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A fully powered randomized controlled cancer trial can be challenging to conduct in children because of difficulties in enrollment of pediatric patients due to low disease incidence. One way to improve the feasibility of trials in pediatric patients, when clinically appropriate, is through borrowing information from comparable external adult trials in the same disease. Bayesian analysis of a pediatric trial provides a way of seamlessly augmenting pediatric trial efficacy data with data from external adult trials. However, not all external adult trial subjects may be equally clinically relevant with respect to the baseline disease severity, prognostic factors, co-morbidities, and prior therapy observed in the pediatric trial of interest. The propensity score matching method provides a way of matching the external adult subjects to the pediatric trial subjects on a set of clinically determined baseline covariates, such as baseline disease severity, prognostic factors and prior therapy. The matching then allows Bayesian information borrowing from only the most clinically relevant external adult subjects. Through a case study in pediatric acute lymphoblastic leukemia (ALL), we examine the utility of propensity score matched mixture and power priors in bringing appropriate external adult efficacy information into pediatric trial efficacy assessment, and present considerations for scaling fixed borrowing from external adult data. [ABSTRACT FROM AUTHOR]

Structural equation models (SEMs) are extensively used in behavioral, social, and psychological research to model relationships between latent variables and observations. However, most models include redundant variables that are not important to relationships within the model. This study uses a Bayesian model selection procedure with mixture priors for SEMs to determine variables that have a meaningful relationship. The posterior probabilities for all possible models are calculated through the MCMC algorithm and the model with the largest probability is selected. The predictors of non-zero fixed-effect coefficients and/or non-zero random-effect variance components in the MCMC procedure are determined without the need for complex model selection criteria. The proposed methodologies are illustrated in a simulation and applied to a multidimensional longitudinal myopia data set in which the dimensionality of the parameter space is reduced and a more parsimonious model is selected. [ABSTRACT FROM AUTHOR]

In this study, efficient Bayes estimators of sensitive proportion are proposed. It is documented that indirect reports increase variances of the estimates. To counteract this increase in variances we divided the total sample size, n = n1+n2, such that n1 individuals record direct responses and n2 individuals record indirect responses. The decision that a group of individuals should report indirect or direct responses would be based on distinct known factors. Bayes estimates and subsequent posterior risks are calculated taking into account different prior distributions, loss functions and a generalized randomized response technique. The impact of design parameters and the number of responses obtained using direct and indirect questioning techniques on the relative efficiencies are investigated. Graphical and numerical results indicate that the proposed estimators are better than the existing. [ABSTRACT FROM AUTHOR]

Basket trials are increasingly used for the simultaneous evaluation of a new treatment in various patient subgroups under one overarching protocol. We propose a Bayesian approach to sample size determination in basket trials that permit borrowing of information between commensurate subsets. Specifically, we consider a randomized basket trial design where patients are randomly assigned to the new treatment or control within each trial subset ("subtrial" for short). Closed-form sample size formulae are derived to ensure that each subtrial has a specified chance of correctly deciding whether the new treatment is superior to or not better than the control by some clinically relevant difference. Given prespecified levels of pairwise (in)commensurability, the subtrial sample sizes are solved simultaneously. The proposed Bayesian approach resembles the frequentist formulation of the problem in yielding comparable sample sizes for circumstances of no borrowing. When borrowing is enabled between commensurate subtrials, a considerably smaller trial sample size is required compared to the widely implemented approach of no borrowing. We illustrate the use of our sample size formulae with two examples based on real basket trials. A comprehensive simulation study further shows that the proposed methodology can maintain the true positive and false positive rates at desired levels. [ABSTRACT FROM AUTHOR]

This article develops and explores a robust Bayes factor derived from a calibration technique that makes it particularly compatible with elicited prior knowledge. Building on previous explorations, the particular robust Bayes factor, dubbed a neutral-data comparison, is adapted for broad comparisons with existing robust Bayes factors, such as the fractional and intrinsic Bayes factors, in configurations defined by informative priors. The calibration technique is furthermore developed for use with flexible parametric priors—that is, mixture prior distributions with components that may be symmetric or skewed—, and demonstrated in an example context from forensic science. Throughout the exploration, the neutral-data comparison is shown to exhibit desirable sensitivity properties, and to show promise for adaptation to elaborate data-analysis scenarios. [ABSTRACT FROM AUTHOR]

