Vijaya trained in medicine and public health in the United States. Her career has included clinical positions in US and Australian Emergency Departments, general medical wards and general practice and digital health, health policy and health services planning roles at the Victorian Department of Health.

In 2008, she secured funding from Australian and Victorian government sources to develop a Victorian Centre for Data Linkage and subsequently served as its Foundation Director between 2009 and 2011. She was Head of the Department of Public Health, La Trobe University between 2018-2021.

Vijaya’s research interests centre around the statistical analysis of large, linked datasets and their use to understand the outcomes of health care in the spectrum of chronic disease from diagnosis to the end of life and investigate health system and hospital quality and performance.

She is currently an Associate Professor of Epidemiology and Biostatistics, Department of Medicine, St Vincent's Hospital, Melbourne Medical School and Professor of Public Health, La Trobe University. In July 2021, she will begin a PhD with the Population Interventions Unit, Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, University of Melbourne.