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.