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Forecasting The Demand for a New Drug in a New Market:
When History Does Not Repeat Itself
Mark Rose, Sandoz Inc.
Phil Merk, IMEDE (formerly at Sandoz Inc.)
ABSTRACT
The past offers few guidelines for forecasting the future of
a drug in a new therapeutic category, but a systems dynamics
model that counts patients instead of prescriptions can help
predict demand for the product.
INTRODUCTION
Most efforts to forecast the demand for a new prescription drug
have taken a historical approach that focused on extrapolating
measures of potential physician activity such as new and refill
prescriptions. This approach is consistent with the traditional
role of physicians as the prime decision-makers in the diagnostic
and therapy selection process. Other factors that are considered
include market size, market growth, market share, promotion and
the competition. It is customary to try to gauge how other drugs
in that or a similar market have performed, which is viable when
the product and market characteristics are known or comparable
(Figure 1).
- Market size -----> |
| |
- Market growth ---> | Physician
| | Forecast
- Market share ----> | Activity | --->
| | of Demand
- Promotion ------- > | (Prescriptions)
| |
- Competition - | |
Figure 1
But what happens when there is no historical precedent - when
a new drug is launched into a new market?
In such a case the past is no longer a relevant guide to the
future; it's time to resort to analytical tools other than
trend lines and to assumptions other than "business as usual".
To forecast demand under these conditions takes a prospective
approach. It is feasible, under certain market conditions,
to develop a framework for forecasting future demand of patients.
What are these conditions?
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First, it is necessary to have a good estimate of the potential
patient population. As with traditional forecasts, which use the
number of prescriptions in a therapeutic class, this represents
an upper limit on the demand. Second, the number of potential
patients who will adopt the new drug each month must be known
with some precision. As with forecasts of attainable prescription
share, an estimate with wide variability will not be very useful.
Third, interaction with and experiences of other patients are
assumed to influence the adoption process. This is relevant when
patient consent is necessary for treatment - undergoing a major
operation - as opposed to cases in which a therapeutic decision
is made by the physician alone. Finally, it is critical to know
how many patients will have to discontinue the drug - the drop-out
rate - in order to forecast the extent of maintenance therapy.
Other characteristics of treatment, such as duration of therapy
and dosing regimen, are useful data in order to convert patient
demand to volume of drug use. A patient-based approach involves
the following factors (Figure 2):
-Potential patient population ----->
New and
“Share of new patients ------------ >
-Other patient experiences --------> Forecast
|
|
— t
Continuing |-->
|
|
|
Patients
-Drop-out rate --------------------> > of Demand
/
/
| |
| Duration of |
| Therapy
| |
| Dosing
| Regimen
| |
Figure 2
"MODELING THROUGH..."
In a seminal paper on new product growth models 15 years ago,
Frank Bass declared (Bass 1969, p.215):
"Long-range forecasting of new product sales is
a guessing game, at best. Some things, however,
may be easier to guess than others."
He also raised a philosophical issue about the use of models,
on the basis of which many long-range forecasts are now being
generated (Bass 1969, p.216):
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"Is it easier to guess the sales curve for the new
product or to guess the parameters of the model?"
When using a microcomputer, is it more desirable to use a series
of numbers on a spreadsheet or to use a series of equations - a
model? The answer boils down to deciding whether one has enough
confidence in the equations to substitute them as a rationale for
long-range forecasting. If one chooses the equations, much fewer
parameters need be estimated; and the fewer the re-estimates, the
easier it is to understand their consequences when the assumptions
change.
The model in this paper is designed to forecast the demand for a
new drug for which new patients can be identified as a key
determinant of demand. Theories of new product growth are used
for modeling the dynamics of changes in demand. We present the
case of a drug that will be used for chronic treatment over a
number of months or years that requires also explicitly tracking
"old" (continuing) patients.
MODELING PATIENTS
The model used here has its roots in the economic literature about
the adoption of a new technology (Mansfield 1961, Chow 1967).
Economists distinguish between adopters and non-adopters of a new
product; they describe and differentiate the rate of adoption of
the product by time of trial. Innovators and early adopters try
it first; then the early majority, the late majority, and the
laggards follow. The population itself is the finite upper limit
- or "ceiling" - on the total number of triers.
