There is growing interest in continuous wearable vital sign sensors for monitoring patients remotely at home. These monitors are usually coupled to an alerting system, which is triggered when vital sign measurements fall outside a predefined normal range. Trends in vital signs, such as an increasing heart rate, are often indicative of deteriorating health, but are rarely incorporated into alerting systems. In this work, we present a novel outlier detection algorithm to identify such abnormal vital sign trends. We introduce a distance-based measure to compare vital sign trajectories. For each patient in our dataset, we split vital sign time series into 180 minute, non-overlapping epochs. We then calculated a distance between all pairs of epochs using the dynamic time warp distance. Each epoch was characterized by its mean pairwise distance (average link distance) to all other epochs, with large distances considered as outliers. We applied this method to a pilot dataset collected over 1561 patient-hours from 8 patients who had recently been discharged from hospital after contracting COVID-19. We show that outlier epochs correspond well with patients who were subsequently readmitted to hospital. We also show, descriptively, how epochs transition from normal to abnormal for one such patient.