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

Due to limited resources of publicly funded health care services, cost-effectiveness analyses have
become a crucial part of the decision to adopt a new treatment or health technology within routine
medical practice. Allocation decisions concerning prioritisation of health care resources across
competing 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 - c0
e1 - e0
where ci and ei
represent the cost and effectiveness respectively, of treatment i = 0,1. The
effectiveness 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 single
index. Traditionally, programmes with the lowest cost per QALY are given priority, with the aim of
maximising health gain in the population under budget constraints. For instance, the UK's National
Institute for Health and Care Excellence typically require the incremental cost per QALY to not be
higher 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 the
health-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 HQoL
via 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 a
curve which linearly interpolates between the longitudinal measurements and takes value 0 after the
observed 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 conditions
where the hazard of death is high and quality-of-life deteriorates heavily prior to death