New Methods and Innovations in Network Meta Regression for Ordinal Response Outcomes with Applications

In this dissertation research, we develop models and carry out statistical inference for meta ordinal outcomes under both frequentist and Bayesian frameworks. Specifically, we develop new regression models based on aggregate trial-level and treatment-level covariates for the underlying cut-off points of the ordinal outcomes as well as for the variances of the random effects to capture heterogeneity across trials. In the frequentist approach, we develop Pearson residuals to detect outlying trials and construct an invariant test statistic to evaluate goodness-of-fit. We also develop a new computational algorithm to compute ranking probabilities to rank multiple treatments. Under the Bayesian framework, we examine the importance of links in fitting ordinal responses in the middle categories. The novel theoretical development allows for incorporating a variety of links regardless of symmetry or asymmetry. We develop an efficient Markov chain Monte Carlo sampling algorithm under different links using latent variables for Bayesian computation. To incorporate high-dimensional random effects for multi-arm trials, we develop a different data augmentation strategy via the Polya-Gamma mixture distribution, under the logit link. We develop another efficient computational algorithm to deal with high-dimensional random effects and it allows for more flexible modeling strategy of variances for the random effects. We then develop Bayesian model comparison measures and model diagnostic tools to facilitate the choices of links, the assessment of goodness-of-fit, and the determination of outlying trials. A case study demonstrating the proposed methodology is conducted using aggregate ordinal outcome data to assess the effectiveness of different treatments in treating Crohn\u27s Disease