A semi-supervised clustering approach for prediction and inference with multidimensional longitudinal outcomes

Understanding longitudinal patterns of health outcomes and their relations is critical in various clinical contexts. However, despite their potential benefits, practical pathways for utilizing multiple outcomes that develop in related ways remain underdeveloped. In this study, we focus on a common scenario where the longitudinal trajectory of one outcome (e.g., glycemic control) may drive heterogeneity in other outcomes of practical importance (e.g., brain, cognitive, behavioral). Under this scenario, our proposed strategy is to identify patient clusters based on the driving outcome and then examine their associations with other outcomes left out from clustering. This two-stage strategy, rather than directly tackling the complex interrelationships among multiple outcomes, provides a practical semi-supervised framework that is easy to interpret and implement. This framework also motivates our emphasis on validation that leverages multidimensional outcomes. We first conduct targeted validation (e.g., high risk vs. rest) of the generated subtypes (e.g., glycemic control) based on a primary outcome of interest (e.g., full-scale IQ). We then extend validation (i.e., validate validation) using various secondary outcomes (e.g., other IQ and brain measures). We applied the proposed method to a pediatric diabetes study, where understanding how the longitudinal course of glycemic control relates to cognitive development is critical for improving care and guidance for affected families.