A Perception-Augmented Hidden Markov Model for Parent-Child Relations in Families of Youth with Type 1 Diabetes

In youth with Type 1 diabetes, adherence to medical treatment regimens requires the involvement of both parent and child. A clinic-integrated behavioral intervention in the Family Management of Diabetes (FMOD) trial was shown to be effective in controlling deterioration in glycemic level; yet the mechanism remains unknown. It is possible that the effectiveness is through improved Parent-Child relation. To investigate whether the intervention improves Parent-Child relations, we proposed a novel approach that allows differential perceptions of parent and child toward the unobserved Parent-Child relationship. Leveraging manifesto data collected from both parent and child in the FMOD trial, the proposed approach extended a standard hidden Markov model by inserting a layer of parent- and child-specific hidden states. We took a Bayesian perspective to estimation and developed an efficient computational algorithm to sample from the joint posterior distribution. Extensive simulations were conducted to demonstrate the performance of the proposed modeling framework. Application to the FMOD trial data reveals that families in the intervention arm are more likely to stay in the Harmonious Parent-Child relation state and less likely to transition from Harmonious to Indifferent state. Compared to parent, child tends to have a more heterogeneous perception of the Parent-Child relation.