Innovation Diffusion and Pioneering Bass Model: Theory and Practical Applications

1
Innovation DiffusionInnovation DiffusionInnovation DiffusionInnovation Diffusion
and Pioneering Bassand Pioneering Bassand Pioneering Bassand Pioneering Bass
Model: Theory andModel: Theory andModel: Theory andModel: Theory and
Practical ApplicationsPractical ApplicationsPractical ApplicationsPractical Applications
Deployment of Top US
20 Drug Sales
Projections within
Pharmaceutical Sector
June 2017
Fabiano De Rosa
P&C and Risk Manager
Marco Berizzi
Chief Financial Officer

ObjectiveObjectiveObjectiveObjective
• Presentation ofPresentation ofPresentation ofPresentation of TheoreticalTheoreticalTheoreticalTheoretical FrameworkFrameworkFrameworkFramework
underlying Innovationunderlying Innovationunderlying Innovationunderlying Innovation DiffusionDiffusionDiffusionDiffusion and Bassand Bassand Bassand Bass
ModelModelModelModel
• OverviewOverviewOverviewOverview ofofofof Estimation Procedures forEstimation Procedures forEstimation Procedures forEstimation Procedures for
Parameters within Bass ModelParameters within Bass ModelParameters within Bass ModelParameters within Bass Model
• Application of Bass Model to Top US 20Application of Bass Model to Top US 20Application of Bass Model to Top US 20Application of Bass Model to Top US 20
Drug SalesDrug SalesDrug SalesDrug Sales Projections withinProjections withinProjections withinProjections within
Pharmaceutical SectorPharmaceutical SectorPharmaceutical SectorPharmaceutical Sector
2
marco.berizzi71@gmail.com
fdrose14@gmail.com

Marco BerizziMarco BerizziMarco BerizziMarco Berizzi
AgendaAgendaAgendaAgenda
• Theoretical Framework underlying InnovationTheoretical Framework underlying InnovationTheoretical Framework underlying InnovationTheoretical Framework underlying Innovation
DiffusionDiffusionDiffusionDiffusion
• Estimation of Parameters within Bass Model
• Application of Bass Model to Top 20 US Drug Sales
Projections
• Annex
• Bibliography and Miscellanea
3
fdrose14@gmail.com

InnovatorsInnovatorsInnovatorsInnovators
EarlyEarlyEarlyEarly
AdoptersAdoptersAdoptersAdopters
EarlyEarlyEarlyEarly
MajorityMajorityMajorityMajority
LateLateLateLate
MajorityMajorityMajorityMajority
LaggardsLaggardsLaggardsLaggards
Time LineTime LineTime LineTime LineTime LineTime LineTime LineTime Line
Overview of Innovation Diffusion ConceptOverview of Innovation Diffusion ConceptOverview of Innovation Diffusion ConceptOverview of Innovation Diffusion Concept
4
marco.berizzi71@gmail.commarco.berizzi71@gmail.com
fdrose14@gmail.com
Innovation DiffusionInnovation DiffusionInnovation DiffusionInnovation Diffusion Study and Detection of Main FactorsStudy and Detection of Main FactorsStudy and Detection of Main FactorsStudy and Detection of Main Factors
• Knowledge of innovation diffusioninnovation diffusioninnovation diffusioninnovation diffusion
dynamicsdynamicsdynamicsdynamics is crucialcrucialcrucialcrucial in order to engageengageengageengage
coherently corporatecorporatecorporatecorporate organizationorganizationorganizationorganization
and to alignalignalignalign the interestsinterestsinterestsinterests of all
corporate stakeholdersstakeholdersstakeholdersstakeholders such as
customerscustomerscustomerscustomers, supplierssupplierssupplierssuppliers, businessbusinessbusinessbusiness
partnerspartnerspartnerspartners, internal resourcesresourcesresourcesresources and
authoritiesauthoritiesauthoritiesauthorities
• The aboveaboveaboveabove dynamicsdynamicsdynamicsdynamics are firstly
analysedanalysedanalysedanalysed by Gabriel TardeTardeTardeTarde,
Friedrich RatzelRatzelRatzelRatzel and Leo
FrobeniusFrobeniusFrobeniusFrobenius in the late part of
19191919thththth centurycenturycenturycentury
• It is due to Everett RogersRogersRogersRogers
the conception of a
theoretical frameworktheoretical frameworktheoretical frameworktheoretical framework
in 1962196219621962 able to detectdetectdetectdetect
main factorsfactorsfactorsfactors
underlying ...
• RogersRogersRogersRogers identifies five categoriesfive categoriesfive categoriesfive categories
of adoptersadoptersadoptersadopters - innovatorsinnovatorsinnovatorsinnovators, earlyearlyearlyearly
adoptersadoptersadoptersadopters, early majorityearly majorityearly majorityearly majority, latelatelatelate
majoritymajoritymajoritymajority and laggardslaggardslaggardslaggards
• … innovation diffusion… innovation diffusion… innovation diffusion… innovation diffusion such as
innovation itselinnovation itselinnovation itselinnovation itself, communicationcommunicationcommunicationcommunication
channels, timetimetimetime and social systemssocial systemssocial systemssocial systems
• The above categoriescategoriescategoriescategories are
basedbasedbasedbased on innovativenessinnovativenessinnovativenessinnovativeness
conceptconceptconceptconcept defined as the
degreedegreedegreedegree to which an individualindividualindividualindividual
adoptsadoptsadoptsadopts a newnewnewnew idea and are
market entry timemarket entry timemarket entry timemarket entry time
aaaaccordingccordingccordingccording to productproductproductproduct
lifelifelifelife cyclecyclecyclecycle phasesphasesphasesphases
• Five categoriescategoriescategoriescategories are
characterized by differentdifferentdifferentdifferent