In many therapeutic areas with unmet medical needs, such as pediatric oncology and rare diseases, one of the deterrent factors for clinical trial interpretability is the limited sample size with less-than-ideal operating characteristics. Single arm is usually the only viable design due to feasibility and ethical concerns. For the trial results to be more interpretable and conclusive, the evaluation of operating characteristics, such as type I error rate and power, and the appropriate utilization of prior information for study design, shall be prespecified and fully investigated during the trial planning phase. So far, very few existing literature addressed optimal sample size determination issues for the planning of pediatric and rare population trials, with majority of research focusing on analysis perspective with focus on Bayesian borrowing. In practice, when a single-arm trial is designed for rare population, it is not uncommon that the only information available is from an earlier trial and/or a few clinical publications based on observational studies, often constituting mixed or uncertain conclusions. In light of this, an optimal Bayesian sample size determination method for single-arm trial with binary or continuous endpoint is proposed, where conflicting prior beliefs can be readily incorporated. Prior effective sample size can be calculated to assess the robustness as well as the prior information borrowed. Moreover, due to the lack of closed-form posterior distributions in general, an alternative approach for calculating Bayesian power is described. Simulation studies are provided to demonstrate the utility of the proposed methods. In addition, a case study in pediatric patients with leukemia is included to illustrate the proposed method with the existing approaches. [ABSTRACT FROM AUTHOR]

Soils have been heralded as a hidden resource that can be leveraged to mitigate and address some of the major global environmental challenges. Specifically, the organic carbon stored in soils, called soil organic carbon (SOC), can, through proper soil management, help offset fuel emissions, increase food productivity, and improve water quality. As collecting data on SOC are costly and time‐consuming, not much data on SOC are available, although understanding the spatial variability in SOC is of fundamental importance for effective soil management. In this manuscript, we propose a modeling framework that can be used to gain a better understanding of the dependence structure of a spatial process by identifying regions within a spatial domain where the process displays the same spatial correlation range. To achieve this goal, we propose a generalization of the multiresolution approximation (M‐RA) modeling framework of Katzfuss originally introduced as a strategy to reduce the computational burden encountered when analyzing massive spatial datasets. To allow for the possibility that the correlation of a spatial process might be characterized by a different range in different subregions of a spatial domain, we provide the M‐RA basis functions weights with a two‐component mixture prior with one of the mixture components a shrinking prior. We call our approach the mixture M‐RA. Application of the mixture M‐RA model to both stationary and nonstationary data show that the mixture M‐RA model can handle both types of data, can correctly establish the type of spatial dependence structure in the data (e.g., stationary versus not), and can identify regions of local stationarity. [ABSTRACT FROM AUTHOR]

The Bayesian‐80 model consists of the prior–likelihood pair. A prior–data conflict arises whenever the prior allocates most of its mass to regions of the parameter space where the likelihood is relatively low. Once a prior–data conflict is diagnosed, what to do next is a hard question to answer. We propose an automatic prior elicitation that involves a two‐component mixture of a diffuse and an informative prior distribution that favours the first component if a conflict emerges. Using various examples, we show that these mixture priors can be useful in regression models as a device for regularizing the estimates and retrieving useful inferential conclusions. [ABSTRACT FROM AUTHOR]

