Antimicrobial-resistant organisms (AMROs) can colonize people without symptoms for long periods of time, during which these agents can spread unnoticed to other patients in healthcare systems. The accurate identification of asymptomatic spreaders of AMRO in hospital settings is essential for supporting the design of interventions against healthcare-associated infections (HAIs). However, this task remains challenging because of limited observations of colonization and the complicated transmission dynamics occurring within hospitals and the broader community. Here, we study the transmission of methicillin-resistant Staphylococcus aureus (MRSA), a prevalent AMRO, in 66 Swedish hospitals and healthcare facilities with inpatients using a data-driven, agent-based model informed by deidentified real-world hospitalization records. Combining the transmission model, patient-to-patient contact networks, and sparse observations of colonization, we develop and validate an individual-level inference approach that estimates the colonization probability of individual hospitalized patients. For both model-simulated and historical outbreaks, the proposed method supports the more accurate identification of asymptomatic MRSA carriers than other traditional approaches. In addition, in silica control experiments indicate that interventions targeted to inpatients with a high-colonization probability outperform heuristic strategies informed by hospitalization history and contact tracing.