Kurland Brenda F, Johnson Laura L, Egleston Brian L, Diehr Paula H
Clinical Research Division, Fred Hutchinson Cancer Research Center, Seattle, Washington 98109, U.S.A. (206) 667-2804,
Stat Sci. 2009;24(2):211. doi: 10.1214/09-STS293.
Diverse analysis approaches have been proposed to distinguish data missing due to death from nonresponse, and to summarize trajectories of longitudinal data truncated by death. We demonstrate how these analysis approaches arise from factorizations of the distribution of longitudinal data and survival information. Models are illustrated using cognitive functioning data for older adults. For unconditional models, deaths do not occur, deaths are independent of the longitudinal response, or the unconditional longitudinal response is averaged over the survival distribution. Unconditional models, such as random effects models fit to unbalanced data, may implicitly impute data beyond the time of death. Fully conditional models stratify the longitudinal response trajectory by time of death. Fully conditional models are effective for describing individual trajectories, in terms of either aging (age, or years from baseline) or dying (years from death). Causal models (principal stratification) as currently applied are fully conditional models, since group differences at one timepoint are described for a cohort that will survive past a later timepoint. Partly conditional models summarize the longitudinal response in the dynamic cohort of survivors. Partly conditional models are serial cross-sectional snapshots of the response, reflecting the average response in survivors at a given timepoint rather than individual trajectories. Joint models of survival and longitudinal response describe the evolving health status of the entire cohort. Researchers using longitudinal data should consider which method of accommodating deaths is consistent with research aims, and use analysis methods accordingly.
已经提出了多种分析方法来区分因死亡导致的数据缺失和无应答情况，并总结因死亡而截断的纵向数据的轨迹。我们展示了这些分析方法是如何从纵向数据分布和生存信息的分解中产生的。使用老年人的认知功能数据对模型进行了说明。对于无条件模型，不存在死亡情况，死亡与纵向应答无关，或者无条件纵向应答是在生存分布上进行平均的。无条件模型，如拟合不平衡数据的随机效应模型，可能会隐含地推算死亡时间之后的数据。完全条件模型按死亡时间对纵向应答轨迹进行分层。完全条件模型在描述个体轨迹方面很有效，无论是从衰老（年龄，或从基线起的年份）还是从死亡（从死亡起的年份）的角度来看。当前应用的因果模型（主分层）是完全条件模型，因为针对一个将存活到稍后时间点的队列，描述了某一时刻的组间差异。部分条件模型总结了幸存者动态队列中的纵向应答。部分条件模型是应答的系列横断面快照，反映了给定时间点幸存者的平均应答而非个体轨迹。生存与纵向应答的联合模型描述了整个队列不断变化的健康状况。使用纵向数据的研究人员应考虑哪种处理死亡的方法与研究目的一致，并相应地使用分析方法。
