Multi‐stage multivariate modeling of temporal patterns in prescription counts for competing drugs in a therapeutic category

This article describes statistical analyses pertaining to marketing data from a large multinational pharmaceutical firm. We describe models for monthly new prescription counts that are written by physicians for the firm's focal drug and for competing drugs, as functions of physician‐specific and time‐varying predictors. Modeling patterns in discrete‐valued time series, and specifically time series of counts, based on large datasets, is the focus of much recent research attention. We first provide a brief overview of Bayesian approaches we have employed for modeling multivariate count time series using Markov Chain Monte Carlo methods. We then discuss a flexible level correlated model framework, which enables us to combine different marginal count distributions and to build a hierarchical model for the vector time series of counts, while accounting for the association among the components of the response vector, as well as possible overdispersion. We employ the integrated nested Laplace approximation (INLA) for fast approximate Bayesian modeling using the R‐INLA package (r‐inla.org). To enhance computational speed, we first build a model for each physician, use features of the estimated trends in the time‐varying parameters in order to cluster the physicians into groups, and fit aggregate models for all physicians within each cluster. Our three‐stage analysis can provide useful guidance to the pharmaceutical firm on their marketing actions. Copyright © 2017 John Wiley & Sons, Ltd.