Thirty years after identification of HIV, the AIDS epidemic continues with an estimated 37 million individuals currently infected worldwide and 1.8 million new infections each year. Research to prevent and treat HIV infection has grown increasingly sophisticated and the analytic challenges have become correspondingly complex. This application is intended to address timely and important statistical issues in HIV/AIDS research. In particular, novel statistical methods will be developed for (i) analysis of data from HIV clinical trials, including methods for implementation trials, trials of pre-exposure prophylaxis (PrEP), and vaccine studies (ii) optimal design and analysis of surveillance studies that are necessary to characterize the HIV epidemic, and (iii) analysis of data from key laboratory assays used in HIV cure and vaccine research. First, statistical methods are proposed that address key challenges in current HIV prevention, treatment and implementation trials. The approaches include causal modeling and model-free/model- agnostic methods that remove the need for complex modeling assumptions. The proposed methods have broad applicability to clinical and implementation studies of HIV/AIDS as well as other fields. Second, statistical methods are proposed to help characterize and describe key features of the HIV epidemic. These include new approaches to spatial-temporal modeling that can provide fine-scale maps (with uncertainty information) of HIV prevalence, incidence, percent suppressed, and other measures, as well as a novel approach to combining the (stochastic) counting process approach to survival analysis with (deterministic) differential equations to analyze interactive and dynamic systems, such as socio-sexual networks. These methods have the potential to provide critical guidance for optimizing the distribution of treatment and prevention resources. Finally, the proposed research will investigate statistical methods for the analysis of key laboratory assays used in cure and vaccine studies, including the quantitative viral load outgrowth assay used to quantify the size of the latent HIV reservoir, and the intra-cellular staining flow-cytometry-based assay used in vaccine research to quantify cytokine production and accumulation after cell stimulation. The proposed research reflects the extensive and ongoing involvement of the investigators in the field of HIV/AIDS research. The statistical problems addressed are motivated by applications in key areas of HIV research. The solutions outlined are highly innovative and directly applicable to current scientific research in vaccine development, HIV prevention trials, implementation research, and other HIV/AIDS related studies.