Innovation DiffusionInnovation DiffusionInnovation DiffusionInnovation Diffusion Dynamics explained byDynamics explained byDynamics explained byDynamics explained by
Pioneering Bass ModelPioneering Bass ModelPioneering Bass ModelPioneering Bass Model
5
Bass Model IntroductionBass Model IntroductionBass Model IntroductionBass Model Introduction
y′ t p q y t 1 y t with p,q >0
For mathematical
04
For mathematical
derivation see
Annex 01-02-03-
04
fdrose14@gmail.com
• InnovationInnovationInnovationInnovation diffusion dynamicsdiffusion dynamicsdiffusion dynamicsdiffusion dynamics are
explainedexplainedexplainedexplained in a structuredstructuredstructuredstructured and scientificscientificscientificscientific
manner in pioneering Bass modelBass modelBass modelBass model
• In his original formulation Bass modelBass modelBass modelBass model
forecastsforecastsforecastsforecasts the numbernumbernumbernumber of new adoptionsnew adoptionsnew adoptionsnew adoptions
for a consumer durable productconsumer durable productconsumer durable productconsumer durable product to be
commercially launchedlaunchedlaunchedlaunched by a corporationcorporationcorporationcorporation
along a certain elapsed timeelapsed timeelapsed timeelapsed time
• The modelmodelmodelmodel is notnotnotnot supposed to
acknowledge replacementacknowledge replacementacknowledge replacementacknowledge replacement
purchasespurchasespurchasespurchases but only initialonly initialonly initialonly initial
purchasespurchasespurchasespurchases of the productproductproductproduct
• Model parametersModel parametersModel parametersModel parameters are given by
the market potentialmarket potentialmarket potentialmarket potential mmmm - which
can be seen as the long run cumulatedlong run cumulatedlong run cumulatedlong run cumulated
numbernumbernumbernumber of new adoptionsnew adoptionsnew adoptionsnew adoptions, the
innovation coefficientinnovation coefficientinnovation coefficientinnovation coefficient pppp and the
imitation coefficientimitation coefficientimitation coefficientimitation coefficient qqqq
• Bass modelBass modelBass modelBass model is entitled alsoalsoalsoalso to be
representedrepresentedrepresentedrepresented excludingexcludingexcludingexcluding the marketmarketmarketmarket
potentialpotentialpotentialpotential mmmm - which can be estimated
separately – forecasting newnewnewnew adoptionsadoptionsadoptionsadoptions
in percentagepercentagepercentagepercentage of the marketmarketmarketmarket
Bass Model Dynamic EquationsBass Model Dynamic EquationsBass Model Dynamic EquationsBass Model Dynamic Equations
• Bass ModelBass ModelBass ModelBass Model is built upon differentialdifferentialdifferentialdifferential
equationsequationsequationsequations which explain increaseincreaseincreaseincrease of newnewnewnew
adoptionsadoptionsadoptionsadoptions at each time t in terms of newnewnewnew
adoptionsadoptionsadoptionsadoptions at t and of constant parametersconstant parametersconstant parametersconstant parameters
• Bass ModelBass ModelBass ModelBass Model can be expressedexpressedexpressedexpressed by oneoneoneone of the
two equationstwo equationstwo equationstwo equations shown below
z′ t p q
z t
m
m z t
where
- y t : n.° of new adoptions in % of the market
- y′ t : increase of n.° of new adoptions in % of
the market
- p, q and m: respectively innovation, imitation
and market potential coefficients
- z t y t m
y′ t p 1 y t q y t 1 y t with p,q >0
2222
InnovationInnovationInnovationInnovation
intensityintensityintensityintensity
ImitationImitationImitationImitation
intensityintensityintensityintensity
1a1a1a1a 1b1b1b1b
1111

Solution of Bass Model Dynamic EquationSolution of Bass Model Dynamic EquationSolution of Bass Model Dynamic EquationSolution of Bass Model Dynamic Equation
6
fdrose14@gmail.com
0% 0
Innovation intensity
Imitation intensity
Increase of n.° of new
adoptions in % of the
market
Time t
Time t
100% 1
0% 0
p
Bass ModelBass ModelBass ModelBass Model ---- GraphicsGraphicsGraphicsGraphics
Solution of Bass Model DifferentialSolution of Bass Model DifferentialSolution of Bass Model DifferentialSolution of Bass Model Differential
EquationEquationEquationEquation
Solution of Bass Model DifferentialSolution of Bass Model DifferentialSolution of Bass Model DifferentialSolution of Bass Model Differential
EquationEquationEquationEquation
• SolutionSolutionSolutionSolution of Bass Model equationBass Model equationBass Model equationBass Model equation
y′ t p 1 y t q y t 1 y t with p,q >0
is givengivengivengiven by following y t function of t
y t

e !
representing time evolutiontime evolutiontime evolutiontime evolution of nnnn....°°°° of newof newof newof new
adoptionsadoptionsadoptionsadoptions in %%%% of the marketmarketmarketmarket
y’ t
# #!$ %
$ !#
%
3333
3333
• Consequently time evolutiontime evolutiontime evolutiontime evolution of y′ t , A t
and B t respectively iiiincreasencreasencreasencrease of n.n.n.n.°°°° of newnewnewnew
adoptionsadoptionsadoptionsadoptions in %%%% of the marketmarketmarketmarket, innovationinnovationinnovationinnovation and
imitation intensityimitation intensityimitation intensityimitation intensity are given by
A t
p q e
e !
and B t
%
!$ e e %
e !
%
4444
4a4a4a4a4a4a4a4a 4b4b4b4b4b4b4b4b
n.° of new adoptions in
% of the market
4a4a4a4a4a4a4a4a
4444
4b4b4b4b4b4b4b4b
1111
1a1a1a1a 1b1b1b1b
For mathematical
04
For mathematical
derivation see
Annex 01-02-03-
04

Bass Model InterpretationBass Model InterpretationBass Model InterpretationBass Model Interpretation
7
fdrose14@gmail.com
Bass ModelBass ModelBass ModelBass Model ---- GraphicsGraphicsGraphicsGraphicsBass ModelBass ModelBass ModelBass Model –––– Rationales and InsightsRationales and InsightsRationales and InsightsRationales and Insights
3333
4a4a4a4a4a4a4a4a
4444
4b4b4b4b4b4b4b4b
y∗ t∗
1
2
1
p
q
0% 0
Innovation intensity
Imitation intensity
adoptions in % of the
market
Time t
Time t
0% 0
t∗
*+
#!$
t∗
*+
#!$
y∗′ t∗
p q ,
4q
n.° of new adoptions in
% of the market
100% 1
p
• IncreaseIncreaseIncreaseIncrease of new adoptionsnew adoptionsnew adoptionsnew adoptions reaches a peakpeakpeakpeak and
then decaysdecaysdecaysdecays along timetimetimetime as shown by red curvered curvered curvered curve
which feeds cumulated green curvefeeds cumulated green curvefeeds cumulated green curvefeeds cumulated green curve representing
n.n.n.n.°°°° of new adoptionnew adoptionnew adoptionnew adoption
• Red curve profileRed curve profileRed curve profileRed curve profile is givengivengivengiven by the sumsumsumsum of yellowyellowyellowyellow
and orange curvesorange curvesorange curvesorange curves which acknowledgeacknowledgeacknowledgeacknowledge
respectively different behaviourrespectively different behaviourrespectively different behaviourrespectively different behaviour of “Innovators”“Innovators”“Innovators”“Innovators”
and “Imitators“Imitators“Imitators“Imitators
• “Innovators”“Innovators”“Innovators”“Innovators” are not influencednot influencednot influencednot influenced in the timingtimingtimingtiming
of their purchasepurchasepurchasepurchase by the numbernumbernumbernumber of peoplepeoplepeoplepeople
who have already boughtalready boughtalready boughtalready bought the productproductproductproduct
while “Imitators”“Imitators”“Imitators”“Imitators” are influencedinfluencedinfluencedinfluenced by the
numbernumbernumbernumber of the previous buyersprevious buyersprevious buyersprevious buyers
• Importance of “Innovators”“Innovators”“Innovators”“Innovators” is greater at firstgreater at firstgreater at firstgreater at first and
then diminishesdiminishesdiminishesdiminishes monotonically with timetimetimetime as shown
by “Innovation intensity”“Innovation intensity”“Innovation intensity”“Innovation intensity” yellow curveyellow curveyellow curveyellow curve
• ““““Imitators”Imitators”Imitators”Imitators” learnlearnlearnlearn from thosethosethosethose who have alreadyalreadyalreadyalready
boughtboughtboughtbought reaching a peakpeakpeakpeak and then progressively
slowing downslowing downslowing downslowing down as shown by “Imitation intensity”“Imitation intensity”“Imitation intensity”“Imitation intensity”
orange curveorange curveorange curveorange curve
• ValueValueValueValue of parametersparametersparametersparameters p and q impactimpactimpactimpact the shapeshapeshapeshape of
green-red-yellow-orange curvescurvescurvescurves, inflection / peakinflection / peakinflection / peakinflection / peak
timetimetimetime, inflection pointinflection pointinflection pointinflection point and peak pointpeak pointpeak pointpeak point
For mathematical
04
For mathematical
derivation see
Annex 01-02-03-
04