Abstract Background Performing well-powered randomised controlled trials (RCTs) of new treatments for rare diseases is often infeasible. However, with the increasing availability of historical data, incorporating existing information into trials with small sample sizes is appealing in order to increase the power. Bayesian approaches enable one to incorporate historical data into a trial’s analysis through a prior distribution. Methods Motivated by a RCT intended to evaluate the impact on event-free survival of mifamurtide in patients with osteosarcoma, we performed a simulation study to evaluate the impact on trial operating characteristics of incorporating historical individual control data and aggregate treatment effect estimates. We used power priors derived from historical individual control data for baseline parameters of Weibull and piecewise exponential models, while we used a mixture prior to summarise aggregate information obtained on the relative treatment effect. The impact of prior-data conflicts, both with respect to the parameters and survival models, was evaluated for a set of pre-specified weights assigned to the historical information in the prior distributions. Results The operating characteristics varied according to the weights assigned to each source of historical information, the variance of the informative and vague component of the mixture prior and the level of commensurability between the historical and new data. When historical and new controls follow different survival distributions, we did not observe any advantage of choosing a piecewise exponential model compared to a Weibull model for the new trial analysis. However, we think that it remains appealing given the uncertainty that will often surround the shape of the survival distribution of the new data. Conclusion In the setting of Sarcome-13 trial, and other similar studies in rare diseases, the gains in power and accuracy made possible by incorporating different types of historical information commensurate with the new trial data have to be balanced against the risk of biased estimates and a possible loss in power if data are not commensurate. The weights allocated to the historical data have to be carefully chosen based on this trade-off. Further simulation studies investigating methods for incorporating historical data are required to generalise the findings.

We consider subgroup analyses within the framework of hierarchical modeling and empirical Bayes (EB) methodology for general priors, thereby generalizing the normal-normal model. By doing this one obtains greater flexibility in modeling. We focus on mixture priors, that is, on the situation where group effects are exchangeable within clusters of subgroups only. We establish theoretical results on accuracy, precision, shrinkage and selection bias of EB estimators under the general priors. The impact of model misspecification is investigated and the applicability of the methodology is illustrated with datasets from the (medical) literature. [ABSTRACT FROM AUTHOR]

We propose a Bayesian hierarchical wavelet methodology for nonparametric regression based on nonlocal priors. Our methodology assumes for the wavelet coefficients a prior that is a mixture of a point mass at zero and a Johnson-Rossell nonlocal prior. We consider two choices of Johnson-Rossell nonlocal priors: the moment prior and the inverse moment prior. To borrow strength across wavelet coefficients, in addition to more traditional specifications from the wavelet literature, we consider a logit specification for the mixture probability and a polynomial decay specification for the scale parameter. To estimate these specifications' hyperparameters, we propose an empirical Bayes methodology based on Laplace approximation that allows fast analytic posterior inference for the wavelet coefficients. To assess performance, we perform a simulation study to compare our methodology to several other wavelet-based methods available in the literature. In terms of mean squared error, our methodology with the inverse moment prior yields superior results for cases of low signal-to-noise ratio, as well as for moderate to large sample sizes. Finally, we illustrate the flexibility of our novel methodology with an application to a functional magnetic resonance imaging (fMRI) dataset from a study of brain activations associated with working memory. [ABSTRACT FROM AUTHOR]

In order to exploit mean-reverting behavior among the price differential between two markets, one can use unit root tests to determine which pairs of assets appear to exhibit mean-reverting behavior. Since nonlinear mean reversion shares the same meaning as local stationarity, this paper proposes a Bayesian hypothesis testing to detect the presence of a local unit root in the mean equation using Markov switching GARCH models. This model incorporates a fat-tailed error distribution to analyze asymmetric effects on both the conditional mean and conditional volatility of financial time series. To implement the test, we propose a numerical approximation of the marginal likelihoods to posterior odds by using an adaptive Markov Chain Monte Carlo scheme. Our simulation study demonstrates that the approximate Bayesian test performs properly. The proposed method utilizes the daily basis between the FTSE 100 Index and Index Futures as an illustration. [ABSTRACT FROM AUTHOR]

