Simultaneous variable selection and de-coarsening in multi-path change-point models

Follow-up studies on a group of units are commonly carried out to explore the possibility that a response distribution has changed at unobservable time points that are different for different units. Often, in practice, there will be many potential covariates, which may not only be associated with the response distribution but also with the distribution of the unobservable change-points. Here, the covariates are allowed to enter the change-point distribution through a proportional odds model whose baseline odds is assumed to be piecewise constant as a function of time. The combination of a large number of putative regression coefficients in the response distributions as well as the change-point distribution, alone leads to a challenging simultaneous variable selection and estimation problem. Moreover, selection and estimation of the parameters that determine the coarseness of the baseline odds function adds a further level of complexity. Using penalized likelihood methods we are able to simultaneously perform variable selection, estimation, and determine the coarseness of the baseline odds function. Our approach is computationally efficient and shown to be consistent in variable selection and parameter estimation. We assess its performance through simulations, and demonstrate its usage in fitting a model for cognitive decline in subjects with Alzheimer’s disease.