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

A decomposition for a stochastic matrix with an application to MANOVA

AbstractThe aim of this paper is to propose a simple method in order to evaluate the (approximate) distribution of matrix quadratic forms when Wishartness conditions do not hold. The method is based upon a factorization of a general Gaussian stochastic matrix as a special linear combination of nonstochastic matrices with the standard Gaussian matrix. An application of previous result is proposed for matrix quadratic forms arising in MANOVA for a multivariate split-plot design with circular dependence structure

Life-cycle forecasting for pharmaceutical drugs. A structured approach with Mathematica

The study of the lifecycle of existing pharmaceutical products within a common therapeutic category may provide some insight into the expected performance of a new drug with comparable efficacy from the medical point of view. Whenever the category is crowded, however, this approach requires the analysis of hundreds, or even thousands, of sales' time series. The aim of this report is to present a technical tool to deal with data inspection, univariate diffusion model fitting, and forecasting storage for a large number of products. This is realized with the software Mathematica (Versions 9 or 10)

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

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

Pleural Mesothelioma: forecasts of the death toll in the area of Casale Monferrato, Italy

In the city of Casale Monferrato, the largest Italian factory that produced asbestos cement goods was active from 1907 to 1985. As a consequence, asbestos fibers scattered in the surrounding area and caused an enormous number of pleural mesotheliomas. Due to the very long latency of this disease, many subjects have not exhibited its symptoms yet. The aim of this paper is to model and predict the future evolution of the number of deaths due to this disease among residents in the area around that city. The model used here is based on a Cellular Automata that is assumed to pass through three steps: exposure, contamination, diagnosis. In that way, forecasts of the future evolution take into account the environmental conditions that changed in time during the last century because of different levels in plant activity. The model is fitted to annual diagnosis data starting from 1954 to 2009. Results show that deaths will not end until 2033, and that in the next two decades, at least 479 more subjects will be diagnosed with this disease

Competition Modelling in Multi-Innovation Diffusions. Part II: Unbalanced Models.

Competition between rival brands within the same category gives rise to special competition/substitution effects of great interest for involved firms. In the companion article, we studied balanced models that are adequate to describe a homogeneous category for which within-brand and cross-brand word-of-mouth effects are indistinguishable. Conversely, in this paper we propose an unbalanced model that, besides separating these two imitative sources, also allows for a change in the parameter values of the first entrant as soon as the second one enters the market. We prove that our model has a closedform solution allowing parameters to be estimated with sales data. Moreover, we compare our model with other unbalanced models, both from a theoretical point of view and from an empirical one, by comparing their performance on pharmaceutical drug data

Regular and promotional sales in new product life-cycle: A competitive approach

In this paper, we consider the application of the Lotka-Volterra model with churn effects, LVch, (Guidolin and Guseo, 2015) to the case of a confectionary product produced in Italy and recently commercialized in a European country. Weekly time series, referring separately to quantities of regular and promotional sales, are available. Their joint inspection highlighted the presence of compensatory dynamics suggesting the study with the LVch to estimate whether competition between regular and promotional sales exists and how it affects product life-cycle. The study of sales under promotion with respect to regular ones represents a new way of dealing with promotional activities effects, whereas the innovation diffusion literature on new product growth has typically considered the effect of pricing and advertising through the generalized Bass model (Bass et al., 1994). In that model, the total amount of sales, regular plus promotional sales, is analyzed with a univariate approach, while price and advertising expenditures are used as exogenous inputs, without a feedback control. Conversely, exploiting the availability of two distinct time series and studying their interaction, our results show that competition has a symmetric character. Regular sales may access the residual market of those under promotion indicating the beneficial effect of promotional efforts, but the reverse effect is also present. Short-term forecasts on the evolution of the two series are then built with a two stage procedure based on an iterated SARMAX. The predicted values are further validated with observed real data. A comparison with Euler standard predictions is also performed

Duncan's model for X-control charts: sensitivity analysis to input parameters.

In this paper a sensitivity analysis for optimal solutions of the wellknown Duncan's model is proposed to misspecification in the cost parameters. The analysis is performed both in the continuous case, i.e. when the production process continues in operation while searches for the assignable cause after a signal are made, and in the more realistic discontinuous case, i.e. when a signal causes a production stop. While similar contributions published in literature perform the sensitivity analysis with a one-factor-at-time scheme, the original contribution of this paper is represented by the focus here given on interactions among changes in values of different cost parameters