A Bayesian predictive approach for dealing with pseudoreplication

BackgroundThe Bayesian approach is now widely recognised as a proper framework for analysing risk in health care. However, the traditional text-book Bayesian approach is in many cases difficult to implement, as it is based on abstract concepts and modelling.MethodsThe essential points of the risk analyses conducted according to the predictive Bayesian approach are identification of observable quantities, prediction and uncertainty assessments of these quantities, using all the relevant information. The risk analysis summarizes the knowledge and lack of knowledge concerning critical operations and other activities, and give in this way a basis for making rational decisions.ResultsIt is shown that Bayesian risk analysis can be significantly simplified and made more accessible compared to the traditional text-book Bayesian approach by focusing on predictions of observable quantities and performing uncertainty assessments of these quantities using subjective probabilities.ConclusionThe predictive Bayesian approach provides a framework for ensuring quality of risk analysis. The approach acknowledges that risk cannot be adequately described and evaluated simply by reference to summarising probabilities. Risk is defined by the combination of possible consequences and associated uncertainties.

We address the problem of the curtailment or continuation of an experiment or trial at some interim point where say N observations are in hand and at least S > N observations had originally been scheduled for a decision. A Bayesian predictive approach is used to determine the probability that if one continued the trial with a further sample of size M where N +M ≥S, one would come to a particular decision regarding a parameter or a future observable. This point of view can also be applied to significance tests if one is willing to admit the calculation as a subjective assessment.

This article is motivated by challenges in conducting Bayesian inferences on unknown discrete distributions, with a particular focus on count data. To avoid the computational disadvantages of traditional mixture models, we develop a novel Bayesian predictive approach. In particular, our Metropolis-adjusted Dirichlet (mad) sequence model characterizes the predictive measure as a mixture of a base measure and Metropolis-Hastings kernels centered on previous data points. The resulting mad sequence is asymptotically exchangeable and the posterior on the data generator takes the form of a martingale posterior. This structure leads to straightforward algorithms for inference on count distributions, with easy extensions to multivariate, regression, and binary data cases. We obtain a useful asymptotic Gaussian approximation and illustrate the methodology on a variety of applications.

While optimal dynamic treatment regimes (DTRs) can be estimated without specification of a predictive model, a model-based approach, combined with dynamic programming and Monte Carlo integration, enables direct probabilistic comparisons between the outcomes under the optimal DTR and alternative (dynamic or static) treatment regimes. The Bayesian predictive approach also circumvents problems related to frequentist estimators under the nonregular estimation problem. However, the model-based approach is susceptible to misspecification, in particular of the "null-paradox" type, which is due to the model parameters not having a direct causal interpretation in the presence of latent individual-level characteristics. Because it is reasonable to insist on correct inferences under the null of no difference between the alternative treatment regimes, we discuss how to achieve this through a "null-robust" reparametrization of the problem in a longitudinal setting. Since we argue that causal inference can be entirely understood as posterior predictive inference in a hypothetical population without covariate imbalances, we also discuss how controlling for confounding through inverse probability of treatment weighting can be justified and incorporated in the Bayesian setting.

Rapid sequestration and prolonged retention of intravenously injected nanoparticles by the liver and spleen (reticuloendothelial system (RES)) presents a major barrier to effective delivery to the target site and hampers clinical translation of nanomedicine. Inspired by biological macromolecular drugs, synthesis of ultrasmall (diameter ≈12-15 nm) porous silica nanoparticles (UPSNs), capable of prolonged plasma half-life, attenuated RES sequestration, and accelerated hepatobiliary clearance, is reported. The study further investigates the effect of tumor vascularization on uptake and retention of UPSNs in two mouse models of triple negative breast cancer with distinctly different microenvironments. A semimechanistic mathematical model is developed to gain mechanistic insights into the interactions between the UPSNs and the biological entities of interest, specifically the RES. Despite similar systemic pharmacokinetic profiles, UPSNs demonstrate strikingly different tumor responses in the two models. Histopathology confirms the differences in vasculature and stromal status of the two models, and corresponding differences in the microscopic distribution of UPSNs within the tumors. The studies demonstrate the successful application of multidisciplinary and complementary approaches, based on laboratory experimentation and mathematical modeling, to concurrently design optimized nanomaterials, and investigate their complex biological interactions, in order to drive innovation and translation.

