Inferences for Exponentiated Gamma Constant-Stress Partially Accelerated Life Test Model Based on Generalized Type-I Hybrid Censored Data

In this paper, the exponentiated gamma distribution (EGD) with generalized Type-I hybrid censored data under constant-stress partially accelerated life test (CSPALT) model is considered. The Bayesian and E-Bayesian estimation methods, as well as the maximum likelihood estimation method, are discussed for the parameter of the distribution and the acceleration factor. The E-Bayesian and Bayesian estimates are derived by using the squared error loss (SEL) and the LINEX loss functions. The MCMC method is applied for deriving the Bayesian and then E-Bayesian estimates. Moreover, a real data set is given for the illustrative purpose. After all, an evaluation is performed for the results of the proposed methods.

On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme

Bayesian estimates involve the selection of hyper-parameters in the prior distribution. To deal with this issue, the empirical Bayesian and E-Bayesian estimates may be used to overcome this problem. The first one uses the maximum likelihood estimate (MLE) procedure to decide the hyper-parameters; while the second one uses the expectation of the Bayesian estimate taken over the joint prior distribution of the hyper-parameters. This study focuses on establishing the E-Bayesian estimates for the Lomax distribution shape parameter functions by utilizing the Gamma prior of the unknown shape parameter along with three distinctive joint priors of Gamma hyper-parameters based on the square error as well as two asymmetric loss functions. These two asymmetric loss functions include a general entropy and LINEX loss functions. To investigate the effect of the hyper-parameters’ selections, mathematical propositions have been derived for the E-Bayesian estimates of the three shape functions that comprise the identity, reliability and hazard rate functions. Monte Carlo simulation has been performed to compare nine E-Bayesian, three empirical Bayesian and Bayesian estimates and MLEs for any aforementioned functions. Additionally, one simulated and two real data sets from industry life test and medical study are applied for the illustrative purpose. Concluding notes are provided at the end.

Estimation of Information Measures for Power-Function Distribution in Presence of Outliers and Their Applications

The measure of entropy has an undeniable pivotal role in the field of information theory. This article estimates the Rényi and q-entropies of the power function distribution in the presence of s outliers. The maximum likelihood estimators as well as the Bayesian estimators under uniform and gamma priors are derived. The proposed Bayesian estimators of entropies under symmetric and asymmetric loss functions are obtained. These estimators are computed empirically using Monte Carlo simulation based on Gibbs sampling. Outcomes of the study showed that the precision of the maximum likelihood and Bayesian estimates of both entropies measures improves with sample sizes. The behavior of both entropies estimates increase with number of outliers. Further, Bayesian estimates of the Rényi and q-entropies under squared error loss function are preferable than the other Bayesian estimates under the other loss functions in most of cases. Eventually, real data examples are analyzed to illustrate the theoretical results.

1090. Does calculation method matter for targeting vancomycin AUC?

Background Recent vancomycin (VAN) guidelines recommend targeting an area under the curve (AUC) concentration of 400-600 for treatment of methicillin resistant Staphylococcus aureus infections. Multiple strategies for calculating AUC exist, including first order pharmacokinetic (foPK) equations and Bayesian models. Most clinical applications of foPK assume unchanged patient status and project ideal administration times to estimate exposure. Bayesian modeling provides the best estimate of true drug exposure and can incorporate changing patient covariates and exact doses. We compared two commonly used foPK methods to Bayesian estimates of VAN AUC. Graphs depict calculated AUCs using the three different methods: 1) Population PK estimated (foPOPPK) 2) Two-level first dose estimated (foFDPK) 3) Bayesian estimated. Methods First order equations were performed using population PK estimates (foPOPPK) to estimate steady state (SS) AUC and initial doses. Two concentrations after first dose were used to estimate SS AUC (foFDPK). A 2-compartment Bayesian model allometrically scaled for weight and adjusted for creatinine clearance was used to determine 24-48 hour AUCs. Differences between AUCs were compared using a mixed-effects analysis, and correlation of foPK equations to Bayesian estimates was described using Spearman’s correlation. Patient results from each method were classified as below (< 400), within (400-600), or above ( >600) targets. Results 65 adult patients were included. The median and IQR for calculated AUCs using foPOPPK, foFDPK, and Bayesian methods were 495.6 (IQR: 76.6), 498.2 (IQR: 107.4), and 472.1 (IQR: 177.9), respectively with p >0.65 for both foPK methods vs. the Bayesian method. AUCs predicted by foPK equations were poorly correlated with Bayesian AUCs (Spearman’s rho= -0.08, p=0.55), while AUCs from foFDPK better correlated with Bayesian AUCs (Spearman’s rho= 0.48, p=0.00). AUCs were within, above, and below target for 54%, 20%, and 26% for the Bayesian model; 95%, 5% and 0% for foPOPPK; and 74%, 12%, and 14% for foFDPK. foPK AUC estimates concurred with Bayesian estimates only 52% of the time. Conclusion AUCs calculated by the three methods did not differ on average, but dosing recommendations for foPK at the patient level varied substantially compared to the Bayesian method. This difference is because Bayesian estimation incorporates actual patient exposures while foPK equations rely on idealized dose timing to predict AUCs. Disclosures Kimberly C. Claeys, PharmD, GenMark (Speaker’s Bureau) Marc H. Scheetz, PharmD, MSc, Nevakar (Grant/Research Support)SuperTrans Medical (Consultant)US Patent #10688195B2 (Other Financial or Material Support, Patent holder)

