Kong Shengchun, Nan Bin, Kalbfleisch John D, Saran Rajiv, Hirth Richard
Gilead Sciences, Inc., Foster City, CA 94404.
Departments of Biostatistics, University of Michigan, Ann Arbor, MI 48109.
J Am Stat Assoc. 2018;113(521):357-368. doi: 10.1080/01621459.2016.1255637. Epub 2017 Nov 13.
We consider a random effects model for longitudinal data with the occurrence of an informative terminal event that is subject to right censoring. Existing methods for analyzing such data include the joint modeling approach using latent frailty and the marginal estimating equation approach using inverse probability weighting; in both cases the effect of the terminal event on the response variable is not explicit and thus not easily interpreted. In contrast, we treat the terminal event time as a covariate in a conditional model for the longitudinal data, which provides a straight-forward interpretation while keeping the usual relationship of interest between the longitudinally measured response variable and covariates for times that are far from the terminal event. A two-stage semiparametric likelihood-based approach is proposed for estimating the regression parameters; first, the conditional distribution of the right-censored terminal event time given other covariates is estimated and then the likelihood function for the longitudinal event given the terminal event and other regression parameters is maximized. The method is illustrated by numerical simulations and by analyzing medical cost data for patients with end-stage renal disease. Desirable asymptotic properties are provided.
我们考虑一种用于纵向数据的随机效应模型，该模型中存在一个受右删失影响的信息性终末事件。分析此类数据的现有方法包括使用潜在脆弱性的联合建模方法和使用逆概率加权的边际估计方程方法；在这两种情况下，终末事件对响应变量的影响都不明确，因此不易解释。相比之下，我们将终末事件时间作为纵向数据条件模型中的一个协变量，这提供了一种直接的解释，同时保持了纵向测量的响应变量与远离终末事件时间的协变量之间通常的感兴趣关系。提出了一种基于两阶段半参数似然的方法来估计回归参数；首先，估计给定其他协变量时右删失终末事件时间的条件分布，然后在给定终末事件和其他回归参数的情况下最大化纵向事件的似然函数。通过数值模拟和分析终末期肾病患者的医疗费用数据来说明该方法。给出了理想的渐近性质。