Bayesian methods are increasingly used in proof-of-concept studies. An important benefit of these methods is the potential to use informative priors, thereby reducing sample size. This is particularly relevant for treatment arms where there is a substantial amount of historical information such as placebo and active comparators. One issue with using an informative prior is the possibility of a mismatch between the informative prior and the observed data, referred to as prior-data conflict. We focus on two methods for dealing with this: a testing approach and a mixture prior approach. The testing approach assesses prior-data conflict by comparing the observed data to the prior predictive distribution and resorting to a non-informative prior if prior-data conflict is declared. The mixture prior approach uses a prior with a precise and diffuse component. We assess these approaches for the normal case via simulation and show they have some attractive features as compared with the standard one-component informative prior. For example, when the discrepancy between the prior and the data is sufficiently marked, and intuitively, one feels less certain about the results, both the testing and mixture approaches typically yield wider posterior-credible intervals than when there is no discrepancy. In contrast, when there is no discrepancy, the results of these approaches are typically similar to the standard approach. Whilst for any specific study, the operating characteristics of any selected approach should be assessed and agreed at the design stage; we believe these two approaches are each worthy of consideration. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the spatial processes, but in applications the data may display strong nonstationary patterns. In this article, we propose a Bayesian variable selection approach based on wavelet tools to address this problem. The proposed approach does not involve any stationarity assumptions on the priors, and instead we impose a mixture prior directly on each wavelet coefficient. We introduce an option to control the priors such that high resolution coefficients are more likely to be zero. Computationally efficient MCMC procedures are provided to address posterior sampling, and uncertainty in the estimation is assessed through posterior means and standard deviations. Examples based on simulated data demonstrate the estimation accuracy and advantages of the proposed method. We also illustrate the performance of the proposed method for real data obtained through remote sensing. [ABSTRACT FROM AUTHOR]

Abstract: We develop a methodology for Bayesian hierarchical multi-subject multiscale analysis of functional Magnetic Resonance Imaging (fMRI) data. We begin by modeling the brain images temporally with a standard general linear model. After that, we transform the resulting estimated standardized regression coefficient maps through a discrete wavelet transformation to obtain a sparse representation in the wavelet space. Subsequently, we assign to the wavelet coefficients a prior that is a mixture of a point mass at zero and a Gaussian white noise. In this mixture prior for the wavelet coefficients, the mixture probabilities are related to the pattern of brain activity across different resolutions. To incorporate this information, we assume that the mixture probabilities for wavelet coefficients at the same location and level are common across subjects. Furthermore, we assign for the mixture probabilities a prior that depends on a few hyperparameters. We develop an empirical Bayes methodology to estimate the hyperparameters and, as these hyperparameters are shared by all subjects, we obtain precise estimated values. Then we carry out inference in the wavelet space and obtain smoothed images of the regression coefficients by applying the inverse wavelet transform to the posterior means of the wavelet coefficients. An application to computer simulated synthetic data has shown that, when compared to single-subject analysis, our multi-subject methodology performs better in terms of mean squared error. Finally, we illustrate the utility and flexibility of our multi-subject methodology with an application to an event-related fMRI dataset generated by Postle (2005) through a multi-subject fMRI study of working memory related brain activation. [Copyright &y& Elsevier]

To address concerns that ethnic differences in any clinical trial may affect the performance of a treatment, separate clinical trials may be required for different regions. If a drug is approved in one region based on a bigger clinical trial, a bridging study with smaller size may be conducted in a new region to evaluate the similarity of the earlier clinical data to the new population. This article applies a Bayesian strategy to combine a bridging study with reference studies to assess treatment effect similarity for binary endpoints. The methods have been illustrated with a numerical example using Markov-chain Monte Carlo (MCMC) techniques. [ABSTRACT FROM PUBLISHER]

A semiparametric testing approach based on the Bayes factor is developed for non-inferiority trials with binary endpoints. The proposed method is shown to work for a broad class of hypotheses by accommodating a variety of dissimilarity measures between two binomial parameters. Two of the unique features of the proposed testing procedure include: (i) construction of a flexible class of conjugate priors using a mixture of beta densities to maintain approximate equality of prior probabilities of the competing hypotheses; and (ii) automatic determination of the cutoff value of the Bayes factor to facilitate the decision making process. In contrast to the use of Jeffreys's rule of thumb, two forms of total weighted average error criteria are used to determine the cutoff value. Through several simulation studies it is demonstrated that the proposed Bayesian procedure has competitive frequentist properties of controlling type I error as compared to the default frequentist test and meanwhile the proposed criterion improves the statistical power, especially in small samples. The method is further illustrated using the data from a streptococcal pharyngitis clinical trial. [ABSTRACT FROM AUTHOR]

