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

由于公共资助的卫生保健服务资源有限，成本效益分析已成为决定在常规医疗实践中采用新治疗或卫生技术的关键部分。在相互竞争的干预措施中，关于卫生保健资源优先次序的分配决策涉及评估成本和健康结果（有效性）的影响，其目的是捕捉患者福祉的所有方面。一种治疗的成本-效果通常用增量成本-效果比来衡量，ICER =c1 - c0e1 - e0，其中ci和ei分别代表治疗i = 0,1的成本和效果。治疗的有效性通常用质量调整生命年（QALY）来量化。质量aly力求将卫生干预措施对死亡率和发病率的影响合并成一个单一指数。传统上，优先考虑按质量aly计算成本最低的方案，目的是在预算有限的情况下最大限度地提高人口的健康收益。例如，英国国家健康与护理卓越研究所（NationalInstitute For Health and Care Excellence）通常要求每次QALY的增量成本不高于2万至3万英镑。对QALY的估计需要结合治疗后的预期生存时间和与健康相关的生活质量（HQoL），通常以完美健康= 1和死亡= 0的量表来衡量。新疗法的试验或研究通常包括通过EQ5D等问卷对患者自我报告的hqold的纵向数据（EuroQoL Group, 1990）。一种常用的（如果在统计学上很幼稚的话）估计个人质量的方法是，根据纵向测量之间的线性插值曲线计算“曲线下面积”，并在观察到的死亡日期之后取值为0。虽然这个总结很容易计算，但在缺少数据的情况下，它可能导致对QALY的估计有偏差（Bell et al, 2014）。在死亡风险高且死亡前生活质量严重恶化的情况下，这种偏差可能最大

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