Highly active antiretroviral therapy (HAART) suppresses the replication of HIV, thereby delivering tangible reductions in morbidity and mortality. The Multi-site Adherence Collaboration in HIV (MACH14) study pooled data from 16 different longitudinal HAART adherence studies to create a large, diverse HIV data system. In longitudinal analysis, parametric models such as a linear mixed model are popularly used to model HIV viral load change over time. The mixed effects model are parsimonious and efficient when the models are correctly specified. However, for the MACH14 data with tremendous heterogeneity between sites, linear assumption for the linear mixed model might not hold, and linear mixed models are usually restrictive and less robust against violations of model assumptions. In contrast, non-parametric and semi-parametric models are more robust against model assumption violations. This dissertation proposed to use non-parametric and semi-parametric regression methods including generalized additive mixed models (GAMM) and Bayesian analysis using splines. The additive mixed model specification with splines, which takes a random component into account on top of the underlying fixed linear component, can model smooth variation about the linear trend, and thus can effectively model the non-linear relationships. The proposed GAMM and Bayesian methodology were applied to model the complex non-linear relationships between medication adherence, viral load change over time, and other factors including subject characteristics, medication regimen type, and medication naive versus experienced at enrollment. Significant non-linear relationships were found with heterogeneity among studies.