van der Laan M J, Hubbard A
Division of Biostatistics, University of California, Berkeley, California 94720, USA.
Biometrics. 1999 Jun;55(2):530-6. doi: 10.1111/j.0006-341x.1999.00530.x.
Zhao and Tsiatis (1997) consider the problem of estimation of the distribution of the quality-adjusted lifetime when the chronological survival time is subject to right censoring. The quality-adjusted lifetime is typically defined as a weighted sum of the times spent in certain states up until death or some other failure time. They propose an estimator and establish the relevant asymptotics under the assumption of independent censoring. In this paper we extend the data structure with a covariate process observed until the end of follow-up and identify the optimal estimation problem. Because of the curse of dimensionality, no globally efficient nonparametric estimators, which have a good practical performance at moderate sample sizes, exist. Given a correctly specified model for the hazard of censoring conditional on the observed quality-of-life and covariate processes, we propose a closed-form one-step estimator of the distribution of the quality-adjusted lifetime whose asymptotic variance attains the efficiency bound if we can correctly specify a lower-dimensional working model for the conditional distribution of quality-adjusted lifetime given the observed quality-of-life and covariate processes. The estimator remains consistent and asymptotically normal even if this latter submodel is misspecified. The practical performance of the estimators is illustrated with a simulation study. We also extend our proposed one-step estimator to the case where treatment assignment is confounded by observed risk factors so that this estimator can be used to test a treatment effect in an observational study.
赵和齐亚蒂斯（1997年）考虑了在按时间顺序排列的生存时间受到右删失的情况下，估计质量调整寿命分布的问题。质量调整寿命通常被定义为直到死亡或其他某个失效时间为止在某些状态下所花费时间的加权总和。他们提出了一个估计量，并在独立删失的假设下建立了相关的渐近理论。在本文中，我们扩展了数据结构，加入了一个直到随访结束时都可观测的协变量过程，并确定了最优估计问题。由于维度诅咒的存在，不存在在中等样本量下具有良好实际性能的全局有效非参数估计量。给定一个基于观测到的生活质量和协变量过程正确设定的删失风险模型，我们提出了一个质量调整寿命分布的闭式一步估计量，如果我们能够正确设定一个关于给定观测到的生活质量和协变量过程的质量调整寿命条件分布的低维工作模型，那么该估计量的渐近方差将达到效率界。即使后一个子模型设定错误，该估计量仍然保持一致性且渐近正态。通过模拟研究说明了估计量的实际性能。我们还将提出的一步估计量扩展到了治疗分配受到观测到的风险因素混淆的情况，以便该估计量可用于在观察性研究中检验治疗效果。
