks analyses under a Bayesian paradigm. In this work, we contribute to the discussion by investigating three rational relationships under a Bayesian decision-theoretic standpoint: coherence, invertibility and union consonance. We characterize and illustrate through simple examples optimal Bayes tests that fulfill each of these requisites separately. We also explore how far one can go by putting these requirements together. We show that although fairly intuitive tests satisfy both coherence and invertibility, no Bayesian testing scheme meets the desiderata as a whole, strengthening the understanding that logical consistency cannot be combined with statistical optimality in general. Finally, we associate Bayesian hypothesis testing with Bayes point estimation procedures. We prove the performance of logically-consistent hypothesis testing by means of a Bayes point estimator to be optimal only under very restrictive conditions.

Computing Expected Value of Partial Sample Information from Probabilistic Sensitivity Analysis Using Linear Regression Metamodeling.

Decision makers often desire both guidance on the most cost-effective interventions given current knowledge and also the value of collecting additional information to improve the decisions made (i.e., from value of information [VOI] analysis). Unfortunately, VOI analysis remains underused due to the conceptual, mathematical, and computational challenges of implementing Bayesian decision-theoretic approaches in models of sufficient complexity for real-world decision making. In this study, we propose a novel practical approach for conducting VOI analysis using a combination of probabilistic sensitivity analysis, linear regression metamodeling, and unit normal loss integral function--a parametric approach to VOI analysis. We adopt a linear approximation and leverage a fundamental assumption of VOI analysis, which requires that all sources of prior uncertainties be accurately specified. We provide examples of the approach and show that the assumptions we make do not induce substantial bias but greatly reduce the computational time needed to perform VOI analysis. Our approach avoids the need to analytically solve or approximate joint Bayesian updating, requires only one set of probabilistic sensitivity analysis simulations, and can be applied in models with correlated input parameters.

Bayesian Sample Size Determination in Two-Sample Poisson Models

Sample size determination is a vital part of clinical studies where cost and safety concerns lead to greater importance of not using more subjects and resources than are required. The Bayesian approach to sample size determination has the advantages of being able to use prior data and expert opinion to possibly reduce the total sample size while also acknowledging all uncertainty at the design stage. We apply a Bayesian decision theoretic approach to the problem of comparing two Poisson rates and find the required sample size to obtain a desired power while controlling the Type I error rate.

Bayesian designs and the control of frequentist characteristics: a practical solution.

Frequentist concepts, such as the control of the type I error or the false discovery rate, are well established in the medical literature and often required by regulators. Most Bayesian designs are defined without explicit considerations of frequentist characteristics. Once the Bayesian design is structured, statisticians use simulations and adjust tuning parameters to comply with a set of targeted operating characteristics. These adjustments affect the use of prior information and utility functions. Here we consider a Bayesian decision theoretic approach for experimental designs with explicit frequentist requisites. We define optimal designs under a set of constraints required by a regulator. Our approach combines the use of interpretable utility functions with frequentist criteria, and selects an optimal design that satisfies a set of required operating characteristics. We illustrate the approach using a group-sequential multi-arm Phase II trial and a bridging trial.

Toward a new application of real-time electrophysiology: online optimization of cognitive neurosciences hypothesis testing.

Brain-computer interfaces (BCIs) mostly rely on electrophysiological brain signals. Methodological and technical progress has largely solved the challenge of processing these signals online. The main issue that remains, however, is the identification of a reliable mapping between electrophysiological measures and relevant states of mind. This is why BCIs are highly dependent upon advances in cognitive neuroscience and neuroimaging research. Recently, psychological theories became more biologically plausible, leading to more realistic generative models of psychophysiological observations. Such complex interpretations of empirical data call for efficient and robust computational approaches that can deal with statistical model comparison, such as approximate Bayesian inference schemes. Importantly, the latter enable the optimization of a model selection error rate with respect to experimental control variables, yielding maximally powerful designs. In this paper, we use a Bayesian decision theoretic approach to cast model comparison in an online adaptive design optimization procedure. We show how to maximize design efficiency for individual healthy subjects or patients. Using simulated data, we demonstrate the face- and construct-validity of this approach and illustrate its extension to electrophysiology and multiple hypothesis testing based on recent psychophysiological models of perception. Finally, we discuss its implications for basic neuroscience and BCI itself.