The Bayes Estimators of the Variance and Scale Parameters of the Normal Model With a Known Mean for the Conjugate and Noninformative Priors Under Stein’s Loss

For the normal model with a known mean, the Bayes estimation of the variance parameter under the conjugate prior is studied in Lehmann and Casella (1998) and Mao and Tang (2012). However, they only calculate the Bayes estimator with respect to a conjugate prior under the squared error loss function. Zhang (2017) calculates the Bayes estimator of the variance parameter of the normal model with a known mean with respect to the conjugate prior under Stein’s loss function which penalizes gross overestimation and gross underestimation equally, and the corresponding Posterior Expected Stein’s Loss (PESL). Motivated by their works, we have calculated the Bayes estimators of the variance parameter with respect to the noninformative (Jeffreys’s, reference, and matching) priors under Stein’s loss function, and the corresponding PESLs. Moreover, we have calculated the Bayes estimators of the scale parameter with respect to the conjugate and noninformative priors under Stein’s loss function, and the corresponding PESLs. The quantities (prior, posterior, three posterior expectations, two Bayes estimators, and two PESLs) and expressions of the variance and scale parameters of the model for the conjugate and noninformative priors are summarized in two tables. After that, the numerical simulations are carried out to exemplify the theoretical findings. Finally, we calculate the Bayes estimators and the PESLs of the variance and scale parameters of the S&P 500 monthly simple returns for the conjugate and noninformative priors.

Peramalan Indeks Saham LQ45 pada Masa Pandemi COVID-19 Menggunakan Analisis Intervensi

Analisis intervensi merupakan metode pemodelan deret waktu yang dipengaruhi oleh suatu peristiwa yang menyebabkan data deret waktu mengalami fluktuatif. Metode analisis intervensi memiliki tujuan untuk mengukur besar dan lamanya efek dari suatu intervensi pada data deret waktu. Terdapat dua jenis variabel analisis intervensi, yaitu fungsi step dan fungsi pulse. Tujuan penelitian ini untuk memodelkan dan meramalkan model intervensi fungsi step pada indeks saham LQ45 dengan waktu intervensi yang diketahui. Deret waktu LQ45 dipengaruhi oleh suatu intervensi, yaitu pandemi COVID-19. Prosedur dalam melakukan metode analisis intervensi diawali dengan mengelompokkan data menjadi dua kelompok, yaitu data sebelum intervensi dan data saat intervensi sampai data terakhir. Data sebelum intervensi digunakan untuk pemodelan ARIMA. Model ARIMA yang didapatkan dari data sebelum terjadinya intervensi digunakan sebagai informasi untuk melakukan identifikasi orde intervensi. Selanjutnya dilakukan estimasi parameter dan pemeriksaan uji asumsi white noise serta uji asumsi berdistribusi normal. Model intervensi yang telah memenuhi kedua asumsi tersebut dapat digunakan untuk peramalan. Peramalan dari indeks saham LQ45 menghasilkan nilai indeks saham LQ45 yang cenderung konstan dan berkisar pada level indeks saham sebesar 883 – 884. Hasil peramalan indeks saham LQ45 sudah sangat baik dengan nilai galat sebesar 7%.

Multi-Targeted Approaches and Drug Repurposing Reveal Possible SARS-CoV-2 Inhibitors

The COVID-19 pandemic caused by SARS-CoV-2 is unprecedented in recent memory owing to the non-stop escalation in number of infections and deaths in almost every country of the world. The lack of treatment options further worsens the scenario, thereby necessitating the exploration of already existing US FDA-approved drugs for their effectiveness against COVID-19. In the present study, we have performed virtual screening of nutraceuticals available from DrugBank against 14 SARS-CoV-2 proteins. Molecular docking identified several inhibitors, two of which, rutin and NADH, displayed strong binding affinities and inhibitory potential against SARS-CoV-2 proteins. Further normal model-based simulations were performed to gain insights into the conformational transitions in proteins induced by the drugs. The computational analysis in the present study paves the way for experimental validation and development of multi-target guided inhibitors to fight COVID-19.