New drug users and new technology consumers have different ceilings.
For consumer durables or industrial products the ceiling is fixed
over the life of the product; for new drug users it is a renewable
number. Furthermore, because some of the new patients are put on
maintenance therapy and others drop out of therapy as time goes
on, one must distinguish between the variable rates of new
patients and continuing patients. Thus our model is broken down
into a two-step process:
| model new patients; then model continuing patients |
THE NEW PATIENT PROCESS
Twenty years ago Professor Edwin Mansfield of Carnegie Tech
published an analytical model to describe the rate of innovation
and imitation (Mansfield 1961). Much of the more recent new
product growth models draw on his concepts. We used his model to
represent the new patient adoption process as continuous over time:
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dn .
-- =b * n(t) * [H-n(t)] (1)
at
where
dn
-- = rate of adoption
at
n(t) = number of adopters - new patients in month t
n = maximum number of adopters in month t
n-n(t) = number of non-adopters in month t
b = coefficient of imitation
In words, equation (1) says:
The rate of change of new patients in month t
is proportional to the interaction between
adopters and non-adopters.
That is, the rate of adoption is proportional to the mathematical
product of the sizes of the two groups. "Interaction" is a
surrogate for the "word-of-mouth" effect - users communicating the
benefits of a new drug to non-users. When there are only a few
users - innovators at first - the rate of adoption is low. As the
number of users grows, the rate of adoption increases; when the
number of users equals the number of non-users, the rate of
adoption is maximal. After most of the population has adopted the
drug, its rate of adoption decreases.
The equation has the properties of a logistic function, which has
the shape of a symmetrical S-shaped curve - a common type of curve
in the new product growth models where no prior knowledge exists
about the rate of adoption (Figure 3).
new
patients
| Ai
|
n= A/a
|
| A ‘ months
Ta T
Figure 3
If after T months, the maximum number of new patients, n,is
approximately reached and an initial number of new patients, Ng,
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is specified, then the coefficient of imitation, b, can be
calculated:
in [(f-n )/n ]
a)
b= je seers os ts (2)
nT/2
This coefficient denotes the rate at which interaction - "word-
of-mouth" effect - between users and non-users occurs.
CONTINUING PATIENTS
To distinguish continuing patients from new patients, one might
think of each group as coming from a different pool. The
following diagram (Figure 4) shows the patient pools and their
"causal" impacts on one another. When potential candidates for
therapy first use a drug, they are new patients. As they return
for more therapy during subsequent months, they become continuing
patients. Some of the latter drop out either because the remedy
was succesful or because they don't respond to therapy.
+
+ ; + =
potential » new patients continuing drop-outs
candidates (adopters) > eC
+ = positive influence
negative influence
Figure 4
The positive and negative signs illustrate the impact of patient
flow from one pool to the next. For instance, the greater the
number of new patients, the greater the number of continuing
patients. And an increase in the number of drop-outs will reduce
the number of continuing patients. Thus, the change in the number
of continuing patients is merely the difference between new and
drop-out patient rates.
SYSTEMS DYNAMICS CONCEPTS
To incorporate the relationships between new and continuing
patients and patient drop-outs, the new patient equation (1)
is restated as follows:
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limit [n(t+4t) - n(t)] = b * n(t) * [fi-n(t)]
dt — Bt->0 At
when 4t = 1
(n(ttl) - n(t)] = b * n(t) * [n-n(t)]
at
or
n(ttl) = n(t) + 4t * { b * n(t) * [A-n(t)] } (3)
where 4t = "change in" t (1 month)
This latter equation represents a simple feedback statement in the
field of systems dynamics. Professor Jay Forrester and his group at
M.I.T. in the late 1950s and early 1960s developed systems dynamics
and the DYNAMO computer language that solves time-dependent problems
of this kind. A foundation book, The Limits To Growth, which
applies systems dynamics to estimating the global limits of natural
and human resources, was published in 1972.
