Finding the Super-Shrink: A Hierarchical Smoothing Spline Implementation in Counseling Psychology
The Outcome Questionairre 45 (OQ45) is an index of mental health functioning often used in psychotherapy and mental-health counseling. Tracking OQ45 over time allows for quantification of the effectiveness of therapy. We propose the use of hierarchical Gaussian processes to model patient mental-health treatment curves and therapist treatment trends across patients. Individual patient curves are assigned a Gaussian process prior centered at a therapist-specific mean curve, which is also assigned a Gaussian process prior. This Bayesian non-parametric modeling yields flexible yet smooth curve estimates and unique quantification of error surrounding the curves. Specifying the hierarchical structure relates individual patient treatment curves in such a way that borrowing strength across curves is possible, allowing for their estimation in entirety even when data are sparse. Additionally, it yields a meaningful representation of therapist differences in the form of mean curves. Therapist curves are visualized via an interactive app along with the posterior outcome metric OQ45 finish-to-start ratio, as a means for comparing therapists' effectiveness.