Subgroup learning for multiple mixed-type outcomes with block-structured covariates

The increasing interest in survey research focuses on inferring grouped association patterns between risk factors and questionnaire responses, with grouping shared across multiple response variables that jointly capture one's underlying status. Aiming to identify important risk factors that are simultaneously associated with the health and well-being of senior adults, a study based on the China Health and Retirement Survey (CHRS) is conducted. Previous studies have identified several known risk factors, yet heterogeneity in the outcome-risk factor association exists, prompting the use of subgroup analysis. A subgroup analysis procedure is devised to model a multiple mixed-type outcome which describes one's general health and well-being, while tackling additional challenges including collinearity and weak signals within block-structured covariates. Computationally, an efficient algorithm that alternately updates a set of estimating equations and likelihood functions is proposed. Theoretical results establish the asymptotic consistency and normality of the proposed estimators. The validity of the proposed method is corroborated by simulation experiments. An application of the proposed method to the CHRS data identifies caring for grandchildren as a new risk factor for poor physical and mental health.