Optimal Staffing and Treatment for Collaborative Care of Diabetes and Depression

About 27% of patients with diabetes also suffer from depression, and the presence of co-morbid depression could increase the cost of care for diabetes by up to 100%. Several randomized clinical trials have demonstrated that physical and mental health are more likely to improve for diabetes patients suffering from depression when regular treatment for depression is provided in a primary care setting (called Collaborative Care). However, Collaborative Care requires additional resource utilization costs and a separate reimbursement model. When managing Collaborative Care, clinics must balance patient health outcomes with the program’s financial sustainability. Important operational levers in Collaborative Care are allocating care managers’ time to patients based on their requirements and the care managers’ staffing level. This staffing and workload allocation influences the revenue, costs, and patient health outcomes. We present a novel Markov Dynamic Programing model that, unlike existing approaches, jointly optimizes both staffing levels and treatment policies for Collaborative Care programs and quantifies the costs and benefits of collaborative care. Mathematically, we model Collaborative Care management at the clinical level as an infinite-horizon Markov Dynamic Program. The objective is a weighted sum of total patient quality-adjusted life years (QALYs) and the clinic profits. The model incorporates insurance payment, resource utilization costs, and disease progression of co-morbid diabetes and depression. We derive structural properties for the joint optimization of the staffing level and allocating care managers’ time to different patient categories. Using these structural properties, we develop a practical and easy-to-implement policy for staffing level and care managers’ time allocation that performs close to the optimal solution. We calibrate the model with data from a large academic medical center and show that our solutions can improve total QALYs and clinic profits compared to current practices. Our analysis also reveals key insights into payment models’ effects on Collaborative Care. Profit under the fixed-fee model responds nonmonotonically to payment rate increases, highlighting complex financial dynamics. Fixed-fee models show a threshold behavior, with high-intensity treatments becoming optimal only above certain payment rates. This threshold varies based on the profit-QALY weight balance, and this threshold is lower under joint-optimization than treatment-only optimization.