Bass Model including Market Potential “m”Bass Model including Market Potential “m”Bass Model including Market Potential “m”Bass Model including Market Potential “m”
8
fdrose14@gmail.com
mp
Bass ModelBass ModelBass ModelBass Model ---- GraphicsGraphicsGraphicsGraphicsBass Model with Market Potential “m”Bass Model with Market Potential “m”Bass Model with Market Potential “m”Bass Model with Market Potential “m”
z t m

e !
representing time evolutiontime evolutiontime evolutiontime evolution of nnnn....°°°° of newof newof newof new
adoptionsadoptionsadoptionsadoptions reaching followingfollowingfollowingfollowing valuevaluevaluevalue at
inflection timeinflection timeinflection timeinflection time t∗
z’ t m
# #!$ %
$ !#
% where z′ t∗
m
#!$ %
.$
5555
• Consequently time evolutiontime evolutiontime evolutiontime evolution of z′ t , A/ t and B/ t
respectively iiiincreasencreasencreasencrease of n.n.n.n.°°°° of newnewnewnew adoptionsadoptionsadoptionsadoptions, the
oneoneoneone due to “innovators”“innovators”“innovators”“innovators” and the oneoneoneone due to
“imitators”“imitators”“imitators”“imitators”:
A/ t m A t and B/ t m B t
6666
6666aaaa6666aaaa 6666bbbb6666bbbb
z′ t p q
z t
m
m z t where z t y t m2222
• Bass ModelBass ModelBass ModelBass Model with market potential “m”market potential “m”market potential “m”market potential “m” is given by
following differential equation:differential equation:differential equation:differential equation:
• SolutionSolutionSolutionSolution of the above equationequationequationequation is givengivengivengiven by
following z t function of t
5555
6666aaaa6666aaaa
6666
6666bbbb6666bbbb
z∗ t∗
m
2
1
p
q
0
Increase due to
“innovators”
Increase due to
“imitators”
adoptions
Time t
Time t
0
t∗
*+
#!$
t∗
*+
#!$
z∗0 t∗
m
#!$ %
.$
n.° of new adoptions
m
z∗
t∗

m
2
1
p
q
For mathematical
04
For mathematical
derivation see
Annex 01-02-03-
04

Generalized Bass ModelGeneralized Bass ModelGeneralized Bass ModelGeneralized Bass Model
9
For mathematical
07
For mathematical
derivation see
Annex 05-06-
07
fdrose14@gmail.com
Generalized Bass Model HighlightsGeneralized Bass Model HighlightsGeneralized Bass Model HighlightsGeneralized Bass Model Highlights
y′ t p q y t 1 y t x t p 1 y t x t q y t 1 y t x t with p,q >0
• Generalized Bass ModelGeneralized Bass ModelGeneralized Bass ModelGeneralized Bass Model (GBM) was developeddevelopeddevelopeddeveloped in 1994199419941994 by Frank BassBassBassBass, Trichy KrishnanKrishnanKrishnanKrishnan and
Dipak JainJainJainJainisisisis
• GBMGBMGBMGBM is an extensionextensionextensionextension of standard Bass Modelstandard Bass Modelstandard Bass Modelstandard Bass Model which includesincludesincludesincludes not only innovation / imitationinnovation / imitationinnovation / imitationinnovation / imitation
driversdriversdriversdrivers but alsoalsoalsoalso managerial variablesmanagerial variablesmanagerial variablesmanagerial variables such as pricingpricingpricingpricing, advertisingadvertisingadvertisingadvertising and marketing strategicmarketing strategicmarketing strategicmarketing strategic
decisionsdecisionsdecisionsdecisions
• GBMGBMGBMGBM acknowledges the above managerial variablesabove managerial variablesabove managerial variablesabove managerial variables through a function of timefunction of timefunction of timefunction of time x t which is
inserted in Bass model equationBass model equationBass model equationBass model equation as it follows:
• SolutionSolutionSolutionSolution of GBMGBMGBMGBM representing time evolutiontime evolutiontime evolutiontime evolution of n.n.n.n.°°°° of new adoptionsnew adoptionsnew adoptionsnew adoptions in %%%% of the marketmarketmarketmarket
is given by following y t function of t
y t
2 3 4 546
2 3 4 546 !
where
- for x t 1 GBM convergesGBM convergesGBM convergesGBM converges to standard Bass Modelstandard Bass Modelstandard Bass Modelstandard Bass Model, for x t > 1 adoption processadoption processadoption processadoption process is
acceleratedacceleratedacceleratedaccelerated over time and x t < 1 adoption processadoption processadoption processadoption process is delayeddelayeddelayeddelayed
- iiiincreasencreasencreasencrease of n.n.n.n.°°°° of new adoptionsnew adoptionsnew adoptionsnew adoptions in %%%% of the marketmarketmarketmarket is equal to
y’ t
# #!$ % 2 3 4 546
$ 2 3 4 546 !#
%
3333
1111 1a1a1a1a 1b1b1b1b

A Stochastic Version of Bass ModelA Stochastic Version of Bass ModelA Stochastic Version of Bass ModelA Stochastic Version of Bass Model
10
For mathematical
11-12-13-14-15
For mathematical
derivation see
Annex 08-09-10-
11-12-13-14-15
fdrose14@gmail.com
Bass ModelBass ModelBass ModelBass Model ---- GraphicsGraphicsGraphicsGraphics
A StochasticA StochasticA StochasticA Stochastic Version of BassVersion of BassVersion of BassVersion of Bass ModelModelModelModel withwithwithwith
Market Potential “m”Market Potential “m”Market Potential “m”Market Potential “m”
A StochasticA StochasticA StochasticA Stochastic Version of BassVersion of BassVersion of BassVersion of Bass ModelModelModelModel withwithwithwith
Market Potential “m”Market Potential “m”Market Potential “m”Market Potential “m”
• A stochasticstochasticstochasticstochastic version of Bass ModelBass ModelBass ModelBass Model with marketmarketmarketmarket
potentialpotentialpotentialpotential m is given by following equationequationequationequation:
0 Time t
8888Expected value of n.° of
new adoptions
m
7777
dz p q
z
m
m z dt c
p
q
z
m
dW
2222
4444
≈
z
<

=%
% =>
!$ 2

=%
% 4 =>4
ds6
- m
#
$
E z m

e !
• SolutionSolutionSolutionSolution of stochasticstochasticstochasticstochastic BassBassBassBass ModelModelModelModel version with zA 0 representing time evolutiontime evolutiontime evolutiontime evolution of n.n.n.n.°°°° of newnewnewnew
adoptionsadoptionsadoptionsadoptions is given by following z t random variable function of t whose expected value is E z :
where
- p q
z
m
m z dt almost coincidescoincidescoincidescoincides with
standard Bass Modelstandard Bass Modelstandard Bass Modelstandard Bass Model equationequationequationequation
- c
p
q
z
m dW represents the random impactrandom impactrandom impactrandom impact
brought by product entryproduct entryproduct entryproduct entry policypolicypolicypolicy
-
p
q
z
m
is productproductproductproduct entryentryentryentry policy effectpolicy effectpolicy effectpolicy effect
- c and WB is respectively the noise parameternoise parameternoise parameternoise parameter
and a standard Brownianstandard Brownianstandard Brownianstandard Brownian motionmotionmotionmotion
4a4a4a4a
8888
5555