Frequently, exposure data are measured over time on a grid of discrete values that collectively define a functional observation. In many applications, researchers are interested in using these measurements as covariates to predict a scalar response in a regression setting, with interest focusing on the most biologically relevant time window of exposure. One example is in panel studies of the health effects of particulate matter (PM), where particle levels are measured over time. In such studies, there are many more values of the functional data than observations in the data set so that regularization of the corresponding functional regression coefficient is necessary for estimation. Additional issues in this setting are the possibility of exposure measurement error and the need to incorporate additional potential confounders, such as meteorological or co-pollutant measures, that themselves may have effects that vary over time. To accommodate all these features, we develop wavelet-based linear mixed distributed lag models that incorporate repeated measures of functional data as covariates into a linear mixed model. A Bayesian approach to model fitting uses wavelet shrinkage to regularize functional coefficients. We show that, as long as the exposure error induces fine-scale variability in the functional exposure profile and the distributed lag function representing the exposure effect varies smoothly in time, the model corrects for the exposure measurement error without further adjustment. Both these conditions are likely to hold in the environmental applications we consider. We examine properties of the method using simulations and apply the method to data from a study examining the association between PM, measured as hourly averages for 1–7 days, and markers of acute systemic inflammation. We use the method to fully control for the effects of confounding by other time-varying predictors, such as temperature and co-pollutants. [ABSTRACT FROM PUBLISHER]

In National Toxicology Program (NTP) studies, investigators want to assess whether a test agent is carcinogenic overall and specific to certain tumor types, while estimating the dose-response profiles. Because there are potentially correlations among the tumors, a joint inference is preferred to separate univariate analyses for each tumor type. In this regard, we propose a random effect logistic model with a matrix of coefficients representing log-odds ratios for the adjacent dose groups for tumors at different sites. We propose appropriate nonparametric priors for these coefficients to characterize the correlations and to allow borrowing of information across different dose groups and tumor types. Global and local hypotheses can be easily evaluated by summarizing the output of a single Monte Carlo Markov chain (MCMC). Two multiple testing procedures are applied for testing local hypotheses based on the posterior probabilities of local alternatives. Simulation studies are conducted and an NTP tumor data set is analyzed illustrating the proposed approach. [ABSTRACT FROM AUTHOR]

We propose a Bayesian semiparametric model for survival data with a cure fraction. We explicitly consider a finite cure time in the model, which allows us to separate the cured and the uncured populations. We take a mixture prior of a Markov gamma process and a point mass at zero to model the baseline hazard rate function of the entire population. We focus on estimating the cure threshold after which subjects are considered cured. We can incorporate covariates through a structure similar to the proportional hazards model and allow the cure threshold also to depend on the covariates. For illustration, we undertake simulation studies and a full Bayesian analysis of a bone marrow transplant data set. [ABSTRACT FROM AUTHOR]

In regression applications with categorical predictors, interest often focuses on comparing the null hypothesis of homogeneity to an ordered alternative. This article proposes a Bayesian approach for addressing this problem in the setting of normal linear and probit regression models. The regression coefficients are assigned a conditionally conjugate prior density consisting of mixtures of point masses at 0 and truncated normal densities, with a (possibly unknown) changepoint parameter included to accommodate umbrella ordering. Two strategies of prior elicitation are considered: (1) a Bayesian Bonferroni approach in which the probability of the global null hypothesis is specified and local hypotheses are considered independent; and (2) an approach which treats these probabilities as random. A single Gibbs sampling chain can be used to obtain posterior probabilities for the different hypotheses and to estimate regression coefficients and predictive quantities either by model averaging or under the preferred hypothesis. The methods are applied to data from a carcinogenesis study. [ABSTRACT FROM AUTHOR]

This article proposes a semiparametric Bayesian approach for inference on an unknown isotonic regression function, f(x), characterizing the relationship between a continuous predictor, X, and a count response variable, /, adjusting for covariates, Z. A Dirichlet process mixture of Poisson distributions is used to avoid parametric assumptions on the conditional distribution of Y given X and Z. Then, to also avoid parametric assumptions on/(x), a novel prior formulation is proposed that enforces the nondecreasing constraint and assigns positive prior probability to the null hypothesis of no association. Through the use of carefully tailored hyperprior distributions, we allow for borrowing of information across different regions of X in estimating f(x) and in assessing hypotheses about local increases in the function. Due to conjugacy properties, posterior computation is straightforward using a Markov chain Monte Carlo algorithm. The methods are illustrated using data from an epidemiologic study of sleep problems and obesity. [ABSTRACT FROM AUTHOR]

