Inference for cumulative risk model under step-stress experiments and its application in nanocrystalline data

With the popularity of step-stress accelerated life testing, researchers are exploring more possibilities for models that relate the life distributions under different stress levels. Cumulative risk model assumes that the effects of stress changes have a lag period before they are fully observed, which guarantees the continuity of the hazard rate function. This paper studies the cumulative risk model for Lomax distribution with step-stress experiments. For maximum likelihood estimation, Newton-Rapson method is adopted to get point estimates. Meanwhile, the asymptotic normality of the maximum likelihood estimator is used to obtain asymptotic confidence intervals. For Bayesian estimation, point estimates and highest posterior density credible intervals under squared error loss function with informative prior and non-informative prior are derived using Metropolis-Hastings method and Metropolis-Hastings within Gibbs algorithm. To evaluate the effects of stress change time and the length of lag period, as well as the performance of different methods, numerical simulations are conducted. Then a real nanocrystalline data set is analyzed.

Updating Knowledge in The Estimation of The Genetics Parameters Multi-trait and Multi-Environment Bayesian Analysis in Rice (Oryza Sativa L.)

Among the multi-trait models used to jointly study several traits and environments, the Bayesian framework has been a preferable tool for using a more complex and biologically realistic model. In most cases, the non-informative prior distributions are adopted in studies using the Bayesian approach. Still, the Bayesian approach tends to present more accurate estimates when it uses informative prior distributions. The present study was developed to evaluate the efficiency and applicability of multi-trait multi-environment (MTME) models under a Bayesian framework utilizing a strategy for eliciting informative prior distribution using previous data from rice. The study involved data pertained to rice genotypes in three environments and five agricultural years (2010/2011 until 2014/2015) for the following traits: grain yield (GY), flowering in days (FLOR) and plant height (PH). Variance components and genetic and non-genetic parameters were estimated by the Bayesian method. In general, the informative prior distribution in Bayesian MTME models provided higher estimates of heritability and variance components, as well as minor lengths for the highest probability density interval (HPD), compared to their respective non-informative prior distribution analyses. The use of more informative prior distributions makes it possible to detect genetic correlations between traits, which cannot be achieved with the use of non-informative prior distributions. Therefore, this mechanism presented for updating knowledge to the elicitation of an informative prior distribution can be efficiently applied in rice genetic selection.

Bayesian Processing of Data on Bursts of Pressure Vessels

Two alternative Bayesian approaches are proposed for the prediction of fragmentation of pressure vessels triggered off by accidental explosions (bursts) of these containment structures. It is shown how to carry out this prediction with post-mortem data on fragment numbers counted after past explosion accidents. Results of the prediction are estimates of probabilities of individual fragment numbers. These estimates are expressed by means of Bayesian prior or posterior distributions. It is demonstrated how to elicit the prior distributions from relatively scarce post-mortem data on vessel fragmentations. Specifically, it is suggested to develop priors with two Bayesian models known as compound Poisson-gamma and multinomial-Dirichlet probability distributions. The available data is used to specify non-informative prior for Poisson parameter that is subsequently transformed into priors of individual fragment number probabilities. Alternatively, the data is applied to a specification of Dirichlet concentration parameters. The latter priors directly express epistemic uncertainty in the fragment number probabilities. Example calculations presented in the study demonstrate that the suggested non-informative prior distributions are responsive to updates with scarce data on vessel explosions. It is shown that priors specified with Poisson-gamma and multinomial-Dirichlet models differ tangibly; however, this difference decreases with increasing amount of new data. For the sake of brevity and concreteness, the study was limited to fire induced vessel bursts known as boiling liquid expanding vapour explosions (BLEVEs).

Bayesian Covariance Representation with Global Informative Prior for 3D Action Recognition

For the merits of high-order statistics and Riemannian geometry, covariance matrix has become a generic feature representation for action recognition. An independent action can be represented by an empirical statistics over all of its pose samples. Two major problems of covariance include the following: (1) it is prone to be singular so that actions fail to be represented properly, and (2) it is short of global action/pose-aware information so that expressive and discriminative power is limited. In this article, we propose a novel Bayesian covariance representation by a prior regularization method to solve the preceding problems. Specifically, covariance is viewed as a parametric maximum likelihood estimate of Gaussian distribution over local poses from an independent action. Then, a Global Informative Prior (GIP) is generated over global poses with sufficient statistics to regularize covariance. In this way, (1) singularity is greatly relieved due to sufficient statistics, (2) global pose information of GIP makes Bayesian covariance theoretically equivalent to a saliency weighting covariance over global action poses so that discriminative characteristics of actions can be represented more clearly. Experimental results show that our Bayesian covariance with GIP efficiently improves the performance of action recognition. In some databases, it outperforms the state-of-the-art variant methods that are based on kernels, temporal-order structures, and saliency weighting attentions, among others.