A STUDY OF GENERALIZED LINEAR MIXED MODEL FOR COUNT DATA USING HIERARCHICAL BAYES METHOD

Poisson Log-Normal Model is one of the hierarchical mixed models that can be used for count data. Several estimation methods can be used to estimate the model parameters. The first objective of this study was to examine the performance of the parameter estimator and model built using the Hierarchical Bayes method via Markov Chain Monte Carlo (MCMC) with simulation. The second objective was applied the Poisson Log-Normal model to the West Java illiteracy Cases data which is sourced from the Susenas data on March 2019. In 2019, the incidence of illiteracy is a very rare occurrence in West Java Province. So that, it is suitable as an application case in this study. The simulation results showed that the Hierarchical Bayes parameter estimator through MCMC has the smallest Root Mean Squared Error of Prediction (RMSEP) value and the absolute bias is relatively mostly similar when compared to the Maximum Likelihood (ML) and Penalized Quasi-Likelihood (PQL) methods. Meanwhile, the empirical results showed that the fixed variable is the number of respondents who have a maximum education of elementary school have the greatest risk of illiteracy. Also, the diversity of census blocks significantly affects illiteracy cases in West Java 2019.

Influence of Different Fixed System in Osteoporotic Lumbar Vertebrae in Fusion：A 3D Finite Element Analysis

Background：Posterior lumbar interbody fusion(PLIF) is the most common surgical method for lumbar fusion surgery, and pedicle screws（PS）can provide effective fixation strength in normal bone. However, pedicle screws are prone to loosening in osteoporotic patients. cortical bone trajectory (CBT) screw fixation and cement augmentation pedicle screw（CAPS） fixation are often used to reduce the risk of loosening. Although several studies are reported that the pullout strength of CBT screws or CAPS screws are higher than PS，There are no relevant studies on different internal fixation stress analysis. The purpose of this study was to compare the stresses of different fixation methods and analyze the stresses of different internal fixation systems through finite element analysis.Methods: Five finite element models were established and tested by simulating PLIF surgery at L4/5. They included: (1) normal model (2) osteoporosis model (3) pedicle screw model; (4) cement augmentation pedicle screw（CAPS）model; (5) cortical bone trajectory (CBT) model. The range of motion (ROM), stress of fusion cage and screw-rod system of different models were analyzed by simulating flexion, extension, left bending, right bending, left rotation and right rotation movements through software.Results: The ROM of the osteoporosis model was increased compared with the normal bone, and the osteoporosis was increased by 5.3%, 17.6%, 11.5%, 11.3%, 7.5%, and 8.3% compared with the normal model during flexion, extension, left bending, right bending, left rotation, and right rotation. After fixation, the ROM decreased, but the difference was not significant between the different fixation models. The stress of the screw-rods is the minimum one in the CAPS group. the PS group is the middle one, and stress of the CBT group is max. The cage stress is the minimum in the CAPS group which is slightly smaller than the cage stress in the PS group. the cage stress was the max in the CBT group.Conclusion: PLIF can decrease the ROM of lumbar vertebra and fusion segment in osteoporosis, but different fixation methods have little effect on ROM. However, there was a great difference in the stress of implant, with the least stress in the CAPS group, the second in the PS group, and the greatest stress in the CBT. The same is true for Cage stress. At the same time, the maximum stress zone to occur at the screw-rod junction, while the maximum stress of cage occurs at the position in contact with the endplate. The study has guiding significance for clinical practice.

Incidence and mortality rates of intracranial hemorrhage in hemophilia: a systematic review and meta-analysis

Intracranial hemorrhage (ICH) is a severe complication that is relatively common among hemophilia patients. This systematic review aimed to obtain more precise estimates of ICH incidence and mortality in hemophilia, which may be important for patients, caregivers, researchers and health policy-makers. PubMed and EMBASE were systematically searched using terms related to "hemophilia" and "intracranial hemorrhage" or "mortality". Studies that allowed calculation of ICH incidence or mortality rates in a hemophilia population of at least 50 patients were included. We summarized evidence on ICH incidence and calculated pooled ICH incidence and mortality in three age groups: (1) persons of all ages with hemophilia, (2) children and young adults below 25 years of age with hemophilia and (3) neonates with hemophilia. Incidence and mortality were pooled with a Poisson-Normal model or a Binomial-Normal model. We included 45 studies that represented 54 470 patients, 809 151 person-years and 5326 live births of hemophilia patients. In persons of all ages, the pooled ICH incidence and mortality rates were 2.3 (95% CI 1.2-4.8) and 0.8 (95% CI 0.5-1.2) per 1000 person-years, respectively. In children and young adults, the pooled ICH incidence and mortality rates were 7.4 (95% CI 4.9-11.1) and 0.5 (95% CI 0.3-0.9) per 1000 person-years, respectively. In neonates, the pooled cumulative ICH incidence was 2.1% (95% CI 1.5-2.8) per 100 live births. ICH was classified as spontaneous in 35-58% of cases. Our findings suggest that ICH is an important problem in hemophilia that occurs among all ages, requiring adequate preventive strategies.

