Department of Statistical Science, University College London, London, UK.
Research Department of Primary Care and Population Health, University College London Medical School, London, UK.
Value Health. 2021 May;24(5):699-706. doi: 10.1016/j.jval.2020.11.018. Epub 2021 Feb 18.
In trial-based economic evaluation, some individuals are typically associated with missing data at some time point, so that their corresponding aggregated outcomes (eg, quality-adjusted life-years) cannot be evaluated. Restricting the analysis to the complete cases is inefficient and can result in biased estimates, while imputation methods are often implemented under a missing at random (MAR) assumption. We propose the use of joint longitudinal models to extend standard approaches by taking into account the longitudinal structure to improve the estimation of the targeted quantities under MAR.
We compare the results from methods that handle missingness at an aggregated (case deletion, baseline imputation, and joint aggregated models) and disaggregated (joint longitudinal models) level under MAR. The methods are compared using a simulation study and applied to data from 2 real case studies.
Simulations show that, according to which data affect the missingness process, aggregated methods may lead to biased results, while joint longitudinal models lead to valid inferences under MAR. The analysis of the 2 case studies support these results as both parameter estimates and cost-effectiveness results vary based on the amount of data incorporated into the model.
Our analyses suggest that methods implemented at the aggregated level are potentially biased under MAR as they ignore the information from the partially observed follow-up data. This limitation can be overcome by extending the analysis to a longitudinal framework using joint models, which can incorporate all the available evidence.
在基于试验的经济评估中,一些个体在某些时间点通常与缺失数据相关联,因此无法评估其相应的汇总结果(例如,质量调整生命年)。将分析仅限于完整病例是低效的,并且可能导致有偏差的估计,而插补方法通常在随机缺失(MAR)假设下实施。我们建议使用联合纵向模型通过考虑纵向结构来扩展标准方法,以改善 MAR 下目标量的估计。
我们比较了在 MAR 下处理缺失的聚合(病例删除、基线插补和联合聚合模型)和离散(联合纵向模型)水平的方法的结果。使用模拟研究比较了这些方法,并将其应用于来自 2 个实际案例研究的数据。
模拟结果表明,根据哪些数据影响缺失过程,聚合方法可能会导致有偏差的结果,而联合纵向模型则在 MAR 下得出有效的推断。对 2 个案例研究的分析支持了这些结果,因为参数估计和成本效益结果都根据纳入模型的数据量而有所不同。
我们的分析表明,在 MAR 下,在聚合水平实施的方法可能存在偏差,因为它们忽略了部分观察随访数据中的信息。通过使用联合模型将分析扩展到纵向框架,可以克服这种局限性,联合模型可以合并所有可用的证据。