We propose prior probability models for variance‐covariance matrices in order to address two important issues. First, the models allow a researcher to represent substantive prior information about the strength of correlations among a set of variables. Secondly, even in the absence of such information, the increased flexibility of the models mitigates dependence on strict parametric assumptions in standard prior models. For example, the model allows a posteriori different levels of uncertainty about correlations among different subsets of variables. We achieve this by including a clustering mechanism in the prior probability model. Clustering is with respect to variables and pairs of variables. Our approach leads to shrinkage towards a mixture structure implied by the clustering. We discuss appropriate posterior simulation schemes to implement posterior inference in the proposed models, including the evaluation of normalising constants that are functions of parameters of interest. The normalising constants result from the restriction that the correlation matrix be positive definite. We discuss examples based on simulated data, a stock return dataset and a population genetics dataset. [ABSTRACT FROM AUTHOR]

Motivated by calibration problems in near-infrared (NIR) spectroscopy, we consider the linear regression setting in which the many predictor variables arise from sampling an essentially continuous curve at equally spaced points and there may be multiple predictands. We tackle this regression problem by calculating the wavelet transforms of the discretized curves, then applying a Bayesian variableselection method using mixture priors to the multivariate regression of predictands on wavelet coefficients. For prediction purposes, we average over a set of likely models. Applied to a particular problem in NIR spectroscopy, this approach was able to find subsets of the wavelet coefficients with overall better predictive performance than the more usual approaches. In the application, the available predictors are measurements of the NIR reflectance spectrum of biscuit dough pieces at 256 equally spaced wavelengths. The aim is to predict the composition (i.e., the fat, Hour, sugar, and water content) of the dough pieces using the spectral variables. Thus we have a multivariate regression of four predictands on 256 predictors with quite high intercorrelation among the predictors. A training set of 39 samples is available to tit this regression. Applying a wavelet transform replaces the 256 measurements on each spectrum with 256 wavelet coefficients that carry the same information. The variable selection method could use subsets of these coefficients that gave good predictions for all four compositional variables on a separate test set of samples. Selecting in the wavelet domain rather than from the original spectral variables is appealing in this application, because a single wavelet coefficient can carry information from a band of wavelengths in the original spectrum. This band can be narrow or wide, depending on the scale of the wavelet selected. [ABSTRACT FROM AUTHOR]

Consider the classical nonparametric regression problem yi = f(ti) + εi = 1,...,n where ti = i/n, and εi are i.i.d. zero mean normal with variance σ2. The aim is to estimate the true function f which is assumed to belong to the smoothness class described by the Besov space Bspq. These are functions belonging to Lp with derivatives up to order s, in Lp sense. The parameter q controls a further finer degree of smoothness. In a Bayesian setting, a prior on Bspq is chosen following Abramovich, Sapalinas and Silverman (1998). We show that the optimal Bayesian estimator of f is then also a.s. in Bspq if the loss function is chosen to be the Besov norm of Bspq. Because it is impossible to compute this optimal Bayesian estimator analytically, we propose a stochastic algorithm based on an approximation of the Bayesian risk and simulated annealing. Some simulations are presented to show that the algorithm performs well and that the new estimator is competitive when compared to the more standard posterior mean. [ABSTRACT FROM AUTHOR]

We develop a Bayesian design method for a clinical program where an investigational product is to be studied concurrently in a set of clinical trials involving related diseases with the goal of demonstrating superiority to a control in each. The approach borrows information on treatment effectiveness using correlated mixture priors using an analysis procedure that is closely related Bayesian model averaging. Mixture priors are constructed by eliciting conjugate priors based on pessimistic and enthusiastic predictions for the data to be observed for each disease and then by eliciting mixture weights for all possible configurations of the pessimistic and enthusiastic priors across the diseases to be studied. The proposed approach provides a robust framework for information borrowing in settings where the diseases may have endpoints based on different data types. We show via simulation that operating characteristics based on the proposed design framework are favorable compared to those based on information borrowing designs using the Bayesian hierarchical model which is poorly suited for information borrowing when there are different data types underpinning the endpoints across which information is to be borrowed., (© The Author 2021. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)