Alzheimer's disease typically begins with a preclinical stage without apparent clinical symptoms. As individuals approach dementia, they exhibit a progressive decline in cognitive skills compared to normal aging. Hence, it is critical to determine first whether individuals experience cognitive decline; second, for those who develop dementia, to determine the time at which the decline rate begins to accelerate. We present a Bayesian hierarchical random change point model with a parameter constraint to distinguish individuals with and without cognitive decline, and to characterize the rate and timing for individuals experiencing cognitive decline. We allow each patient to have a unique random intercept, random slope before the change point, random change point time, and random slope after the change point that is constrained to have a negative value. We first develop a Gibbs sampler under unconstrained parameter space and then obtain draws from the posterior density for the constrained parameter using an isotonic transformation. This leads to efficient posterior inference for order-restricted piecewise regression and also allows us to test the null hypothesis of no change point.