A two-stage Bayesian design with sample size reestimation and subgroup analysis for phase II binary response trials

In many clinical trials, the primary endpoint is time to an event of interest, for example, time to cardiac attack or tumor progression, and the statistical power of these trials is primarily driven by the number of events observed during the trials. In such trials, the number of events observed is impacted not only by the number of subjects enrolled but also by other factors including the event rate and the follow-up duration. Consequently, it is important for investigators to be able to monitor and predict accurately patient accrual and event times so as to predict the times of interim and final analyses and enable efficient allocation of research resources, which have long been recognized as important aspects of trial design and conduct. The existing methods for prediction of event times all assume that patient accrual follows a Poisson process with a constant Poisson rate over time; however, it is fairly common in real-life clinical trials that the Poisson rate changes over time. In this paper, we propose a Bayesian joint modeling approach for monitoring and prediction of accrual and event times in clinical trials. We employ a nonhomogeneous Poisson process to model patient accrual and a parametric or nonparametric model for the event and loss to follow-up processes. Compared to existing methods, our proposed methods are more flexible and robust in that we model accrual and event/loss-to-follow-up times jointly and allow the underlying accrual rates to change over time. We evaluate the performance of the proposed methods through simulation studies and illustrate the methods using data from a real oncology trial.

Bayesian inference-based deep learning approach for performance prediction and uncertainty quantification of solar photovoltaic-driven heat pump systems

Erratum to: A data-adaptive Bayesian regression approach for polygenic risk prediction.

Computational Biology

A crucial decision in designing a spatial sample for soil survey is the number of sampling locations required to answer, with sufficient accuracy and precision, the questions posed by decision makers at different levels of geographic aggregation. In the Indian Soil Health Card (SHC) scheme, many thousands of locations are sampled per district. In this paper the SHC data are used to estimate the mean of a soil property within a defined study area, e.g., a district, or the areal fraction of the study area where some condition is satisfied, e.g., exceedence of a critical level. The central question is whether this large sample size is needed for this aim. The sample size required for a given maximum length of a confidence interval can be computed with formulas from classical sampling theory, using a prior estimate of the variance of the property of interest within the study area. Similarly, for the areal fraction a prior estimate of this fraction is required. In practice we are uncertain about these prior estimates, and our uncertainty is not accounted for in classical sample size determination (SSD). This deficiency can be overcome with a Bayesian approach, in which the prior estimate of the variance or areal fraction is replaced by a prior distribution. Once new data from the sample are available, this prior distribution is updated to a posterior distribution using Bayes’ rule. The apparent problem with a Bayesian approach prior to a sampling campaign is that the data are not yet available. This dilemma can be solved by computing, for a given sample size, the predictive distribution of the data, given a prior distribution on the population and design parameter. Thus we do not have a single vector with data values, but a finite or infinite set of possible data vectors. As a consequence, we have as many posterior distribution functions as we have data vectors. This leads to a probability distribution of lengths or coverages of Bayesian credible intervals, from which various criteria for SSD can be derived. Besides the fully Bayesian approach, a mixed Bayesian-likelihood approach for SSD is available. This is of interest when, after the data have been collected, we prefer to estimate the mean from these data only, using the frequentist approach, ignoring the prior distribution. The fully Bayesian and mixed Bayesian-likelihood approach are illustrated for estimating the mean of log-transformed Zn and the areal fraction with Zn-deficiency, defined as Zn concentration <0.9 mg kg −1, in the thirteen districts of Andhra Pradesh state. The SHC data from 2015–2017 are used to derive prior distributions. For all districts the Bayesian and mixed Bayesian-likelihood sample sizes are much smaller than the current sample sizes. The hyperparameters of the prior distributions have a strong effect on the sample sizes. We discuss methods to deal with this. Even at the mandal (sub-district) level the sample size can almost always be reduced substantially. Clearly SHC over-sampled, and here we show how to reduce the effort while still providing information required for decision-making. R scripts for SSD are provided as supplementary material.

