Covariate-Adjusted Regression for Distorted Longitudinal Data With Informative Observation Times

In many longitudinal studies, repeated response and predictors are not directly observed, but can be treated as distorted by unknown functions of a common confounding covariate. Moreover, longitudinal data involve an observation process which may be informative with a longitudinal response process in practice. To deal with such complex data, we propose a class of flexible semiparametric covariate-adjusted joint models. The new models not only allow for the longitudinal response to be correlated with observation times through latent variables and completely unspecified link functions, but they also characterize distorted longitudinal response and predictors by unknown multiplicative factors depending on time and a confounding covariate. For estimation of regression parameters in the proposed models, we develop a novel covariate-adjusted estimating equation approach which does not rely on forms of link functions and distributions of frailties. The asymptotic properties of resulting parameter estimators are established and examined by simulation studies. A longitudinal data example containing calcium absorption and intake measurements is provided for illustration. Supplementary materials for this article are available online.在诸多纵向研究中，重复响应与预测变量往往无法直接观测，而是会受到某一共同混杂协变量的未知函数作用而发生扭曲。此外，纵向数据涉及的观测过程在实际应用中常与纵向响应过程存在信息关联。为处理这类复杂数据，本文提出一类灵活的半参数协变量调整联合模型。该新型模型不仅允许纵向响应通过潜变量与完全未指定的联系函数与观测时刻建立关联，还可通过依赖于时间与混杂协变量的未知乘性因子，刻画发生扭曲的纵向响应与预测变量。针对所提模型中的回归参数估计问题，本文开发了一种全新的协变量调整估计方程方法，该方法无需依赖联系函数的具体形式以及脆弱项的分布假设。文中推导了所得参数估计量的渐近性质，并通过模拟研究对其渐近性能进行了验证与考察。此外，本文还提供了一个包含钙吸收与摄入测量值的纵向数据实例以作演示说明。本文的补充材料可在线获取。