Overview of BassOverview of BassOverview of BassOverview of Bass ModelModelModelModel Major Versions andMajor Versions andMajor Versions andMajor Versions and
Extensions (1/4)Extensions (1/4)Extensions (1/4)Extensions (1/4)
11
fdrose14@gmail.com
VersVersVersVers ----
ExtExtExtExt
ExtExtExtExt
Solution ySolution ySolution ySolution y----z,z,z,z, InflectionInflectionInflectionInflection
Point y* andPoint y* andPoint y* andPoint y* and OtherOtherOtherOther
EquationEquationEquationEquation DescriptionDescriptionDescriptionDescription
y′
q y 1 – y ,

1 y 1 σ
Sharif /
Kabir (‘76)
• 0≤ F ≤ 1
• y∗ 0.33 – 0.50
Internal-influence
model
y′ q y Ln
1
y
Gompertz • y e
L
• y* 0.37
Internal-influence
model for small /
closed social systems
y′ q y 1 – yMansfield
(‘61)
• y
1
1 L
• y* 0.50
Internal-influence
model
y′ q y 1 – y ,Floyd
(‘62)
Internal-influence
model
• na
• y* 0.33
y′
q
P
yP
1 y QVon
Bertalanf.
(‘57)
Internal-influence
model
• θ ≥ 0
• y* 0.00 1.00
y′ q y 1 yTNelder
(‘62)
Internal-influence
model
• y
1
1 ϕ L V/X
• y∗ 0.00 1.00
z′ p q
z
m
m z g P tRobinson
/ Lakhani
(‘75)
Mixed-influence model
incorporating the
effect of price
• P t is price at time t

Extensions (Extensions (Extensions (Extensions (2222/4)/4)/4)/4)
12
fdrose14@gmail.com
ExtExtExtExt
ExtExtExtExt
y′ p q y 1 y ![Jeuland
(‘80)
• γ ≥ 0
• y∗ 0.00 – 0.50
y′ q y]
1 yNSRL (‘81) • na
• y∗ 0.00 1.00
Internal-influence
model
Sharif /
Ramanna
-than (‘81)
• Mixed-influence
model
• Dynamic model
where market
potential m is a
function of time
z′ p q
z t
m t
m t z
where m t mAe^B
z mAe^B

XV X%
%
T_
XV X%
%
XV
q qT_
XV
where ϕ g p q , 4pq
ϕ, g p q
ϕ`
XV X%
%

a6
b6
XV X%
%
!
a6
b6
with 0 < zA ≤ mA
Norton /
Bass (‘82)
• Mixed-influence
model
• Diffusion of
successive
generations of
technology
A three generation model
• z t y t m 1 y, t τ,
• z, t y, t τ,
m, y t m 1 y` t τ`
• z` t y` t τ`
m` y, t τ, m, y t m
where i-th generation is
introduced at τe and ye t τe
0 for t < τe
ye′ p q ye 1 ye
where i 1,2,…,n is
technology generation

Extensions (3/4)Extensions (3/4)Extensions (3/4)Extensions (3/4)
13
fdrose14@gmail.com
ExtExtExtExt
ExtExtExtExt
Solution ySolution ySolution ySolution y----z, Inflectionz, Inflectionz, Inflectionz, Inflection
Point y* and OtherPoint y* and OtherPoint y* and OtherPoint y* and Other
y′
q
t
y 1 yStanford
Research
Inst. (‘86)
Internal-influence
model
• y
1
!
g^
• y∗ 0.00 – 0.50
• T^
time of 50%
penetration
y′ p q y]
1 yNUI (‘83) • na
• y∗ 0.00 1.00
z′ p q
z
m
m z
where p a b ln A
Horsky /
Simon
(‘83)
• Coefficient of innovation p is
a function of advertising A
incorporating the
effect of advertising
y′e pe qeye k δemym

mne
∗ 1 ye
with i 1,…,n
Multi-
country
and multi-
brands
models
(’87 -’15)
• Mixed-influence
model
• Cross-country /
brand diffusion
where new
adoptions in one
country / brand
have an impact on
new adoptions in
other countries /
brands
• Representation for
country / brand i
• opq represents cross-country
/ brand effects between
country / brand i and
country / brand j

Extensions (Extensions (Extensions (Extensions (4444/4)/4)/4)/4)
14
fdrose14@gmail.com
ExtExtExtExt
ExtExtExtExt
y′ q 1 kt /t
u tFLOG
(‘88)
Internal-influence
model
• y
1
1 L v,=
with c, q, μ and k constants
where
- t μ,k {[ 1 kt /t
]u

1}/μ with μ ≠ 0 and k ≠ 0
- t μ,k 1/k Ln 1 kt
with μ 0 and k ≠ 0
- t μ,k euB
1 /μ with μ ≠ 0
and k 0
-t μ,k t with μ 0 and k 0
• y∗ 0.00 1.00
Network -
Cellular
Automat.
- Agent
based
models
(’93 -’17)
• Mixed-influence
models
• Models have a
micro perspective
simulating diffusion
respectively among
nodes / cells /
agents through
codified rules and
criteria
• Various equations • Various solutions and
information

• Theoretical Framework underlying Innovation Diffusion
• Estimation of Parameters within Bass ModelEstimation of Parameters within Bass ModelEstimation of Parameters within Bass ModelEstimation of Parameters within Bass Model
• Application of Bass Model to Top 20 US Drug Sales
Projections
• Annex
15
fdrose14@gmail.com