INVESTIGATING THE RELATIONSHIPS BETWEEN EXPRESSED CANCER RELATED GENES AND SURVIVAL OF PATIENTS WITH BREAST CANCER

Cancer stem cells are regulated by complex interactions with the components of the tumor microenvironment through networks of Cytokins and growth factors. These interactions are mediated by group of proteins and microRNAs (miRs), which are expressed or repressed. These expression levels are critical for cancer stem cell formation and expansion, enabling the promotion of tumor cell proliferation and migration, as well as for the survival of cancer recurrence and patient survival. Micro array and RNA deep sequencing (RNA-seq) provide tools with ability to generate transcriptome information, deciphering global gene expression patterns and quantifying a large dynamic range of expression levels. In this study 94 breast cancer patients were investigated based on miR and mRNA expression levels in which WDR1, APC and AKAP13 genes were identified as genes that play important role in the survival of patients and these genes differed significantly with respect to survival of patients. We used the Pearson correlation to identify the over-expressed and under-expressed genes. We demonstrated that parametric survival models can be used to model outcomes for breast cancer, and for our dataset the log-normal model demonstrated the best fit compared to other parametric models. Through the use of log-normal model, we examined how each of the identified genes influence the survival of breast cancer patients.

Effect of Nano-eugenol and Aerobic Exercise Against the Streptozotocin Toxicity and Inflammatory Mediators P38-MAPK, NPY, and A-Rα2A in the Dorsal Root Ganglia of Diabetic Rats

Background: The aim of this study was to investigate the effects of nano-eugenol combined with aerobic exercise against the streptozotocin toxicity and inflammatory mediators P38-MAPK, NPY and A-Rα2A in the dorsal root ganglia of diabetic rats. Methods: Twenty-five, 8-week-old Wistar male rats were divided into 5 groups: 1) normal control group (normal model); 2) diabetic control group (diabetic model); 3), diabetic + exercise group (diabetic+exercise model); 4) diabetic group + nano-eugenol (diabetic+nano model); and 5) diabetic + exercise + nano-eugenol (diabetic+exercise+nano model). Diabetes was induced in the experimental groups 2 through 5 by the intraperitoneal injection of streptozotocin at 4mg/100 grams of the rats’ body weight. The nano-eugenol supplement was also gavaged into the supplement groups 4 and 5 only. Groups 3 and 5 exercised progressively at a speed of 8 to 20 meter/min for 5 to 30 min, five days a week over the 8-week study duration. Results: The diabetic rats that exercised and were treated with the nano-eugenol, showed a significant decrease in P38-MAPK gene expression compared to the normal model group (P=0.001). The study of the therapeutic modalities also showed that only the diabetic + exercise + nano-eugenol group showed a significant increase in NPY and A-Rα2A genes compared to the normal model (P=0.001). Conclusion: Based on the results, the use of nano-eugenol supplementation combined with aerobic exercise is likely to be effective in controlling the neurological damages due to diabetes by negatively regulating the P38-MAPK gene while positively regulating the NPY and A-Rα2A genes in the DRG region.

Robust Fitting of a Wrapped Normal Model to Multivariate Circular Data and Outlier Detection

In this work, we deal with a robust fitting of a wrapped normal model to multivariate circular data. Robust estimation is supposed to mitigate the adverse effects of outliers on inference. Furthermore, the use of a proper robust method leads to the definition of effective outlier detection rules. Robust fitting is achieved by a suitable modification of a classification-expectation-maximization algorithm that has been developed to perform a maximum likelihood estimation of the parameters of a multivariate wrapped normal distribution. The modification concerns the use of complete-data estimating equations that involve a set of data dependent weights aimed to downweight the effect of possible outliers. Several robust techniques are considered to define weights. The finite sample behavior of the resulting proposed methods is investigated by some numerical studies and real data examples.