The Successful Launch and Diffusion of New Therapies - Innovation and Marketing in the Pharmaceutical Industry - page 195

Where K is the number of linear spline basis functions, and k k is the truncation point
or knot where the broken lines are tied together. The combination of linear spline basis
functions described in ( 7.4 ) gives a piecewise linear function called a spline.
Additional sales-derived metrics have previously been developed and can be
used to build forecasting models. One such metric is new product takeoff, which
refers to the first strong increase in sales after an initial period of low sales. The
metric of takeoff has been developed for and applied to high-tech products and
durables (Agarwal and Bayus 2002 ; Golder and Tellis 1997 ; Tellis et al. 2003 ; Van
Everdingen et al. 2009 ), although it has not been tested, let alone used for forecast-
ing purposes, in pharmaceutical markets. Another sales-based metric is third-quarter
sales level, which Corstjens et al. ( 2005 ) proposed as a good measure for the ulti-
mate success of new drugs. According to their logic, third-quarter sales could be
used as a predictor for long-term commercial success.
The use of sales models in forecasting is similar to the use of diffusion models.
First, like diffusion models, sales models can be used to make forecasts once the
product is available in the market, and initial sales patterns can be used to reliably
calibrate the model. Often, at least 1 year of monthly data needs to be available to
be able to achieve a reliable calibration of the model. Second, one can use the pat-
tern of sales growth of another molecule to predict the growth pattern of a soon-to-
be launched molecule that is similar in terms of clinical support and market
conditions (e.g., market structure and spending).

7.1.3 Prescription Count Models

The number of prescriptions written for a given drug is essentially a count variable
with a considerable number of zeroes and a relatively small number of frequently
occurring outcomes (Manchanda et al. 2005 ). Thus, the distribution across physi-
cians of a new drug's prescriptions can be captured in individual-level prescription
count models. Accordingly, several marketing scholars have used such models to
investigate physicians' prescribing behavior and the factors affecting it. The stan-
dard count model is the Poisson regression model. In this model, the conditional
mean and variance are specified as identical.

k

l exp( − l )

pt pt

(7.5)

Pr( RX pt = k | l ) =

pt

k !

In this equation, λ pt is the mean prescription rate, p represents the physician, and
t represents the time period. Manchanda and Chintagunta ( 2004 ) use a Poisson
model to examine the influence of detailing on the number of prescriptions written.
The Poisson parameter in their model is allowed to be physician-specific and a func-
tion of detailing efforts, and the effect of detailing is also allowed to be physician-
specific and a function of the characteristics of detailing directed to the physician,
observed physician characteristics, and unobserved factors.
The negative binomial (NBD) regression model is another count model
widely used in pharmaceutical marketing. One of the main advantages of the NBD