In this work, we compare the impacts given by statistics and Bayesian statistics. Bayesian statistics is a new statistical method proposed by [C. Ma, P. S. Corasaniti, and B. A. Bassett, arXiv:1603.08519[astro-ph.CO](2016)] recently, which gives a fully account for the standard-candle parameter dependence of the data covariance matrix. For this two statistical methods, we explore the possible redshift-dependence of stretch-luminosity parameter α and color-luminosity parameter β by using redshift tomography. By constraining the ΛCDM model, we check the consistency of cosmology-fit results given by the SN sample of each redshift bin. We also adopt the linear parametrization to explore the possible evolution of α and β and the deceleration parameter q(z) for CPL, JBP, BA and Wang models. We find that: (i) Using the full JLA data, at high redshift α has a trend of decreasing at more than 1.5σ confidence level (CL), and β has a significant trend of decreasing at more than 19σ CL. (ii) Compared with statistics (constant α, β) and Bayesian statistics (constant α, β), Bayesian statistics (linear α and β) yields a larger best-fit value of fractional matter density from JLA+CMB+GC data, which is much closer to slightly deviates from the best-fit result given by other cosmological observations. (iii) The figure of merit (FoM) given by JLA+CMB+GC data from Bayesian statistics is also larger than the FoM from statistics, which indicates that former statistics has a better accuracy. (iv) q(z) given by both statistical methods favor an eternal cosmic acceleration at 1σ CL.

A Bayesian, Phase II Randomized Trial of Extracorporeal Photopheresis (ECP) Plus Steroids Versus Steroids-Alone in Patients with Newly Diagnosed Acute Graft Vs. Host Disease (GVHD): The Addition of ECP Improves Gvhd Response and the Ability to Taper Steroids

A Bayesian predictive inference approach, for the development of classical sliding window detection processes, is the focus of this article. It will be demonstrated that this methodology can produce such detectors with the constant false alarm rate (CFAR) property for clutter modeled by statistics, which are invariant with respect to a group of scale and power transformations. For such a clutter model, it will be shown that the derived detector achieves optimality in the sense of strong consistency. This implies that the Bayesian CFAR detector will have the best performance, in the class of CFAR detectors, for this specific clutter distribution. Although these Bayesian detectors are produced under the assumption of homogeneous clutter, they nonetheless provide the practical engineer with a benchmark on potential CFAR performance. To illustrate the results, the optimal CFAR detector for the Weibull-distributed clutter is derived. Although the Pareto Type I clutter model fits into the class of scale- and power-invariant distributions, there is complexity in the derivation of the Bayesian decision rule. Hence, this special case is also examined, and it will be shown that the Bayesian CFAR corresponds to a well-known detector for this clutter environment.

Recently, several works have shown that the Bayesian approaches to global bandwidth and variable (local and adaptive) bandwidths selection in binomial kernel estimation for probability mass functions (pmfs) outperform the common classical methods, such as mean integrated squared error (MISE) and cross-validation (CV) methods. In this article, we first review the global, local, and adaptive binomial kernel estimator combined with the Bayesian approaches for selecting the bandwidths. Then we compare them by using several count data sets with different designs, in particular for small and moderate sample sizes. All the Bayesian bandwidth selection approaches are also applied to a real count data sets. In general, in terms of integrated squared error (ISE) and execution times, the local Bayesian approach outperforms the other Bayesian approaches.