This paper introduces a novel semiparametric Bayesian approach for bivariate meta-Regression. The method extends traditional binomial models to trinomial distributions, accounting for positive, neutral, and negative treatment effects. Using a conditional Dirichlet process, we develop a model to compare treatment and control groups across multiple clinical centers. This approach addresses the challenges posed by confounding factors in such studies. The primary objective is to assess treatment efficacy by modeling response outcomes as trinomial distributions. We employ Gibbs sampling and the Metropolis-Hastings algorithm for posterior computation. These methods generate estimates of treatment effects while incorporating auxiliary variables that may influence outcomes. Simulations across various scenarios demonstrate the model’s effectiveness. We also establish credible intervals to evaluate hypotheses related to treatment effects. Furthermore, we apply the methodology to real-world data on economic activity in Iran from 2009 to 2021. This application highlights the practical utility of our approach in meta-analytic contexts. Our research contributes to the growing body of literature on Bayesian methods in meta-analysis. It provides valuable insights for improving clinical study evaluations.

Background: Breast cancer is one of the most common cancers among women. Breast cancer treatment strate-gies in Nigeria need urgent strengthening to reduce mortality rate because of the disease. This study aimed to determine the relationship between the ages at diagnosis and established the prognostic factors of modality of treatment given to breast cancer patient in Nigeria. Methods: The data was collected for 247 women between years 2011-2015 who had breast cancer in two dif-ferent hospitals in Ekiti State, Nigeria. Model estimation is based on Bayesian approach via Markov Chain Mon-te Carlo. A multilevel model based on generalized Linear mixed model is used to estimate the random effect. Results: The mean age of the patients (at the time of diagnosis) was 42. 2 yr with 52% of the women aged be-tween 35-49 yr. The results of the two approaches are almost similar but preference is given to Bayesian because the approach is more robust than the frequentist. Significant factors of treatment modality are age, educational level and breast cancer type. Conclusion: Differences in socio-demographic factors such as educational level and age at diagnosis signifi-cantly influence the modality of breast cancer treatment in western Nigeria. The study suggests the use of Bayes-ian multilevel approach in analyzing breast cancer data for the practicality, flexibility and strength of the method.

In a multiple Linear Regression model, there are instances where one has to update the Regression parameters. In such models as new data become available, by adding one row to the design matrix, the least-squares estimates for the parameters must be updated to reflect the impact of the new data. We will modify two existing methods of calculating Regression coefficients in multiple Linear Regression to make the computations more efficient. By resorting to an initial solution, we first employ the Sherman-Morrison formula to update the inverse of the transpose of the design matrix multiplied by the design matrix. We then modify the calculation of the product of the transpose of design matrix and the design matrix by the Cholesky decomposition method to solve the system. Finally, we compare these two modifications by several appropriate examples.

Following a Bayesian statistical inference paradigm, we provide an alternative methodology for analyzing a multivariate logistic Regression. We use a multivariate normal prior in the Bayesian analysis. We present a unique Bayes estimator associated with a prior which is admissible. The Bayes estimators of the coefficients of the model are obtained via MCMC methods. The proposed procedure is illustrated by analyzing a data set which has previously been analyzed by various authors. It is shown that our model is more precise and computationally less taxing.