Semiparametric Estimation of Longitudinal Medical Cost Trajectory

Estimating the average monthly medical costs from disease diagnosis to a terminal event such as death for an incident cohort of patients is a topic of immense interest to researchers in health policy and health economics because patterns of average monthly costs over time reveal how medical costs vary across phases of care. The statistical challenges to estimating monthly medical costs longitudinally are multifold; the longitudinal cost trajectory (formed by plotting the average monthly costs from diagnosis to the terminal event) is likely to be nonlinear, with its shape depending on the time of the terminal event, which can be subject to right censoring. The goal of this article is to tackle this statistically challenging topic by estimating the conditional mean cost at any month t given the time of the terminal event s. The longitudinal cost trajectories with different terminal event times form a bivariate surface of t and s, under the constraint t ⩽ s. We propose to estimate this surface using bivariate penalized splines in an expectation-maximization algorithm that treats the censored terminal event times as missing data. We evaluate the proposed model and estimation method in simulations and apply the method to the medical cost data of an incident cohort of stage IV breast cancer patients from the Surveillance, Epidemiology, and End Results–Medicare Linked Database. Supplementary materials for this article are available online.