Bayesian Analysis of Dynamic Cumulative Residual Entropy for Lindley Distribution

Dynamic cumulative residual (DCR) entropy is a valuable randomness metric that may be used in survival analysis. The Bayesian estimator of the DCR Rényi entropy (DCRRéE) for the Lindley distribution using the gamma prior is discussed in this article. Using a number of selective loss functions, the Bayesian estimator and the Bayesian credible interval are calculated. In order to compare the theoretical results, a Monte Carlo simulation experiment is proposed. Generally, we note that for a small true value of the DCRRéE, the Bayesian estimates under the linear exponential loss function are favorable compared to the others based on this simulation study. Furthermore, for large true values of the DCRRéE, the Bayesian estimate under the precautionary loss function is more suitable than the others. The Bayesian estimates of the DCRRéE work well when increasing the sample size. Real-world data is evaluated for further clarification, allowing the theoretical results to be validated.

Modelling medieval masonry construction: taxa-specific and habitat-contingent Bayesian techniques for the interpretation of radiocarbon data from Mortar-Entrapped Relict Limekiln Fuels

Using data from simulated and actual case studies, this paper assesses the accuracy and precision of Bayesian estimates for the constructional date of medieval masonry buildings, generated from the radiocarbon evidence returned by different assemblages of wood-charcoal mortar-entrapped relict limekiln fuel (MERLF). The results from two theoretical studies demonstrate how Bayesian model specifications can be varied to generate a chronologically continuous spectrum of distributions from radiocarbon datasets subject Inbuilt Age (IA). Further analysis suggests that the potential for these distributions to contain the date of the constructional event depends largely upon the accuracy of the latest radiocarbon determination within each dataset, while precision is predicated on dataset age range, dataset size and model specification. These theoretical studies inform revised approaches to the radiocarbon evidence emerging from six culturally important Scottish medieval masonry buildings, each of which is associated with a wood-charcoal MERLF assemblage of different botanical character. The Bayesian estimates generated from these radiocarbon datasets are remarkably consistent with the historical and archaeological evidence currently associated with these sites, while age range distributions suggest the IA of each MERLF assemblage has been constrained by the taxa-specific and environmentally contingent lifespans and post-mortem durabilities of the limekiln fuel source. These studies provide further evidence that Bayesian techniques can generate consistently accurate chronological estimates for the construction of medieval masonry buildings from MERLF radiocarbon data, whatever the ecological provenance of the limekiln fuel source. Estimate precision is contingent upon source ecology and craft technique but can be increased by a more informed approach to materials analysis and interpretation.

E-Bayesian Estimation of Reliability Characteristics of a Weibull Distribution with Applications

Given a progressively type-II censored sample, the E-Bayesian estimates, which are the expected Bayesian estimates over the joint prior distributions of the hyper-parameters in the gamma prior distribution of the unknown Weibull rate parameter, are developed for any given function of unknown rate parameter under the square error loss function. In order to study the impact from the selection of hyper-parameters for the prior, three different joint priors of the hyper-parameters are utilized to establish the theoretical properties of the E-Bayesian estimators for four functions of the rate parameter, which include an identity function (that is, a rate parameter) as well as survival, hazard rate and quantile functions. A simulation study is also conducted to compare the three E-Bayesian and a Bayesian estimate as well as the maximum likelihood estimate for each of the four functions considered. Moreover, two real data sets from a medical study and industry life test, respectively, are used for illustration. Finally, concluding remarks are addressed.

Estimation and Prediction for Gompertz Distribution under General Progressive Censoring

In this article, we discuss the estimation of the parameters for Gompertz distribution and prediction using general progressive Type-II censoring. Based on the Expectation–Maximization algorithm, we calculate the maximum likelihood estimates. Bayesian estimates are considered under different loss functions, which are symmetrical, asymmetrical and balanced, respectively. An approximate method—Tierney and Kadane—is used to derive the estimates. Besides, the Metropolis-Hasting (MH) algorithm is applied to get the Bayesian estimates as well. According to Fisher information matrix, we acquire asymptotic confidence intervals. Bootstrap intervals are also established. Furthermore, we build the highest posterior density intervals through the sample generated by the MH algorithm. Then, Bayesian predictive intervals and estimates for future samples are provided. Finally, for evaluating the quality of the approaches, a numerical simulation study is implemented. In addition, we analyze two real datasets.