The Annals of Applied Statistics

Modeling competition between two pharmaceutical drugs using innovation diffusion models

Renato Guseo and Cinzia Mortarino

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The study of competition among brands in a common category is an interesting strategic issue for involved firms. Sales monitoring and prediction of competitors’ performance represent relevant tools for management. In the pharmaceutical market, the diffusion of product knowledge plays a special role, different from the role it plays in other competing fields. This latent feature naturally affects the evolution of drugs’ performances in terms of the number of packages sold. In this paper, we propose an innovation diffusion model that takes the spread of knowledge into account. We are motivated by the need of modeling competition of two antidiabetic drugs in the Italian market.

Article information

Ann. Appl. Stat., Volume 9, Number 4 (2015), 2073-2089.

Received: March 2015
Revised: July 2015
First available in Project Euclid: 28 January 2016

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Competition innovation diffusion dynamic market potential communication network nonlinear regression


Guseo, Renato; Mortarino, Cinzia. Modeling competition between two pharmaceutical drugs using innovation diffusion models. Ann. Appl. Stat. 9 (2015), no. 4, 2073--2089. doi:10.1214/15-AOAS868.

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Supplemental materials

  • Supplementary materials. In Appendix 1 we provide details regarding the closed-form solution of the proposed model. In Appendix 2 we propose an alternative estimation method to deal with monthly sales data instead of cumulative observations. In Appendix 3 we discuss the construction of predictive confidence bands. In Appendix 4 we present a SARMAX refinement for the first-order model fitting for short-term forecasting purposes. Finally, in Appendix 5 we show the results of a simulation study to assess the reliability of inferences.