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.

GB0139, an inhaled small molecule inhibitor of galectin-3, in COVID-19 pneumonitis: a randomised, controlled, open-label, phase 2a experimental medicine trial of the safety, pharmacokinetics, and potential therapeutic value

Rationale: High galectin-3 levels predict poor outcomes in patients with COVID-19. Galectin-3 activates monocytes and macrophages which are directly implicated in COVID-19 immunopathology and the cytokine storm. GB0139 is a potent thiodigalactoside galectin-3 inhibitor and may reduce the severe effects of the disease. We report safety and pharmacokinetics and pharmacodynamics of the inhaled galectin-3 inhibitor, GB0139, and assess clinical outcomes and key systemic inflammatory biomarkers in hospitalised patients with COVID-19 (ClinicalTrials.gov/EudraCT identifier: NCT04473053/2020-002230-32). Methods: Adults with COVID-19 requiring oxygen, and with pneumonitis on x-ray, were randomised to receive standard of care (SOC; including dexamethasone; n=21) or SOC plus 10 mg GB0139 twice daily for 48 hours, then once daily for ≤14 days (n=20). Results: Patients aged 27–87 years were enrolled from July 2020; the final patient completed the 90-day follow-up in April 2021. GB0139+SOC was well tolerated with no treatment-related serious adverse events reported. Incidences of adverse events were similar between treatment arms (40 with GB0139+SOC vs 35 with SOC). Plasma GB0139 was measurable in all patients after inhaled exposure, with moderate interpatient variability, and demonstrated target engagement with decreased circulating galectin (overall treatment effect post-hoc over days 2–7: p=0·0099 vs SOC). Rate of decline in fraction of inspired oxygen (%) requirement was significantly greater in the GB0139+SOC arm with a posterior mean difference of −1 ·51 (95% highest posterior density: −2·90, −0·189) versus SOC. Plasma levels of biomarkers associated with inflammation, coagulopathy, major organ function and fibrosis showed a downward trend versus SOC. Conclusions: GB0139+SOC was well tolerated and achieved clinically relevant plasma concentrations and target engagement. This, and the reduction in markers associated with inflammatory, coagulation, fibrosis, and reduction in inspired oxygen (%) over SOC alone, indicates the therapeutic potential for inhaled GB0139 in hospitalised patients with COVID-19.

Inverted Topp-Leone Distribution: Contribution to a Family of J-Shaped Frequency Functions in Presence of Random Censoring

In this paper, Bayesian and non-Bayesian estimation of the inverted Topp-Leone distribution shape parameter are studied when the sample is complete and random censored. The maximum likelihood estimator (MLE) and Bayes estimator of the unknown parameter are proposed. The Bayes estimates (BEs) have been computed based on the squared error loss (SEL) function and using Markov Chain Monte Carlo (MCMC) techniques. The asymptotic, bootstrap (p,t), and highest posterior density intervals are computed. The Metropolis Hasting algorithm is proposed for Bayes estimates. Monte Carlo simulation is performed to compare the performances of the proposed methods and one real data set has been analyzed for illustrative purposes.

Comparing Uncertainty Associated With 1-, 2-, and 3D Aerial Photogrammetry-Based Body Condition Measurements of Baleen Whales

Body condition is a crucial and indicative measure of an animal’s fitness, reflecting overall foraging success, habitat quality, and balance between energy intake and energetic investment toward growth, maintenance, and reproduction. Recently, drone-based photogrammetry has provided new opportunities to obtain body condition estimates of baleen whales in one, two or three dimensions (1D, 2D, and 3D, respectively) – a single width, a projected dorsal surface area, or a body volume measure, respectively. However, no study to date has yet compared variation among these methods and described how measurement uncertainty scales across these dimensions. This associated uncertainty may affect inference derived from these measurements, which can lead to misinterpretation of data, and lack of comparison across body condition measurements restricts comparison of results between studies. Here we develop a Bayesian statistical model using known-sized calibration objects to predict the length and width measurements of unknown-sized objects (e.g., a whale). We use the fitted model to predict and compare uncertainty associated with 1D, 2D, and 3D photogrammetry-based body condition measurements of blue, humpback, and Antarctic minke whales – three species of baleen whales with a range of body sizes. The model outputs a posterior predictive distribution of body condition measurements and allows for the construction of highest posterior density intervals to define measurement uncertainty. We find that uncertainty does not scale linearly across multi-dimensional measurements, with 2D and 3D uncertainty increasing by a factor of 1.45 and 1.76 compared to 1D, respectively. Each standardized body condition measurement is highly correlated with one another, yet 2D body area index (BAI) accounts for potential variation along the body for each species and was the most precise body condition metric. We hope this study will serve as a guide to help researchers select the most appropriate body condition measurement for their purposes and allow them to incorporate photogrammetric uncertainty associated with these measurements which, in turn, will facilitate comparison of results across studies.

Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring

The point and interval estimations for the unknown parameters of an exponentiated half-logistic distribution based on adaptive type II progressive censoring are obtained in this article. At the beginning, the maximum likelihood estimators are derived. Afterward, the observed and expected Fisher’s information matrix are obtained to construct the asymptotic confidence intervals. Meanwhile, the percentile bootstrap method and the bootstrap-t method are put forward for the establishment of confidence intervals. With respect to Bayesian estimation, the Lindley method is used under three different loss functions. The importance sampling method is also applied to calculate Bayesian estimates and construct corresponding highest posterior density (HPD) credible intervals. Finally, numerous simulation studies are conducted on the basis of Markov Chain Monte Carlo (MCMC) samples to contrast the performance of the estimations, and an authentic data set is analyzed for exemplifying intention.

Bayesian Estimation for the Coefficients of Variation of Birnbaum–Saunders Distributions

The Birnbaum–Saunders (BS) distribution, which is asymmetric with non-negative support, can be transformed to a normal distribution, which is symmetric. Therefore, the BS distribution is useful for describing data comprising values greater than zero. The coefficient of variation (CV), which is an important descriptive statistic for explaining variation within a dataset, has not previously been used for statistical inference on a BS distribution. The aim of this study is to present four methods for constructing confidence intervals for the CV, and the difference between the CVs of BS distributions. The proposed methods are based on the generalized confidence interval (GCI), a bootstrapped confidence interval (BCI), a Bayesian credible interval (BayCI), and the highest posterior density (HPD) interval. A Monte Carlo simulation study was conducted to evaluate their performances in terms of coverage probability and average length. The results indicate that the HPD interval was the best-performing method overall. PM 2.5 concentration data for Chiang Mai, Thailand, collected in March and April 2019, were used to illustrate the efficacies of the proposed methods, the results of which were in good agreement with the simulation study findings.

Estimating sexual size dimorphism in fossil species from posterior probability densities

Accurate characterization of sexual dimorphism is crucial in evolutionary biology because of its significance in understanding present and past adaptations involving reproductive and resource use strategies of species. However, inferring dimorphism in fossil assemblages is difficult, particularly with relatively low dimorphism. Commonly used methods of estimating dimorphism levels in fossils include the mean method, the binomial dimorphism index, and the coefficient of variation method. These methods have been reported to overestimate low levels of dimorphism, which is problematic when investigating issues such as canine size dimorphism in primates and its relation to reproductive strategies. Here, we introduce the posterior density peak (pdPeak) method that utilizes the Bayesian inference to provide posterior probability densities of dimorphism levels and within-sex variance. The highest posterior density point is termed the pdPeak. We investigated performance of the pdPeak method and made comparisons with the above-mentioned conventional methods via 1) computer-generated samples simulating a range of conditions and 2) application to canine crown-diameter datasets of extant known-sex anthropoids. Results showed that the pdPeak method is capable of unbiased estimates in a broader range of dimorphism levels than the other methods and uniquely provides reliable interval estimates. Although attention is required to its underestimation tendency when some of the distributional assumptions are violated, we demonstrate that the pdPeak method enables a more accurate dimorphism estimate at lower dimorphism levels than previously possible, which is important to illuminating human evolution.

