The medical trend diagnosis system TrenDx has been applied as a prototype for diagnosing pediatric growth disorders, and as a proof of concept in detecting clinically significant trends in hemodynamics and blood gases in intensive care unit patients. TrenDx diagnoses trends by matching patient data to patterns of normal and abnormal trends called trend templates that define disorders as typical patterns of relevant variables. These patterns consist of a partially ordered set of temporal intervals with uncertain endpoints. Bound to each temporal interval are value constraints on real-valued functions of measurable parameters. The temporal uncertainty in trend templates allows TrenDx to conclude both what trend pattern best matches the data and also when significant landmarks and phase transitions have occurred within the best matching trend. The temporal uncertainty in trend templates requires that TrenDx consider alternate temporal worlds in monitoring patient data. The number of temporal worlds grows worst case polynomially in the number of time slices of data. To manage the competing temporal worlds, TrenDx employs two techniques: beam search based on regression scores, and temporal granularity in the trend template definitions. These two techniques, described here in detail, allow TrenDx to choose different points in the trade-off between accuracy of trend detection and algorithm efficiency.