Estimating Healthcare Expenditure Using Parametric Change Point Models

Estimating healthcare expenditures is important for policymakers and clinicians. The expenditure of patients facing a life-threatening illness can often be segmented into four distinct phases: diagnosis, treatment, stable, and terminal phases. The diagnosis phase encompasses healthcare expenses incurred prior to the disease diagnosis, attributed to frequent healthcare visits and diagnostic tests. The second phase, following diagnosis, typically witnesses high expenditure due to various treatments, gradually tapering off over time and stabilizing into a stable phase, and eventually to a terminal phase. In this project, we introduce a pre-disease phase preceding the diagnosis phase, serving as a baseline for healthcare expenditure, and thus propose a five-phase to evaluate the healthcare expenditures. We use a piecewise linear model with three population-level change points and $4p$ subject-level parameters to capture expenditure trajectories and identify transitions between phases, where p is the number of covariates. To estimate the model’s coefficients, we apply generalized estimating equations, while a grid-search approach is used to estimate the change-point parameters by minimizing the residual sum of squares. In our analysis of expenditures for stages I–III pancreatic cancer patients using the SEER-Medicare database, we find that the diagnostic phase begins one month before diagnosis, followed by an initial treatment phase lasting three months. The stable phase continues until eight months before death, at which point the terminal phase begins, marked by a renewed increase in expenditures.