Evaluating Quality Adjusted Life Years in the Absence of Standard Utility Values- A Dynamic Joint Modelling Approach

Estimation of Quality Adjusted Life Years (QALYs) is pivotal towards cost-effectiveness analysis (CEA) of medical interventions. Most of the CEA studies employ multi-state decision analytic modelling approach, where fixed utility values are assigned to each disease state and total QALYs are calculated on the basis of total lengths of stay in each state. In this paper, we have formulated a new approach to CEA by defining utility as a function of a longitudinal covariate which is significantly associated with disease progression. Association parameter between the longitudinal covariate and survival times is estimated through joint modelling of the longitudinal linear mixed effects model and the Weibull accelerated failure time survival model. Metropolis-Hastings algorithm and Monte Carlo integration are used to predict expected survival times of each censored case using the joint model. Fitted longitudinal model is further used to project values of the longitudinal covariate at all time points for each patient. Utility values calculated using these projected covariate values are used to evaluate QALYs for each patient. Retrospective survival data of HIV/ AIDS patients undergoing treatment at the Antiretroviral Therapy centre of Ram Manohar Lohia hospital in New Delhi is used to demonstrate the implementation of the proposed methodology. A simulation exercise is also carried out to gauge the predictive capability of the joint model in projecting the values of the longitudinal covariate. The proposed dynamic approach to calculate QALY provides a promising alternative to the popular multi-state decision analytic modelling approach, especially when the standard utility values for different stages of the concerned disease are not available.