Clinical care and large observational studies are characterized by periods of intense health monitoring during hospital visits followed by long periods of low-intensity or no-monitoring between visits. Data obtained during in-hospital visits come from a host of new technologies, such as very densely sampled biosignal recordings (EEG, ECG, health scores) and high resolution multi-modality imaging (MRI, CT, PET). A major characteristic of this type of data is that it is collected for a period of time that is subject-spcific. Indeed, the in-hospital length and amount of monitoring varies between subjects, and is highly informative both for studying health outcomes in the hospital and after discharge. One among many examples is a recent study of subjects admitted to the Intensive Care Unit (ICU) with Acute Respiratory Distress Syndrome (ARDS). For each subject the Sequential Organ Failure Assessment (SOFA) score, a commonly- used scoring system to measure organ dysfunction in the ICU, was collected daily for each subject for the duration of their ICU stay. The ICU length of stay is different by subject and likely to be highly informative of current and future health outcomes. In this application, a set of relevant problems are conceptualized and distilled to statistical aims to address specific complexities associated with this type of data sampling. Specifically, the proposal addresses the following fundamental unsolved problems in studies that collect high density biosignals: 1) introducing statistical models for the association between high density biosignals with uneven support and health outcomes; 2) developing functional registration-by-prediction models that transform the support of biosignals to provide best prediction of health outcomes; and 3) developing models for describing the cross-sectional and longitudinal variability of biosignals obtained in studies with rare -but intense- health monitorin. While focus lies on research studies that collect quasi- continuous ultra-high resolution biosignals for subject-specific lengths of time, methods will be generalizable to many other studies with similar data sampling structures. 2