The core concept of systems dynamics is that a system at a certain
level at a given time period moves to a new level in the next time
period at a certain rate of change:
|
| level (time + 1) = level (time) + rate of change |
|
If the rate of change from one level to another is dependent on the
current level of the system, then there is a feedback phenomenon.
That is, past performance affects current performance.
In equation (3), the new patient model, the rate of change in the
use of a drug by new patients is dependent on the current levels of
adoption n(t) and non-adoption [f-n(t)]. Similarly, the rate of
change of drop-outs is dependent on the current level of continuing
patients and affects the future level of continuing patients. Thus,
both time-dependent relationships fall into a classic feedback
system readily solvable using DYNAMO.
CALCULATIONS
The equations and parameters to solve this problem can be described
in two steps. The first step, using DYNAMO notation (Roberts et al
1983, Chapter 14), is as follows:
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NEWPAT.K
NEWPAT.J + (DT) (RATE.JK) (4a)
RATE.KL = B * NEWPAT.K * (NPMAX - NEWPAT.K) (4b)
where
NEWPAT = number of new patients (adopters)
RATE = rate of new patients
NPMAX = maximum number of new patients (h)
(market "ceiling" of new patients in a month)
B = coefficient of imitation
(calculated using equation (2) )
DT = change in months (=1)
The first equation (4a) provides the number of new patients in
month K based on the number of new patients in the previous month 7
In the second step one calculates the number of continuing patients
in month K by adding the new patients and subtracting the drop-outs:
CONPAT.K = CONPAT.J + (DT) (NPRATE.JK-DORATE.JK) (5a)
NPRATE.KL = NEWPAT.K (5b)
DORATE.KL = constant * CONPAT.K (5¢)
where
CONPAT = number of continuing patients
NPRATE = number of new patients (from equation (4a))
DORATE = number of drop-outs
constant = rate of drop-outs per month
DT = change in months (=1)
Suppose, for example, that the initial number of new patients is
100 and the market "ceiling" (NPMAX) is 1000 patients. What are
the numbers of new and continuing patients if the drop-out rate is
assumed to be 1 percent per month? If it is 10 percent per month?
The number of new and continuing patients can be calculated (Table 1)
over a 12-month period using equations (4a-4b) and (5a-5c).
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Continuing Continuing
New Patients Patients
Month Patients 1% Drop-out 10% Drop-out
BE 133 100 100
2 175 232 223
3 228 405 376
4 293 629 566
5 368 915 802
6 454 1274 1090
7 544 1715 1435
8 635 2242 1836
9 720 2855 2287
10 794 3547 2779
11 854 4385 3295
12 900 5116 3819
Table 1
Note that with a 1 percent drop-out rate the number of continuing
patients increases to more than 5 times the number of new patients
after 12 months; an increase in the monthly drop-out rate from
1 percent to 10 percent can reduce the number of continuing patients
by one-third.
These equations were applied to the forecast of a Sandoz product -
using an IBM PC with Micro-DYNAMO from Pugh-Roberts Associates,Inc.
in Cambridge, Massachusetts. A spreadsheet, used before this model
was developed, required more than three hours to run a 60-month
forecast. With this model we reduced the computational effort to
less than 1 minute! In addition, it was possible to calculate the
impact on other related variables: the number of bottles and sales
revenue.
In summary, in situations in which market conditions permit
forecasting of product demand using patient estimates, we have
found that the concepts and tools of systems dynamics can be very
useful in developing a patient-based, new drug growth model. With
this model one can quickly analyze the consequences for a forecast
of changes in marketing and therapy variables and policies.
REFERENCES
Bass, Frank, "A New Product Model For Consumer Durables",
Management Science, Vol. 15, No. 5, Jan. 1969, p. 215-227.
Chow, G., "Technical Change And The Demand For Computers",
The American Economic Review, 1967, pp. 1117-1130.
Mansfield, E., "Technical Change And The Rate Of Imitation",
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Econometrica, Oct. 1961, pp.741-766.
Roberts, Nancy, David Andersen, Ralph Deal, Michael Garet,
William Shaffer, Introduction To Computer Simulation,
Reading: Addison-Wesley, 1983.
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