Modeling competition between two pharmaceutical drugs using innovation diffusion models

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.Comment: Published at http://dx.doi.org/10.1214/15-AOAS868 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Diffusion of innovations dynamics, biological growth and catenary function. Static and dynamic equilibria

The catenary function has a well-known role in determining the shape of chains and cables supported at their ends under the force of gravity. This enables design using a specific static equilibrium over space. Its reflected version, the catenary arch, allows the construction of bridges and arches exploiting the dual equilibrium property under uniform compression. In this paper, we emphasize a further connection with well-known aggregate biological growth models over time and the related diffusion of innovation key paradigms (e.g., logistic and Bass distributions over time) that determine selfsustaining evolutionary growth dynamics in naturalistic and socio-economic contexts. Moreover, we prove that the ‘local entropy function’, related to a logistic distribution, is a catenary and vice versa. This special invariance may be explained, at a deeper level, through the Verlinde’s conjecture on the origin of gravity as an effect of the entropic force

Modelling seasonality in innovation diffusion. A regressive approach

Although the literature on innovation diffusion is very wide, up to now not much attention has been paid on modelling the seasonal component often present in sales data. In this paper we develop two innovation diffusion models that take into account not only the evolutionary trend of sales but also their intra-year oscillations, that are due to seasonal effects. In particular, we treat seasonality as a deterministic component to be estimated with conventional NLS techniques jointly with the trend. The results obtained by applying these models to the life-cycle of a pharmaceutical drug show a clearly better performance in providing short-term forecasts. Moreover, this methodology proves more parsimonious with respect to the autoregressive method, based on SARMA models

Heterogeneity in Diffusion of Innovations Modelling: A Few Fundamental Types

Heterogeneity of agents in aggregate systems is an important issue in the study of innovation diffusion. In this paper, we propose a modelling approach to latent heterogeneity, based on a few fundamental types, which avoids cumbersome integrations with not easy to motivate a priori distributions. This approach gives rise to a discrete non-parametric Bayesian mixture model with a possibly multimodal distributional behaviour. The result is inspired by two alternative theories: the first is based on the Rosenblueth two-point distributions (TPD), and the second is related to Cellular Automata models. From a statistical point of view, the proposed reduction allows for the recognition of discrete heterogeneous sub-populations by assessing their significance within a realistic diffusion process. An illustrative application is discussed with reference to Compact Cassettes for pre-recorded music in Italy

A Class of Automata Networks for Diffusion of Innovations Driven by Riccati Equations : Automata Networks for Diffusion of Innovations.

Innovation diffusion processes are generally described at aggregate level with models like the Bass model (1969) and the Generalized Bass Model (1994). However, the recognized importance of communication channels between agents has recently suggested the use of agent-based models, like Cellular Automata. We argue that an adoption process is nested in a communication network that evolves dynamically and implicitly generates a non-constant potential market. Using Cellular Automata we propose a two- phase model of an innovation diffusion process. First we describe the Communication Network necessary for the awareness of an innovation. Then, we model a nested process representing the proper adoption dynamics. Through a "Mean Field Approximation" we propose a continuous representation of the discrete time equations derived by our Automata Network. This constitutes a special non autonomous Riccati equation, not yet described in well-known international catalogues. The main results refer to the closed form solution of this equation and to the corresponding statistical analysis for identification and inference. We discuss an application in the field of bank services

Cellular Automata with Network Incubation in Information Technology Diffusion.

Innovation diffusion of network goods determines direct network externalities that exhibit delayed full benefits, depressing sales for long periods. We model a multiplicative dynamic market potential driven by a latent heterogeneous individual threshold derived from a basic economic theory by Economides and Himmelberg (1995) which is embedded in a special Cellular Automata representation. The corresponding mean field approximation of its aggregate version is a Riccati equation with a closed form solution. This allows the detection of a change-point time separating an incubation period from a subsequent take-off due to a sufficient critical mass acting as a collective threshold. Weighted nonlinear least squares methodology is the main inferential technique. An application is analysed with reference to USA fax machine diffusion

Competition Modelling in Multi-Innovation Diffusions. Part I: Balanced Models

Diffusion of innovations within simultaneous processes examined as univariate models of separate trajectories cannot take into account and properly explain systematic perturbations due to competition-substitution effects. This inability is quite evident in special product categories such as pharmaceutical drugs based upon equivalent or similar active compounds. A second relevant aspect in multiple competition is represented by the choice to model the word-of-mouth effect either at the category level (balanced model) or at the brand level, separating within-brand effect from cross-brand one (unbalanced model). The choice has to be grounded on the features of the products to be described. In this paper, balanced models will be studied, while the companion article is devoted to unbalanced ones. A third relevant aspect in simultaneous competing diffusions is the separation between synchronic and diachronic market entries. In the latter case, the proposed model is further extended in order to detect whether the beginning of competition alters the first entrant's diffusion parameters. The resulting differential system has a closed-form solution that allows an empirical validation through sales data of the assumptions underlying the model structure. An application to pharmaceutical drugs competition is discussed. Finally, we approach here the topic of agent heterogeneity by introducing a multivariate Cellular Automata representation which allows a feasible description of Complex Systems of this type with a direct specification of substitution effect between competing product

A nuclear power renaissance?

Nuclear energy has been experiencing a revival in many countries, since it is considered to be a possible substitute for fossil fuels for electricity generation. This calls for a focused analysis, in order to evaluate whether conditions exist for its wide employment. While typical aspects against this option have to do with waste management, security of power plants and related health concerns, other issues less frequently considered by politics, mass media, and public opinion seem particularly crucial to understand if we are really going to face a nuclear energy renaissance. In particular, nuclear energy is well known to depend on parallel dynamics of uranium extraction and reactor startup. In this paper we apply an innovation diffusion framework to model co-evolutionary processes of uranium extraction, reactor startup and nuclear energy consumption at a world level. We also perform an analysis of nuclear consumption dynamics in France, Japan, and the USA, which are the three countries that are mostly invested in it. The results obtained by analyzing all of these processes do not seem to support the idea of a new era for nuclear energy

Modeling competition among pharmaceutical drugs

Competition between rival brands within the same category gives rise to special competition/substitution effects of great interest to the involved forms. The study of competition in the pharmaceutical market highlights special behavior in the diffusion of knowledge about the products that may differ from other competing arenas. This latent feature naturally affects the evolution of the drugs' performances, in terms of number of packages sold. The aim of this paper is to propose a new model structure within the family of innovation diffusion models that specifically takes the step of knowledge spread into account. We show the application of this model with nonlinear regression methods and a comparison with alternative models to antidiabetic drug sales recorded monthly in the Italian market