Bass Model Parameter Estimation ApproachBass Model Parameter Estimation ApproachBass Model Parameter Estimation ApproachBass Model Parameter Estimation Approach
16
fdrose14@gmail.com
Introduction to BassIntroduction to BassIntroduction to BassIntroduction to Bass Model ParameterModel ParameterModel ParameterModel Parameter Estimation ApproachEstimation ApproachEstimation ApproachEstimation Approach
• In case the productproductproductproduct is NNNNot Already Availableot Already Availableot Already Availableot Already Available on the MarketMarketMarketMarket and has to be commerciallycommerciallycommerciallycommercially
launchedlaunchedlaunchedlaunched by a corporation, it is advisable to follow a MMMManagerial Approachanagerial Approachanagerial Approachanagerial Approach based both by
quantitativequantitativequantitativequantitative proceduresproceduresproceduresprocedures and qualitative valuationsqualitative valuationsqualitative valuationsqualitative valuations and defined by the stepsstepsstepssteps shown below:
- iiiidentificationdentificationdentificationdentification of “innovative” productsinnovative” productsinnovative” productsinnovative” products which are analogousanalogousanalogousanalogous to the current productcurrent productcurrent productcurrent product
(analogies based on similarities in expected market behavior work better than analogies
based on product similarities)
- eeeestimationstimationstimationstimation of parametersparametersparametersparameters p and q from past datapast datapast datapast data relative to analogous “innovative”innovative”innovative”innovative”
productsproductsproductsproducts (i.e. consider a basket of products analogous and take the average)
- eeeestimationstimationstimationstimation of parameterparameterparameterparameter m relative to product market potentialmarket potentialmarket potentialmarket potential through qualitativequalitativequalitativequalitative
judgementjudgementjudgementjudgement
• In case the productproductproductproduct is Already AvailableAlready AvailableAlready AvailableAlready Available on the MarketMarketMarketMarket and has been commercially launchedcommercially launchedcommercially launchedcommercially launched
by a corporation, it is possible to follow two different approachestwo different approachestwo different approachestwo different approaches shown below:
aa
bb
cc
- Machine ApproachMachine ApproachMachine ApproachMachine Approach completelycompletelycompletelycompletely based on
quantitative proceduresquantitative proceduresquantitative proceduresquantitative procedures and defined by
the stepsstepsstepssteps shown below:
- detectiondetectiondetectiondetection of past datapast datapast datapast data retrieved
during productproductproductproduct early lifeearly lifeearly lifeearly life
- quantitative estimationquantitative estimationquantitative estimationquantitative estimation of p, q and m
parametersparametersparametersparameters based on the above pastpastpastpast
datadatadatadata
1111
2222
dd
ee
- Managerial ApproachManagerial ApproachManagerial ApproachManagerial Approach defined by the
stepsstepsstepssteps shown below:
- detectiondetectiondetectiondetection of past datapast datapast datapast data retrieved
during productproductproductproduct early lifeearly lifeearly lifeearly life
- estimationestimationestimationestimation of m through qualitativequalitativequalitativequalitative
judgementjudgementjudgementjudgement
- quantitative estimationquantitative estimationquantitative estimationquantitative estimation of p and q
parametersparametersparametersparameters based on the above
past datapast datapast datapast data
2a2a2a2a 2b2b2b2b
ff
gg
hh
Bass Model parameter estimationBass Model parameter estimationBass Model parameter estimationBass Model parameter estimation is approached differentlydifferentlydifferentlydifferently according to the phasephasephasephase of life cyclelife cyclelife cyclelife cycle in
which the product currently staysproduct currently staysproduct currently staysproduct currently stays

Bass Model Parameter Quantitative EstimationBass Model Parameter Quantitative EstimationBass Model Parameter Quantitative EstimationBass Model Parameter Quantitative Estimation
Methodology and ProceduresMethodology and ProceduresMethodology and ProceduresMethodology and Procedures
17
fdrose14@gmail.com
Bass Model ParameterBass Model ParameterBass Model ParameterBass Model Parameter
Quant.Quant.Quant.Quant. EstimatEstimatEstimatEstimat. Procedures. Procedures. Procedures. Procedures
Bass Model ParameterBass Model ParameterBass Model ParameterBass Model Parameter
Quant.Quant.Quant.Quant. EstimatEstimatEstimatEstimat. Procedures. Procedures. Procedures. Procedures
• In case the productproductproductproduct is Not Already AvailableNot Already AvailableNot Already AvailableNot Already Available
- estimationestimationestimationestimation of parametersparametersparametersparameters p and q from pastpastpastpast
datadatadatadata relative to analogous “innovative” productsinnovative” productsinnovative” productsinnovative” products
Bass ModelBass ModelBass ModelBass Model ParameterParameterParameterParameter QuantitativeQuantitativeQuantitativeQuantitative
EstimationEstimationEstimationEstimation MethodologyMethodologyMethodologyMethodology
Bass ModelBass ModelBass ModelBass Model ParameterParameterParameterParameter QuantitativeQuantitativeQuantitativeQuantitative
EstimationEstimationEstimationEstimation MethodologyMethodologyMethodologyMethodology
• In case the productproductproductproduct is
Already availableAlready availableAlready availableAlready available withwithwithwith
Machine ApproachMachine ApproachMachine ApproachMachine Approach
- estimationestimationestimationestimation of p, q
and m parametersparametersparametersparameters
based on pastpastpastpast
datadatadatadata retrieved
during productproductproductproduct
earlyearlyearlyearly lifelifelifelife
Accomplished retrievingretrievingretrievingretrieving
estimatesestimatesestimatesestimates of p and q
from data basedata basedata basedata base made
available by business
information providers
Accomplished
usingusingusingusing one of
the followingfollowingfollowingfollowing
proceduresproceduresproceduresprocedures
• The most popularmost popularmost popularmost popular proceduresproceduresproceduresprocedures
used to estimateestimateestimateestimate Bass modelBass modelBass modelBass model
parametersparametersparametersparameters are based on:
- linear regression analysislinear regression analysislinear regression analysislinear regression analysis
coupled with ordinaryordinaryordinaryordinary leastleastleastleast
squaressquaressquaressquares (OLS) method
- maximum likelihood estimationmaximum likelihood estimationmaximum likelihood estimationmaximum likelihood estimation
(MLE) method
- Non linear regression analysisNon linear regression analysisNon linear regression analysisNon linear regression analysis
coupled with least squaresleast squaresleast squaresleast squares (NLS)
method
• Other proceduresproceduresproceduresprocedures used to
estimateestimateestimateestimate Bass model parametersBass model parametersBass model parametersBass model parameters
are based on:
- mix usemix usemix usemix use of the above linearlinearlinearlinear
regression analysisregression analysisregression analysisregression analysis / ordinary/ ordinary/ ordinary/ ordinary
least squaresleast squaresleast squaresleast squares (OLS) method with
nnnnonononon linear regression analysislinear regression analysislinear regression analysislinear regression analysis /
least squaresleast squaresleast squaresleast squares
- Algebraic estimationAlgebraic estimationAlgebraic estimationAlgebraic estimation (AE)
method
- Genetic algorithmGenetic algorithmGenetic algorithmGenetic algorithm (GA) method
- Difference equationDifference equationDifference equationDifference equation (DE)
method through Bass model
discretization
1111
bb
2a2a2a2a
Accomplished usingusingusingusing one of the
following proceduresfollowing proceduresfollowing proceduresfollowing procedures
ee
• In case the productproductproductproduct is
Already availableAlready availableAlready availableAlready available withwithwithwith
Managerial ApproachManagerial ApproachManagerial ApproachManagerial Approach
- estimationestimationestimationestimation of p
and q parametersparametersparametersparameters
based on pastpastpastpast
datadatadatadata retrieved
during productproductproductproduct
earlyearlyearlyearly lifelifelifelife
2b2b2b2b
hh

