The HIV care cascade is a conceptual model describing essential steps in the continuum of HIV care. The cascade framework has been widely applied to define population-level metrics and milestones for monitoring and assessing strategies designed to identify new HIV cases, link individuals to care, initiate antiviral treatment and ultimately suppress viral load. Comprehensive modeling of the entire cascade is challenging because data on key stages of the cascade are sparse. Many approaches rely on simulations of assumed dynamical systems, frequently using data from disparate sources as inputs. However, growing availability of large-scale longitudinal cohorts of individuals in HIV care affords an opportunity to develop and fit coherent statistical models using single sources of data, and to use these models for both predictive and causal inferences. Using data from 90,000 individuals in HIV care in Kenya, we model progression through the cascade using a multistate transition model fitted using Bayesian Additive Regression Trees (BART), which allows considerable flexibility for the predictive component of the model. We show how to use the fitted model for predictive inference about important milestones and causal inference for comparing treatment policies. Connections to agent-based mathematical modeling are made. This is joint work with Yizhen Xu, Tao Liu, Rami Kantor and Ann Mwangi.