Bayesian Analysis of an Optimal Five Period Cross-over Design

A crossover design is a repeated measurements design such that each experimental unit receives different treatments during the different time periods. In a majority of bioequivalence studies, design and analysis of cross-over using classical methods such as analysis of variance (ANOVA) and test are normally associated with erroneous results. The Bayesian method is desirable in the analysis of crossover designs to eliminate errors associated with carryover effects. The objective of this study was to compare the Bayesian and the - test analysis methods on treatments and carryover effects for an optimal two treatments, five periods and four sequence C (2, 5, 4) design. The treatments and residual estimates were obtained using Best Linear Unbiased Estimation (BLUE) method. In the Bayesian method of analysis, the posterior quantities were obtained for the mean intervals of treatments and carry-over effects and the highest posterior density (HPD) graphs were plotted and interpreted using conditional probability statements. For validation purposes, the Bayesian method results were compared with the existing -tests results. From the Bayesian analysis, the probability of significant treatment difference in the presence of carryover effects was 1, while from the -test, the calculated value of 11.73 was greater than the two sided tabulated value at 95 level of significance. The two analysis methods implied significant differences in the treatment effects. In conclusion, it was established that Bayesian method of analysis can be used for bioequivalence analysis even when the carry-over effects are present and hence it is highly recommended for bioequivalence studies.

Bayesian and Classical Inference for the Generalized Log-Logistic Distribution with Applications to Survival Data

The generalized log-logistic distribution is especially useful for modelling survival data with variable hazard rate shapes because it extends the log-logistic distribution by adding an extra parameter to the classical distribution, resulting in greater flexibility in analyzing and modelling various data types. We derive the fundamental mathematical and statistical properties of the proposed distribution in this paper. Many well-known lifetime special submodels are included in the proposed distribution, including the Weibull, log-logistic, exponential, and Burr XII distributions. The maximum likelihood method was used to estimate the unknown parameters of the proposed distribution, and a Monte Carlo simulation study was run to assess the estimators’ performance. This distribution is significant because it can model both monotone and nonmonotone hazard rate functions, which are quite common in survival and reliability data analysis. Furthermore, the proposed distribution’s flexibility and usefulness are demonstrated in a real-world data set and compared to its submodels, the Weibull, log-logistic, and Burr XII distributions, as well as other three-parameter parametric survival distributions, such as the exponentiated Weibull distribution, the three-parameter log-normal distribution, the three-parameter (or the shifted) log-logistic distribution, the three-parameter gamma distribution, and an exponentiated Weibull distribution. The proposed distribution is plausible, according to the goodness-of-fit, log-likelihood, and information criterion values. Finally, for the data set, Bayesian inference and Gibb’s sampling performance are used to compute the approximate Bayes estimates as well as the highest posterior density credible intervals, and the convergence diagnostic techniques based on Markov chain Monte Carlo techniques were used.

PSVIII-5 Genetic parameters of thrombin as a proxy for horn fly abundance in beef cattle

Horn flies (Haematobia irritans) are a major nuisance to cattle, especially in warm, humid regions, and are estimated to cause economic losses in excess of $1 billion annually to the U.S. beef cattle industry. Variation in horn fly tolerance has been reported within and across breeds, and heritability estimates ranging between 10 and 80% show a clear genetic basis. However, collecting fly abundance phenotypes is costly and logistically demanding, which precludes large-scale implementation. Consequently, finding correlated phenotypes and endo-phenotypes that are heritable and relatively easy to measure would facilitate implementation of horn fly tolerance genetic improvement programs. Thrombin (TH), a blood coagulation precursor, has a reported association with horn fly count variation within and across cattle breeds. In this study, the genetic basis of thrombin in beef cattle was investigated. Blood samples and horn fly count were collected on 360 cows and heifers twice during the summer of 2019 (June and August). Due to uncertainty associated with assessment of horn fly abundance and thrombin and the fact that economic losses occur only when fly abundance exceeds a certain threshold, thrombin was categorized into 4 classes (1=TH > 500 ng/ml; 2=250< TH< 500 ng/ml; 3=100< TH< 250 ng/ml; and 4=TH< 100 ng/ml). The trait was analyzed using linear (continuous) and threshold (discrete) mixed models. Both models included farm, pregnancy status, and cow age as fixed effects and additive and permanent environment random effects. The pedigree included 642 animals. Estimates of heritability were 0.24 and 0.29 using linear and threshold models, respectively. Estimates of repeatability were slightly higher using the threshold model (0.21 vs 0.19). Despite the small data size, all estimates were non-zero based on their respective highest posterior density intervals. These results indicate reasonable genetic variation for thrombin that could be harnessed for improvement of horn fly tolerance in cattle.