Linear Regression AnalysisLinear Regression AnalysisLinear Regression AnalysisLinear Regression Analysis andandandand OrdinaryOrdinaryOrdinaryOrdinary
Least SquaresLeast SquaresLeast SquaresLeast Squares (OLS) M(OLS) M(OLS) M(OLS) Method (1/3)ethod (1/3)ethod (1/3)ethod (1/3)
18
fdrose14@gmail.com
Linear Regression Analysis and Ordinary Least Squares (OLS) methodLinear Regression Analysis and Ordinary Least Squares (OLS) methodLinear Regression Analysis and Ordinary Least Squares (OLS) methodLinear Regression Analysis and Ordinary Least Squares (OLS) method ----
IntroductionIntroductionIntroductionIntroduction
Linear Regression Analysis and Ordinary Least Squares (OLS) methodLinear Regression Analysis and Ordinary Least Squares (OLS) methodLinear Regression Analysis and Ordinary Least Squares (OLS) methodLinear Regression Analysis and Ordinary Least Squares (OLS) method ----
• RegressionRegressionRegressionRegression analysisanalysisanalysisanalysis is a statistical processstatistical processstatistical processstatistical process for estimatingestimatingestimatingestimating the relationshiprelationshiprelationshiprelationship among
variablesvariablesvariablesvariables given N random observationsrandom observationsrandom observationsrandom observations sampling from the populationspopulationspopulationspopulations as shown
below:
• OLSOLSOLSOLS allows to generate an estimationestimationestimationestimation of the above linear relationshipabove linear relationshipabove linear relationshipabove linear relationship or in other words to
produce an estimationestimationestimationestimation of the above parameters minimizingabove parameters minimizingabove parameters minimizingabove parameters minimizing the sumsumsumsum of the squaredsquaredsquaredsquared
distancesdistancesdistancesdistances between the observed dataobserved dataobserved dataobserved data of the dependent variabledependent variabledependent variabledependent variable and the predicted datapredicted datapredicted datapredicted data – by
the linear regression model – of the dependent variabledependent variabledependent variabledependent variable
• The linearlinearlinearlinear regression modelregression modelregression modelregression model assumes a linearlinearlinearlinear –––– with respect to parameterswith respect to parameterswith respect to parameterswith respect to parameters ---- relationshiprelationshiprelationshiprelationship
between a dependent variabledependent variabledependent variabledependent variable (or criterion variable) and an independent variableindependent variableindependent variableindependent variable (or
covariate or regressor or explanatory variable)
• In a multiple linear regression modellinear regression modellinear regression modellinear regression model a dependent variabledependent variabledependent variabledependent variable and a setsetsetset of independentindependentindependentindependent
variablesvariablesvariablesvariables are considered
Y f X, β + ε
• The preliminary stepThe preliminary stepThe preliminary stepThe preliminary step before introducing the concept of regression, linear regression and OLS is
the definitiondefinitiondefinitiondefinition of the equation describingequation describingequation describingequation describing the relationshiprelationshiprelationshiprelationship between variablesvariablesvariablesvariables
belonging to certain populationscertain populationscertain populationscertain populations as shown below:
where Y is a dependentdependentdependentdependent randomrandomrandomrandom variablevariablevariablevariable, X is an independentindependentindependentindependent deterministicdeterministicdeterministicdeterministic
Ye βA+β Xe +β,Xe, ⋯ β#Xe# εe where i 1,…,N
Ye f Xe, β + εe where i 1,…,N
min SSE ∑ εe† ,‡
eˆ ∑ Ye Ye
‰ ,‡
eˆ where Ye
‰ βA
Š+βŠXe +β,
ŠXe, ⋯ β#
ŠXe#
mathematicalFor mathematical
derivation see
Annex 16-17
variablevariablevariablevariable, β is a parameterparameterparameterparameter and ε is a randomrandomrandomrandom error variableerror variableerror variableerror variable

Linear Regression AnalysisLinear Regression AnalysisLinear Regression AnalysisLinear Regression Analysis andandandand OrdinaryOrdinaryOrdinaryOrdinary
Least SquaresLeast SquaresLeast SquaresLeast Squares (OLS) M(OLS) M(OLS) M(OLS) Method (2/3ethod (2/3ethod (2/3ethod (2/3))))
19
fdrose14@gmail.com
Linear Regression Analysis andLinear Regression Analysis andLinear Regression Analysis andLinear Regression Analysis and OLSOLSOLSOLS methodmethodmethodmethod –––– Application to Bass ModelApplication to Bass ModelApplication to Bass ModelApplication to Bass Model
z′ t pm p q z
q
m
z,
2222
‹ ‹ V
B B
pm p q zB
$
m
zB
,
zŒ
B a b zB c zB
,
where a pm, b q - p and c
$
m
• DiscretizationDiscretizationDiscretizationDiscretization of the above equationabove equationabove equationabove equation
zŒ
t pm q p zB
q
m
zB
,
• SubstitutionSubstitutionSubstitutionSubstitution and algebra manipulationalgebra manipulationalgebra manipulationalgebra manipulation
• DetectionDetectionDetectionDetection of """"populationpopulationpopulationpopulation"""" equation zŒ
= a b z c z, ε
• DetectionDetectionDetectionDetection of "OLS"OLS"OLS"OLS estimatedestimatedestimatedestimated dependentdependentdependentdependent variablevariablevariablevariable"""" zŒ
B
Š = a• bŽ z ,B c• z,,B where t tA ,…,T
• Receipt of Bass Model equationBass Model equationBass Model equationBass Model equation including
market potential
zB zB pm p q zB
q
m
zB
,
min SSE a•, bŽ, c• ∑ zŒ
B zŒ
B
Š ,
•
BˆB6
∑ zŒ
B a• bŽ z ,B c• z,,B
,•
BˆB6
• EstimationEstimationEstimationEstimation of BassBassBassBass model parametersmodel parametersmodel parametersmodel parameters is accomplished by findingfindingfindingfinding a•, bŽ and c• which are able to
zŒ
B a b z ,B c z,,B after replacing firstly zB
,
z,,B• then zB z ,B and z,,B• z,,B
z ,B
z ,,B
0
zŒ
B
zŒ
B
Š
zŒ
B Š a• bŽ z ,B c• z,,B
k zŒ
B zŒ
B
Š ,
•
BˆB6
zŒ
B a b z ,B c z,,B εB
• DetectionDetectionDetectionDetection of "regression""regression""regression""regression" equation zŒ
B = a b z ,B c z,,B εB where t tA ,…,T
derivation see
Annex 16-17

Linear Regression Analysis and OrdinaryLinear Regression Analysis and OrdinaryLinear Regression Analysis and OrdinaryLinear Regression Analysis and Ordinary
Least Squares (OLS)Least Squares (OLS)Least Squares (OLS)Least Squares (OLS) Method (3/3Method (3/3Method (3/3Method (3/3))))
20
fdrose14@gmail.com
bŽ
∑ ‹5
‹5
‹V, ‹V ∑ ‹%, ‹%
%g
‘ 6
∑ ‹5
‹5
‹%, ‹%
g
‘ 6
∑ ‹V, ‹V ‹%, ‹%
g
‘ 6
g
‘ 6
∑ ‹V, ‹V
%g
‘ 6
∑ ‹%, ‹%
%g
‘ 6
∑ ‹V, ‹V ‹%, ‹%
g
‘ 6
%
c•
∑ ‹5
‹5
‹%, ‹% ∑ ‹V, ‹V
%g
‘ 6
∑ ‹5
‹5
‹V, ‹V
g
‘ 6
∑ ‹V, ‹V ‹%, ‹%
g
‘ 6
g
‘ 6
∑ ‹V, ‹V
%g
‘ 6
∑ ‹%, ‹%
%g
‘ 6
∑ ‹V, ‹V ‹%, ‹%
g
‘ 6
%
a• zŒ
- bŽ z - c• z,
Linear Regression Analysis and OLS methodLinear Regression Analysis and OLS methodLinear Regression Analysis and OLS methodLinear Regression Analysis and OLS method –––– Bass Model ParameterBass Model ParameterBass Model ParameterBass Model Parameter
EstimationEstimationEstimationEstimation
Linear Regression Analysis and OLS methodLinear Regression Analysis and OLS methodLinear Regression Analysis and OLS methodLinear Regression Analysis and OLS method –––– Bass Model ParameterBass Model ParameterBass Model ParameterBass Model Parameter
EstimationEstimationEstimationEstimation
• MinimizationMinimizationMinimizationMinimization of SSESSESSESSE allows to find optimaloptimaloptimaloptimal a•, bŽ and c•
• In the light of the factfactfactfact that (see previous slide) a pm, b q - p and c
$
m
, it easily followsfollowsfollowsfollows
that – mc q and
’
m
p. Then it descendsdescendsdescendsdescends that q – p - mc -
’
m
b and that cm,
bm a 0
• SolvingSolvingSolvingSolving the above equationequationequationequation, it easily followsfollowsfollowsfollows that m
“” “% .’•
,•
and so q - c
“” “% .’•
,•
and p a
“” “% .’•
,•
• EstimationEstimationEstimationEstimation of Bass modelBass modelBass modelBass model parametersparametersparametersparameters is so given by
m –B
“‰” “‰% .’•••
,••
q –B - c•
“‰” “‰% .’•••
,••
p –B a•
“‰” “‰% .’•••
,••
where zŒ
, z and z, are averageaverageaverageaverage valuesvaluesvaluesvalues with respect to timetimetimetime
derivation see
Annex 16-17

