Timelines of longitudinal studies are often anchored by specific events. In the absence of fully observed the anchoring event times, the study timeline becomes undefined, and the traditional longitudinal analysis loses its temporal reference. In this paper, we considered an analytical situation where the anchoring events are interval-censored. We demonstrated that by expressing the regression parameter estimators as stochastic functionals of a plug-in estimate of the unknown anchoring event time distribution, the standard longitudinal models could be extended to accommodate the situation of less well-defined timelines. We showed that for a broad class of longitudinal models, the functional parameter estimates are consistent and asymptotically normally distributed with a convergence rate under mild regularity conditions. Applying the developed theory to linear mixed-effects models, we further proposed a hybrid computational procedure that combines the strengths of the Fisher's scoring method and the expectation-expectation (EM) algorithm, for model parameter estimation. We conducted a simulation study to validate the asymptotic properties and to assess the finite sample performance of the proposed method. A real data analysis was used to illustrate the proposed method. The method fills in a gap in the existing longitudinal analysis methodology for data with less well defined timelines.
Keywords: Empirical process; Interval censoring; Longitudinal data; Nonparametrics; Pseudo-likelihood.