Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced methods for functional principal component analysis often assuming independence between the observation times and longitudinal outcomes. Yet such assumptions are fragile in real-world settings where observation times may be driven by outcome-related reasons. Rather than ignoring the informative observation time process, we explicitly model the observational times by a counting process dependent on time-varying prognostic factors. Identification of the mean, covariance function, and functional principal components ensues via inverse intensity weighting. We propose using weighted penalized splines for estimation and establish consistency and convergence rates for the weighted estimators. Simulation studies demonstrate that the proposed estimators are substantially more accurate than the existing ones in the presence of a correlation between the observation time process and the longitudinal outcome process. We further examine the finite-sample performance of the proposed method using the Acute Infection and Early Disease Research Program study.

翻译：函数主成分分析已被证明对于揭示纵向结果的变异模式具有重要价值，这些模式构成了预测和模型构建的关键基础。数十年的研究推动了函数主成分分析方法的发展，通常假设观测时间与纵向结果相互独立。然而，在现实场景中，观测时间可能受结果相关因素驱动，此类假设显得较为脆弱。我们并未忽略信息性观测时间过程，而是通过依赖于时变预后因素的计数过程对观测时间进行显式建模。通过逆强度加权法，我们实现了均值、协方差函数及函数主成分的识别。我们提出使用加权惩罚样条进行估计，并为加权估计量建立了一致性与收敛速率。模拟研究表明，当观测时间过程与纵向结果过程存在相关性时，所提出的估计量较现有方法具有显著更高的准确性。我们进一步利用急性感染与早期疾病研究计划的数据，检验了所提出方法在有限样本下的性能。