Estimation of Quality-Adjusted Life Years via Joint Longitudinal-Survival Modelling

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Due to limited resources of publicly funded health care services, cost-effectiveness analyses havebecome a crucial part of the decision to adopt a new treatment or health technology within routinemedical practice. Allocation decisions concerning prioritisation of health care resources acrosscompeting interventions involve evaluating the impact of both costs and health outcomes(effectiveness) which aim to capture all aspects of patient well-being.The cost-effectiveness of a treatment is usually measured in terms of the incremental costeffectiveness ratio,ICER =c1 - c0e1 - e0where ci and eirepresent the cost and effectiveness respectively, of treatment i = 0,1. Theeffectiveness of a treatment is most often quantified in terms of quality-adjusted life years (QALY).The QALY seeks to combine the effects of health interventions on mortality and morbidity into a singleindex. Traditionally, programmes with the lowest cost per QALY are given priority, with the aim ofmaximising health gain in the population under budget constraints. For instance, the UK's NationalInstitute for Health and Care Excellence typically require the incremental cost per QALY to not behigher than some figure in the range £20,000 to £30,000.Estimation of QALY requires a combination of the expected survival time post-treatment and thehealth-related quality-of-life (HQoL), usually measured on a scale where perfect health = 1 and death= 0. Trials or studies of new treatments often include longitudinal data on patients' self-reported HQoLvia questionnaires such as the EQ5D (EuroQoL Group, 1990). A common, if statistically naive,approach used to estimate an individual's QALY is to calculate the `area under the curve' based on acurve which linearly interpolates between the longitudinal measurements and takes value 0 after theobserved date of death. While this summary is simple to compute, it may result in a biased estimate of QALY in the presence of missing data (Bell et al, 2014). The bias is likely to be highest for conditionswhere the hazard of death is high and quality-of-life deteriorates heavily prior to death