The Successful Launch and Diffusion of New Therapies - Innovation and Marketing in the Pharmaceutical Industry - page 194

more readily available than data on past adoption by physicians or by patients. One
type of sales model, using observations of aggregate sales, explicitly accounts for
the trial and repeat-purchase process by identifying distributions for trial rates and
for repeat-purchase rates (Hardie et al. 1998 ; Shankar et al. 1998 ). Parametric sales
models typically rely on the assumptions that there is a linear relationship between
the model variables and that the repeat-purchase rate for a given brand is constant.
Shankar et al. ( 1998 ), for instance, propose a model in which the sales of a new
product are decomposed into trial and repeat purchases as follows:

ST
t

=+ − r CT ( (7.2)

t t 1

where S t represents the sales of the new product at time t , T t represent the trial pur-
chases at time t , CT ( t − 1) represent the cumulative trial purchases until t − 1, and ρ is
the repeat-purchase rate. The authors further model trials as affected by both conta-
gion and marketing-mix effects.
Several researchers have implemented trial-repeat models to investigate sales
growth of new pharmaceuticals, incorporating, for instance, the influence of detail-
ing visits (i.e., sales calls by pharmaceutical representatives), word-of-mouth
effects, and competition (Ding and Eliashberg 2008 ; Hahn et al. 1994 ; Lilien et al.
1981 ; Rao and Yamada 1988 ; Shankar et al. 1998 ).
The validity of the interpretation of trial-repeat models critically hinges upon the
validity of the models' identifying assumptions with regard to the trial-repeat-
purchase process. Therefore, in forecasting the sales of new drugs, other scholars
have preferred semi-parametric methods, which do not entail any assumptions on
the underlying purchase process. For instance, Stremersch and Lemmens ( 2009 )
used regression splines to model new drug sales across the world. This flexible
approach can be viewed as a compromise between linear regression and nonpara-
metric regression sales models. The advantage of splines compared with other spec-
ifications lies in the fact that splines do not impose any assumption (linear, quadratic,
or cubic) regarding the interactions among explanatory variables over time. Such
flexibility is important in the case of sales growth models of pharmaceuticals.
Stremersch and Lemmens ( 2009 ) investigated the role of regulatory regimes in
explaining differences in the sales growth of new drugs across 55 countries all
around the world. Their model is of the following form (with REG rt representing r
regulatory conditions and OTHER pt representing p other variables, such as other
country or drug characteristics):

sales =× +× + b REG b OTHER e (7.3)

it rt rt pt pt it

The general idea behind splines is to represent the evolution of a smoothly vary-
ing function through a linear combination of basis functions. These functions are
usually polynomial functions of low degree. The time-varying coefficients of any
explanatory variable of drug sales (such as the REG or OTHER vectors in ( 7.3 )) can
then be expressed as follows (Stremersch and Lemmens 2009 ):

K

∑

b

bbb =++ t u tk ( − ) (7.4)

t 0 1 k k +

k = 1