Innovative Adaptive Study Design in Transfusion-Dependent Beta-Thalassemia: Bayesian Design with Concurrent Randomization and Borrowing from Historical Data

Background Clinical development of new therapies in transfusion-dependent beta-thalassemia has several challenges. Patient enrollment in rare diseases requires multi-center multi-country studies, and the lack of reliable surrogate endpoint for dose selection requires powering for clinical endpoints usually used in Phase 3 trials. An acceptable endpoint from a regulatory perspective which is based on responders analysis, such as proportion of patients experiencing ≥50% reduction in Red Blood Cell (RBC) transfusion burden and a reduction of ≥2 units, requires 12 weeks screening period to establish baseline transfusion burden for reliable comparison. Importantly, higher randomization ratio of treatment:placebo can improve patients' motivation to enroll into a trial, but it is less statistically efficient and requires higher sample size. We designed a Phase-2b, double-blind, randomized, placebo controlled, multi-center study with Vamifeport (NCT04938635) to assess the efficacy and safety of multiple doses of a new therapy in adults with transfusion-dependent beta-thalassemia. The proposed design follows the Bayesian framework with borrowing from published historical control data. The historical control data is used to construct an informative prior for the control arm to reduce the burden of patients randomized to a control arm and improve the trial's efficiency in performing dose selection. Study Design and Methods Adults (18 to 65 y.o.) with documented diagnosis of β-thalassemia or hemoglobin E / β-thalassemia will be randomized to three doses of the investigational drug or placebo plus best supportive care. RBC transfusion dependence is defined as at least 6 RBC Units in the 24 weeks prior to randomization and no transfusion-free period for ≥35 days during that period. The primary endpoint is the proportion of patients experiencing ≥33% reduction of RBC units from baseline and a reduction of ≥2 units assessed from week 13 to week 24. The key secondary endpoints include proportion of patients experiencing ≥33% reduction from week 37 to week 48; proportion of patients experiencing ≥50% reduction over any consecutive 12-week interval from week 1 to week 48 and the mean change from baseline in RBC transfusions (units) from week 13 to week 24. The primary and key-secondary analysis will be conducted in a hierarchical fashion to account for multiplicity. We proposed a Bayesian design with the use of noninformative, or weakly informative, priors for the active dose arms while using a robustified informative prior for the control arm. Historical control data will be "borrowed" in an informative prior for the control arm rate from the Phase 3 trial - BELIEVE. The robustification is required in order to control the level of borrowing depending on the level of prior-data conflict. Prior-data conflict can arise from multiple sources like population heterogeneity between the historical and current study. Therefore, the selection of historical data (BELIEVE trial) addresses similarity in inclusion / exclusion criteria, standard of care etc. The robustification of the informative prior does not take into account prior-data conflict in terms of population or study characteristics but directly focuses on the informative prior of the parameter of interest and the corresponding likelihood of the current data. For example, in the BELIEVE study, out of 112 patients randomized to the control arm, 5 patients (4.5%) had a ≥33% reduction in transfusion burden over 24 weeks. A prior-data conflict may arise if the Phase-2b trial of interest here, suggests that the proportion is substantially different that 4.5% and this can inflate the frequentist Type-I or Type-II error rates examined via simulations. We evaluated Type-I error rates of the proposed design with 5000 Monte-Carlo runs for each scenario of the response rates. Using informative prior with no prior-data conflict the type-I error with no robustification is ≈ 2.4%. As the prior-data conflict increases, without robustification, the type-I error cannot be controlled. However, with a robustification weight of 0.5 the type-I errors can be controlled in line with regulatory requirements. Discussion A proposed Bayesian design with robustified informative prior for the control arm helps reduce patients' burden of randomization to control arm and reduce overall sample size for a rare disease trial when recruitment and trial duration are challenging. Disclosures Muehlemann: Vifor Pharma AG: Consultancy. Mukherjee: Vifor Pharma AG: Consultancy. Taher: Bristol Myers Squibb: Consultancy, Research Funding; Vifor Pharma: Consultancy, Research Funding; Agios Pharmaceuticals: Consultancy; Ionis Pharmaceuticals: Consultancy, Research Funding; Novartis: Consultancy, Research Funding. Gudmundsdottir: Vifor Pharma AG: Current Employment. Morin: Vifor Pharma AG: Current Employment. Richard: Vifor Pharma AG: Current Employment.

