Modeling Dual Treatment Outcomes in Mental Health: A Joint Statistical Framework for Discrete and Ordinal Responses

Mental health disorders continue to be the leading cause of declining well-being, day-to-day function, and overall quality of life for people of all ages. Understanding the factors that shape treatment progress and long-term recovery is essential for improving clinical decision-making and personalized patient care. This study uses a sequence of quantitative models, including ordered logit, multinomial logit, and a joint correlated framework, to analyze how demographic, behavioral, and other treatment-related variables influence both intermediate and final recovery trajectories. The Kaggle dataset comprises 500 patient observations with comprehensive information on demographics, diagnoses, medication types, therapy modalities, and adherence to their treatment plan. The results indicate that sleep quality has a significant impact on treatment progress, while age and symptom severity are the strongest determinants of the outcome of therapy. The joint model identifies a weak correlation between intermediate progress and long-term improvement. Overall, the findings indicate that lifestyle factors, such as sleep quality and recovery behaviors, play an important role in short-term therapeutic success, while demographic and clinical factors primarily influence the outcome of therapy.