  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.
