The Successful Launch and Diffusion of New Therapies - Innovation and Marketing in the Pharmaceutical Industry - page 192

investigate diffusion patterns and to forecast demand. This model investigates the
aggregate first-purchase growth process in a given social system. In this model, also
called the mixed-influence model, an adopter of a new product is potentially subject
to two types of influence: internal influence, i.e., influence that occurs within the
social system, and external influence, i.e., influence that is external to the social
system. Internal influence results from interactions between adopters (e.g., physi-
cians or patients who have adopted in the past) and potential adopters (e.g., physi-
cians and patients who will adopt in the future) in the social system. External
influence includes all influence outside the social system, such as, for instance, com-
mercial efforts by the firm (i.e., detailing, sampling, advertising, conferences, etc.).
The basic premise underlying the Bass model is that the conditional probability
of adoption at a given time in a given social system is increasing in the portion of
the social system that has already adopted the new product:

d
d

N
t

pm Nq N

n ==-+ -

t

( )

m mN

t

( ) (7.1)

t t t

where m represents the potential number of eventual adopters, N t represents the
cumulative number of adopters by time t , and n t is the number of adopters at time t .
The parameter q in ( 7.1 ) reflects the influence of past adopters (i.e., internal influ-
ence), and the parameter p reflects an influence that is independent of previous
adoption (i.e., external influence). The internal influence parameter can reflect
word-of-mouth effects between physicians (which also includes opinion leader-
ship), as well as the adoption of common treatment standards across physicians. For
a review of the literature on the Bass model and a meta-analysis of the estimates
produced by prior research (including in the field of pharmaceuticals), see Van den
Bulte and Stremersch ( 2004 ).
Several extensions of the original Bass model have been introduced over the past
4 decades in order to reflect a number of market complexities. Such extensions
incorporate, for instance, the notion of the influence of marketing-mix variables on
the diffusion process (Krishnan et al. 1999 ; Lehmann and Esteben-Bravo 2006 ;
Mesak and Darrat 2002 ; Libai et al. 2005 ), product replacement and repeat pur-
chases (Islam and Meade 2000 ; Lilien et al. 1981 ), substitution between generations
(Bayus 1992 ; Danaher et al. 2001 ; Islam and Meade 1997 ; Mahajan and Muller
1996 ; Padmanabhan and Bass 1993 ), competition among products (Kim et al. 1999 ;
Givon et al. 1995 ; Eliashberg and Jeuland 1986 ), and heterogeneity in the social
system (Goldenberg et al. 2002 ; Moore, 1992 ; Van den Bulte and Joshi 2007 ).
Beyond its many applications across a wide variety of industries, the Bass model
and its successors have been repeatedly used in the study of the diffusion of new
medical treatments. Berndt et al. ( 2003 ), for instance, studied the diffusion of anti-
ulcer drugs in the USA. They used the Bass ( 1969 ) model to characterize network
effects in drug diffusion. In another diffusion study, Vakratsas and Kolsarici ( 2008 )
distinguished between early market and main market adopters in a diffusion model
for a new pharmaceutical drug. This notion of differentiating between two segments
of adopters is similar to the dual-market approach suggested for technological mar-
kets (e.g., Goldenberg et al. 2002 ; Moore, 1992 ). However, in the context of the
adoption of a new pharmaceutical drug, Vakratsas and Kolsarici ( 2008 ) associate