Semiparametric Mixed Effect Model with Application to the Longitudinal Knee Osteoarthritis (OAK) Data.

Motivated by the study of the longitudinal development and progression of knee osteoarthritis (OA) over a 15-year period, this study developed non-parametric mixed-effect models for ordinal outcomes. A stochastic mixed-effect model was used to evaluate the similarity of trajectories associated with increasing disease severity of OA in both knees. Then, a non-parametric mixed-effects model, based on cubic B-splnes, was developed to characterize the unknown nonlinear trend of logits as a function of time1-order. A Markov Transition Model was developed to characterize the transitions among multi-states of knee OA. This newly developed approach allows more flexible functional dependence of the ordinal outcome, levels of increasing knee OA severity, on the covariates.