Meta-analysis of multi-arm trials has been used increasingly in recent years, the aims of which are to combine evidence from all possible similar studies and draw inferences about the effectiveness of multiple compared-treatments. Antiplatelet therapy is a pharmacologic therapy which aims to inhibit platelet activation and aggregation in the setting of arterial thrombosis. Throughout the thesis we use binary data from antiplatelet therapy to apply the model and sensitivity analysis. The normal approximation model using empirical logistic transform has been employed to compare different treatments in multi-arm trials, allowing studies of both direct and indirect comparisons. The issue of direct-indirect comparison is studied in detail, borrowing the strength from the indirect comparisons and making inferences about appropriately chosen parameters. Additionally, a hierarchical structure of the model addresses the problem of heterogeneity among different studies. However the model requires a large sample size of each individual study. When the sample size is small, an exact logistic regression model is introduced. Both unconditional and conditional maximum likelihood approaches are performed to make inferences for the logistic regression model. We use Gaussian-Hermite quadrature to approximate the integral involved in the likelihood functions. Both approaches have been examined to different cases in the simulation study. Studies with statistically significant results (positive results) are potentially more likely to be submitted or selected more rapidly than studies with non-significant results (negative results). This leads to false-positive results or an incorrect, usually over-optimistic, conclusion, a problem known as selection bias in the meta-analysis. A funnel plot is a graphical tool which is used to detect selection bias in this research. We apply the idea of a sensitivity analysis by defining a selection model to the available data of a meta-analysis, by allowing different amounts of selection bias in the model and investigate how sensitive the main interest parameter is when compared to the estimates of the standard model. We also examine the sensitivity analysis by the simulation study.