A Framework for Estimating Quality Adjusted Life Years Using Joint Models of Longitudinal and Survival Data

OBJECTIVES: Quality of life (QoL) scores are integral in cost-effectiveness analysis, providing a direct quantification of how much time patients spend at different severity levels. There are a variety of statistical challenges with modeling and utilizing QoL data appropriately. QoL data, and other repeatedly measured outcomes such as prostate-specific antigen (PSA), are often treated as time-varying covariates, which only change value when a new measurement is taken - this is biologically implausible. Additionally, such data often exhibits both between and within subject correlations, which must be taken into account, and are associated with survival endpoints. The proposed framework utilizes "progression" or similar intermediate endpoints or biomarkers like EQ-5D, and models them jointly with overall survival, allowing us to directly calculate quality adjusted life years (QALYs).

METHODS: Motivated by the prostate cancer trial setting, we simulated data representing repeatedly measured PSA levels, utilities and overall survival. Using numerical integration and the delta method, we then derive analytical estimates of QALYs, differences in QALYs and restricted time horizon QALYs from the estimated multivariate joint model, along with uncertainty.

RESULTS: PSA and utilities were modeled flexibly using linear mixed effects submodels with restricted cubic splines to capture the nonlinear development over follow-up time. An interaction with treatment was also included to allow different trajectories in those treated and those on placebo. Both PSA and utility were linked to survival through their current value and slopes, with a Weibull survival submodel. Treatment was estimated to provide an additional 1.074 QALYs (95% CI: 0.635, 1.513) across a lifetime horizon.

CONCLUSIONS: Deriving QALYs from a joint model of longitudinal and survival data accounts for all of the statistical and biological intricacies of the data, providing a more appropriate, and accurate, estimate for use in cost-effectiveness modeling, and hence reducing uncertainty.