Non LinearNon LinearNon LinearNon Linear Regression Analysis andRegression Analysis andRegression Analysis andRegression Analysis and LeastLeastLeastLeast SquaresSquaresSquaresSquares
(NLS(NLS(NLS(NLS)))) Method (1/3)Method (1/3)Method (1/3)Method (1/3)
21
fdrose14@gmail.com
Non Linear Regression Analysis and Least SquaresNon Linear Regression Analysis and Least SquaresNon Linear Regression Analysis and Least SquaresNon Linear Regression Analysis and Least Squares (NLS(NLS(NLS(NLS) method) method) method) method ––––
Ye f Xe , Xe,, … , Xe#; βA, β , … , βt + εe
• The nonnonnonnon-linearlinearlinearlinear regressionregressionregressionregression modelmodelmodelmodel assumes a nonnonnonnon-linearlinearlinearlinear –––– with respect to parameterswith respect to parameterswith respect to parameterswith respect to parameters ----
relationshiprelationshiprelationshiprelationship between a dependent variabledependent variabledependent variabledependent variable (or criterion variable) and an independentindependentindependentindependent
variablevariablevariablevariable (or covariate or regressor or explanatory variable)
• In a multiple nonnonnonnon----linearlinearlinearlinear regression modelregression modelregression modelregression model a dependent variabledependent variabledependent variabledependent variable and a setsetsetset of independentindependentindependentindependent
variablesvariablesvariablesvariables are considered
• Non linear least squaresNon linear least squaresNon linear least squaresNon linear least squares (on beyond NLSNLSNLSNLS) allows to generate an estimationestimationestimationestimation of the above nonabove nonabove nonabove non----
linear relationshiplinear relationshiplinear relationshiplinear relationship or in other words to produce an estimationestimationestimationestimation of the above parametersabove parametersabove parametersabove parameters
minimizingminimizingminimizingminimizing the sumsumsumsum of the squared distancessquared distancessquared distancessquared distances between the observed dataobserved dataobserved dataobserved data of the dependentdependentdependentdependent
variablevariablevariablevariable Ye and the predicted datapredicted datapredicted datapredicted data – by the non-linear regression model – of the dependentdependentdependentdependent
variablevariablevariablevariable Ye
‰
min SSE ∑ Ye Ye
‰ ,‡
eˆ where Ye
‰ f Xe , Xe,, … , Xe#; βA
Š, βŠ, … , βt
Š
where i 1,…,N are the N random observationsrandom observationsrandom observationsrandom observations sampling from the populationspopulationspopulationspopulations, p is the
numbernumbernumbernumber of independent variablesindependent variablesindependent variablesindependent variables and k is the numbernumbernumbernumber of parametersparametersparametersparameters
• The above squared distancessquared distancessquared distancessquared distances are also defined as the residualsresidualsresidualsresiduals εe† or in other terms the
differencesdifferencesdifferencesdifferences between the sample datasample datasample datasample data Ye of the dependent variabledependent variabledependent variabledependent variable and the relativerelativerelativerelative
fitted valuesfitted valuesfitted valuesfitted values Ye
‰ as shown below
εe† Ye Ye
‰ where i 1,…,N

(NLS(NLS(NLS(NLS)))) Method (Method (Method (Method (2222/3)/3)/3)/3)
22
fdrose14@gmail.com
Application to Bass ModelApplication to Bass ModelApplication to Bass ModelApplication to Bass Model
Application to Bass ModelApplication to Bass ModelApplication to Bass ModelApplication to Bass Model
• DetectionDetectionDetectionDetection of """"populationpopulationpopulationpopulation"""" equation
z m

e !
ε
• DetectionDetectionDetectionDetection of "NLS"NLS"NLS"NLS estimatedestimatedestimatedestimated dependentdependentdependentdependent variable"variable"variable"variable"
z
B
˜ m†
† †

†
†
e † † !
where t t™, … , T
• Receipt of Bass Model equationBass Model equationBass Model equationBass Model equation solutionsolutionsolutionsolution including
market potential z t m

e !
• EstimationEstimationEstimationEstimation of BassBassBassBass model parametersmodel parametersmodel parametersmodel parameters is
accomplished by findingfindingfindingfinding m†, p† and q• able to
• DetectionDetectionDetectionDetection of "regression""regression""regression""regression" equation
z
t m

e !
εB
where t t™, … , T
min SSE p•, q•, m† ∑ z
B
z
B
˜
,•
BˆB™
with z
B
˜ m†
† †

†
†
e † † !
Note: An alternative approach is given by this regression equation zŒ t m

e !
V
e V !
εB
• There’s no explicit formulano explicit formulano explicit formulano explicit formula for parametersparametersparametersparameters p•, q• and m† which minimise SSEminimise SSEminimise SSEminimise SSE but there’s
possibilitypossibilitypossibilitypossibility to use LevenbergLevenbergLevenbergLevenberg----MarquardtMarquardtMarquardtMarquardt searchsearchsearchsearch patternpatternpatternpattern
0 Time t
z
B
z
B
˜
m
z
B
˜ m†
1 e #†!$† B

