Su Li, Daniels Michael J
MRC Biostatistics Unit, Cambridge Institute of Public Health, Robinson Way, Cambridge CB2 0SR, U.K.
Stat Med. 2015 May 30;34(12):2004-18. doi: 10.1002/sim.6465. Epub 2015 Mar 12.
In long-term follow-up studies, irregular longitudinal data are observed when individuals are assessed repeatedly over time but at uncommon and irregularly spaced time points. Modeling the covariance structure for this type of data is challenging, as it requires specification of a covariance function that is positive definite. Moreover, in certain settings, careful modeling of the covariance structure for irregular longitudinal data can be crucial in order to ensure no bias arises in the mean structure. Two common settings where this occurs are studies with 'outcome-dependent follow-up' and studies with 'ignorable missing data'. 'Outcome-dependent follow-up' occurs when individuals with a history of poor health outcomes had more follow-up measurements, and the intervals between the repeated measurements were shorter. When the follow-up time process only depends on previous outcomes, likelihood-based methods can still provide consistent estimates of the regression parameters, given that both the mean and covariance structures of the irregular longitudinal data are correctly specified and no model for the follow-up time process is required. For 'ignorable missing data', the missing data mechanism does not need to be specified, but valid likelihood-based inference requires correct specification of the covariance structure. In both cases, flexible modeling approaches for the covariance structure are essential. In this paper, we develop a flexible approach to modeling the covariance structure for irregular continuous longitudinal data using the partial autocorrelation function and the variance function. In particular, we propose semiparametric non-stationary partial autocorrelation function models, which do not suffer from complex positive definiteness restrictions like the autocorrelation function. We describe a Bayesian approach, discuss computational issues, and apply the proposed methods to CD4 count data from a pediatric AIDS clinical trial.
在长期随访研究中，当个体随时间被反复评估，但评估时间点不常见且间隔不规则时，会观察到不规则的纵向数据。对此类数据的协方差结构进行建模具有挑战性，因为这需要指定一个正定的协方差函数。此外，在某些情况下，为不规则纵向数据仔细建模协方差结构对于确保均值结构中不产生偏差可能至关重要。出现这种情况的两个常见场景是“结果依赖型随访”研究和“可忽略缺失数据”研究。“结果依赖型随访”发生在健康状况不佳的个体有更多随访测量且重复测量间隔较短时。当随访时间过程仅取决于先前的结果时，假设不规则纵向数据的均值和协方差结构都被正确指定且不需要随访时间过程的模型，基于似然的方法仍可提供回归参数的一致估计。对于“可忽略缺失数据”，不需要指定缺失数据机制，但基于似然的有效推断需要正确指定协方差结构。在这两种情况下，协方差结构的灵活建模方法都至关重要。在本文中，我们开发了一种灵活的方法，使用偏自相关函数和方差函数对不规则连续纵向数据的协方差结构进行建模。特别是，我们提出了半参数非平稳偏自相关函数模型，该模型不像自相关函数那样受到复杂的正定限制。我们描述了一种贝叶斯方法，讨论了计算问题，并将所提出的方法应用于一项儿科艾滋病临床试验的CD4计数数据。
