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Postural instability is an important measure of Parkinson's disease conditions. Because of the fluctuation of clinical symptoms and large inter-rater and intra-rater variation, traditional method of analyzing postural instability using its onset time measure can result in controversial conclusion of treatment benefit. We propose a Brownian motion based latent structure model to study treatment's effect on postural instability The new method not only incorporates patient's multiple onset times, but also the special covariate structure of postural instability process. The proposed model does not require even-spaced visiting schedules, and the correlation of the binary process is naturally built through the underlying latent Brownian motion process. Theoretical and computational properties of the proposed model are examined. A dataset from a double-blinded multicenter Parkinson's disease clinical trial is used to demonstrate the methodology.