A Weakly Informative Prior for Resonance Frequencies

We derive a weakly informative prior for a set of ordered resonance frequencies from Jaynes’ principle of maximum entropy. The prior facilitates model selection problems in which both the number and the values of the resonance frequencies are unknown. It encodes a weakly inductive bias, provides a reasonable density everywhere, is easily parametrizable, and is easy to sample. We hope that this prior can enable the use of robust evidence-based methods for a new class of problems, even in the presence of multiplets of arbitrary order.

Global Information for Multidimensional Tests

New measures of test information, termed global information, quantify test information relative to the entire range of the trait being assessed. Estimating global information relative to a non-informative prior distribution results in a measure of how much information could be gained by administering the test to an unspecified examinee. Currently, such measures have been developed only for unidimensional tests. This study introduces measures of multidimensional global test information and validates them in simulated data. Then, the utility of global test information is tested in neuropsychological data collected as part of Rush University’s Memory and Aging Project. These measures allow for direct comparison of complex tests calibrated in different samples, facilitating test development and selection.

Constrained Adjusted Maximum a Posteriori Estimation of Bayesian Network Parameters

Maximum a posteriori estimation (MAP) with Dirichlet prior has been shown to be effective in improving the parameter learning of Bayesian networks when the available data are insufficient. Given no extra domain knowledge, uniform prior is often considered for regularization. However, when the underlying parameter distribution is non-uniform or skewed, uniform prior does not work well, and a more informative prior is required. In reality, unless the domain experts are extremely unfamiliar with the network, they would be able to provide some reliable knowledge on the studied network. With that knowledge, we can automatically refine informative priors and select reasonable equivalent sample size (ESS). In this paper, considering the parameter constraints that are transformed from the domain knowledge, we propose a Constrained adjusted Maximum a Posteriori (CaMAP) estimation method, which is featured by two novel techniques. First, to draw an informative prior distribution (or prior shape), we present a novel sampling method that can construct the prior distribution from the constraints. Then, to find the optimal ESS (or prior strength), we derive constraints on the ESS from the parameter constraints and select the optimal ESS by cross-validation. Numerical experiments show that the proposed method is superior to other learning algorithms.

A Similarity-Weighted Informative Prior Distribution for Bayesian Multiple Regression Models

Specifying accurate informative prior distributions is a question of carefully selecting studies that comprise the body of comparable background knowledge. Psychological research, however, consists of studies that are being conducted under different circumstances, with different samples and varying instruments. Thus, results of previous studies are heterogeneous, and not all available results can and should contribute equally to an informative prior distribution. This implies a necessary weighting of background information based on the similarity of the previous studies to the focal study at hand. Current approaches to account for heterogeneity by weighting informative prior distributions, such as the power prior and the meta-analytic predictive prior are either not easily accessible or incomplete. To complicate matters further, in the context of Bayesian multiple regression models there are no methods available for quantifying the similarity of a given body of background knowledge to the focal study at hand. Consequently, the purpose of this study is threefold. We first present a novel method to combine the aforementioned sources of heterogeneity in the similarity measure ω. This method is based on a combination of a propensity-score approach to assess the similarity of samples with random- and mixed-effects meta-analytic models to quantify the heterogeneity in outcomes and study characteristics. Second, we show how to use the similarity measure ωas a weight for informative prior distributions for the substantial parameters (regression coefficients) in Bayesian multiple regression models. Third, we investigate the performance and the behavior of the similarity-weighted informative prior distribution in a comprehensive simulation study, where it is compared to the normalized power prior and the meta-analytic predictive prior. The similarity measure ω and the similarity-weighted informative prior distribution as the primary results of this study provide applied researchers with means to specify accurate informative prior distributions.