Use of indirect transition estimates in discrete -state multiple -stage models.

Abstract

We develop a new approach to modeling transitions between states of progression for a chronic disease and its complications or comorbidities. An ideal technique is to conduct a large, longitudinal study and evaluate probabilities of transition between stages. Unfortunately, this is limited by time, expense, and changing standards of health care. In an attempt to avoid large, longitudinal studies, the standard technique for modeling, is to pick a single study from the medical literature that best describes each transition in the theoretical model. Unfortunately, this prevents use of many studies and does not provide mechanisms for model building. We develop a method which estimates transition rates from compilation of generally available literature including: data which does not differentiate between various stages in the model, data which does not measure intermediate stages in the model, and longitudinal data. We present a likelihood for model parameters under these various sampling schemes; both for discrete-time Markov chains and continuous-time Markov and semi-Markov models. Large-sample properties of our technique are discussed and simulations are presented to examine the finite-sample properties. We also consider effects of model misspecification on the properties of our estimates. Finally, we present applications from a model of complications in diabetes.