Random-coefficients hidden-Markov Poisson regression models for inferring a competitor's promotion strategy

In this paper we consider the case of a drug manufacturer who has physician-level information on the prescription volume for its own brand and its competitor, has complete physician-level data on its own free-sampling plan, but has only sparse data on the competitor's promotion strategy. We investigate whether one is able to predict the competitor's promotion strategy from such limited data, We treat the competitor's promotion as a latent (unobservable) event, and propose a hidden Markov model (HMM) to describe its progression over time. Analysis of actual and simulated data shows that the HMM improves our ability to infer the missing promotion event if promotions are serially correlated. A simpler model assuming that the probability of transition from one sampling state to the other is independent of the current state is adequate if the serial correlation among promotions is weak.