A terminal trend model for longitudinal medical cost data and survival

A joint modeling approach on survival and longitudinal data has proven to be valuable in end of life applications, especially when there is a strong relationship between the longitudinal measurements and survival outcomes in the presence of high mortality rates. We have implemented a novel joint modeling approach, a flexible terminal trend model, to study the trends and factors influencing end of life cost in clinic observational cohorts with significant mortality by comparing the differences in trajectories due to risk and treatment factors. The motivating data consisted of insurance claims for a cohort of patients with hip fracture among US Medicare beneficiaries age 66 and older during 2007–2011. We have developed a joint modeling approach for survival and cost data to study individual level trajectories of health care cost data and survival, using two regression submodels: a piecewise exponential model for survival time, and a retrospective spline regression model for costs. Model estimation through maximum likelihood methods is developed and evaluated through simulations. An approximation based on a conditional approach is shown to have superior properties and to be far more efficient.