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Longitudinal data are often plagued with sparsity of time points wheremeasurements are available. The functional data analysis perspective has beenshown to provide an effective and flexible approach to address this problem forthe case where measurements are sparse but their times are randomly distributedover an interval. Here we focus on a different scenario where available datacan be characterized as snippets, which are very short stretches oflongitudinal measurements. For each subject the stretch of available data ismuch shorter than the time frame of interest, a common occurrence inaccelerated longitudinal studies. An added challenge is introduced if a timeproxy that is basic for usual longitudinal modeling is not available. Thissituation arises in the case of Alzheimer's disease and comparable scenarios,where one is interested in time dynamics of declining performance, but the timeof disease onset is unknown and the chronological age does not provide ameaningful time reference for longitudinal modeling. Our main methodologicalcontribution is to address this problem with a novel approach. Key quantitiesfor our approach are conditional quantile trajectories for monotonic processesthat emerge as solutions of a dynamic system, and for which we obtain uniformlyconsistent estimates. These trajectories are shown to be useful to describeprocesses that quantify deterioration over time, such as hippocampal volumes inAlzheimer's patients.

Dynamic Modeling with Conditional Quantile Trajectories for Longitudinal Snippet Data, with Application to Cognitive Decline of Alzheimer's Patients