q•
p•
e #†!$† B 1
k z
B z
B
˜
,
•
BˆB6
z t m
1 e #!$ B

q
p
e #!$ B 1
εB

(NLS(NLS(NLS(NLS)))) Method (3/3)Method (3/3)Method (3/3)Method (3/3)
23
fdrose14@gmail.com
Non Linear Regression Analysis and Least SquaresNon Linear Regression Analysis and Least SquaresNon Linear Regression Analysis and Least SquaresNon Linear Regression Analysis and Least Squares (NLS(NLS(NLS(NLS) method) method) method) method ----
NumericNumericNumericNumeric optimization algorithmoptimization algorithmoptimization algorithmoptimization algorithm
Non Linear Regression Analysis and Least SquaresNon Linear Regression Analysis and Least SquaresNon Linear Regression Analysis and Least SquaresNon Linear Regression Analysis and Least Squares (NLS(NLS(NLS(NLS) method) method) method) method ----
NumericNumericNumericNumeric optimization algorithmoptimization algorithmoptimization algorithmoptimization algorithm
• Lack of an explicitexplicitexplicitexplicit formulaformulaformulaformula for parametersparametersparametersparameters p•, q• and m† which minimise SSEminimise SSEminimise SSEminimise SSE is mainly due to the
fact that derivativesderivativesderivativesderivatives of SSE p•, q•, m† are not linearnot linearnot linearnot linear within the above parametersabove parametersabove parametersabove parameters
• Levenberg / MarquardtLevenberg / MarquardtLevenberg / MarquardtLevenberg / Marquardt SearchSearchSearchSearch PatternPatternPatternPattern is a numeric optimization algorithmnumeric optimization algorithmnumeric optimization algorithmnumeric optimization algorithm which linearizeslinearizeslinearizeslinearizes
the SSE derivativederivativederivativederivative equationsequationsequationsequations and puts in place an iterative processiterative processiterative processiterative process as shown – on a generalgeneralgeneralgeneral
basisbasisbasisbasis – in the below steps:
- DefinitionDefinitionDefinitionDefinition of optimization problem on a general basisgeneral basisgeneral basisgeneral basis
min
š‰
SSE ∑ εe† ,‡
eˆ ∑ Ye Ye
‰ ,‡
eˆ ∑ Ye f Xe, βŽ ,‡
eˆ
- IgnitionIgnitionIgnitionIgnition of iiiiterationterationterationteration providing an initialinitialinitialinitial guessguessguessguess for parameter vectorparameter vectorparameter vectorparameter vector β
- SubstitutionSubstitutionSubstitutionSubstitution of parameter vectorparameter vectorparameter vectorparameter vector βŽ with a new estimatenew estimatenew estimatenew estimate βŽ o at each iterationeach iterationeach iterationeach iteration step
- DeterminationDeterminationDeterminationDetermination of o is gained by minimizationminimizationminimizationminimization of a “linearized” versionlinearized” versionlinearized” versionlinearized” version of the above
optimizationoptimizationoptimizationoptimization problem
min
]
SSE› ≈ ∑ Ye f Xe, βŽ
œ• žŸ,š‰
œš‰ δ
,
‡
eˆ or in vector notation Y f βŽ Jδ
•
Y f βŽ Jδ
where SSESSESSESSE reaches its minimumminimumminimumminimum when its gradientits gradientits gradientits gradient is equal to zerozerozerozero
where putting derivativesderivativesderivativesderivatives of SSE› equal to zeroequal to zeroequal to zeroequal to zero it follows a set of linear equationslinear equationslinear equationslinear equations J•
J δ
J•
Y f βŽ which can be solvedsolvedsolvedsolved by δ
- Search pattern performanceSearch pattern performanceSearch pattern performanceSearch pattern performance is augmentedaugmentedaugmentedaugmented adding the termtermtermterm λ diag J•
J as it follows
J•
J λ diag J•
J δ J•
Y f βŽ

Maximum Likelihood Estimation ProcedureMaximum Likelihood Estimation ProcedureMaximum Likelihood Estimation ProcedureMaximum Likelihood Estimation Procedure
24
fdrose14@gmail.com
MLE MethodMLE MethodMLE MethodMLE Method ---- DescriptionDescriptionDescriptionDescription
• MLE procedureMLE procedureMLE procedureMLE procedure is a statistical processstatistical processstatistical processstatistical process for estimatingestimatingestimatingestimating the parametersparametersparametersparameters of a populationpopulationpopulationpopulation which –
given observed datagiven observed datagiven observed datagiven observed data – finds those parameter valuesparameter valuesparameter valuesparameter values able to maximizemaximizemaximizemaximize the likelihoodlikelihoodlikelihoodlikelihood of
makingmakingmakingmaking the above observationsabove observationsabove observationsabove observations
• Application of MLEMLEMLEMLE aimed at estimating Bass Model parametersestimating Bass Model parametersestimating Bass Model parametersestimating Bass Model parameters follows below steps:
- DefinitionDefinitionDefinitionDefinition of unconditional probabilityunconditional probabilityunconditional probabilityunconditional probability for adoption by time tadoption by time tadoption by time tadoption by time t as
L a, b, c, zŒ
te 1 F t•
‹5 B g ∏ F te F te
‹5 B Ÿ•
eˆ where i 1, … , T
y t c
¤
’ ¤ !
where a
#
$
, b p q, c probability of eventually adopting m/M, M total
number of potential adopters
- DefinitionDefinitionDefinitionDefinition of likelihood function L as
where zŒ
te is the observedobservedobservedobserved numbernumbernumbernumber of individualsindividualsindividualsindividuals who adoptadoptadoptadopt the innovationinnovationinnovationinnovation in time intervaltime intervaltime intervaltime interval
te , te with i 1,…, T
l zŒ
t • ln 1 c
1 e “ •
a e “ • 1
k zŒ
t e ln c ln
1 e “BŸ
a e “BŸ 1
1 e “BŸ V
a e “BŸ V 1
•
eˆ
- CalculationCalculationCalculationCalculation of likelihood function L loglogloglog, l a, b, c, zŒ
te - where i 1, … , T as
- There’s no explicit formulano explicit formulano explicit formulano explicit formula for parametersparametersparametersparameters a•, bŽ and c• which maximisemaximisemaximisemaximise l but there’s possibilitypossibilitypossibilitypossibility
to use HookeHookeHookeHooke––––Jeeves’Jeeves’Jeeves’Jeeves’ accelerated searchsearchsearchsearch patternpatternpatternpattern

• Application of Bass Model to Top 20 US Drug SalesApplication of Bass Model to Top 20 US Drug SalesApplication of Bass Model to Top 20 US Drug SalesApplication of Bass Model to Top 20 US Drug Sales
ProjectionsProjectionsProjectionsProjections
- A Full 100% Machine ApproachA Full 100% Machine ApproachA Full 100% Machine ApproachA Full 100% Machine Approach
- A Managerial Approach
- Delta Consensus vs Bass Model within Machine and
Managerial Approach
• Annex
25
fdrose14@gmail.com
Fabiano De RosaFabiano De RosaFabiano De RosaFabiano De Rosa

• Past sales dataPast sales dataPast sales dataPast sales data on annualannualannualannual basis are normally
retrievedretrievedretrievedretrieved by manufacturer official annual reportofficial annual reportofficial annual reportofficial annual report or
press releasespress releasespress releasespress releases
• First year salesFirst year salesFirst year salesFirst year sales are proposed on a likelikelikelike----forforforfor----like basislike basislike basislike basis
in case drugdrugdrugdrug becomes commercially available notavailable notavailable notavailable not
immediatelyimmediatelyimmediatelyimmediately at 1111stststst of JanuaryJanuaryJanuaryJanuary
• Time lineTime lineTime lineTime line of forecast is fixed at 2022202220222022 and 2025202520252025
• ConsensusConsensusConsensusConsensus – by major equity investment banking
analyst estimates released in August 2016 - on salessalessalessales
figuresfiguresfiguresfigures at 2022202220222022 is presentedpresentedpresentedpresented
• EstimationEstimationEstimationEstimation of Bass modelBass modelBass modelBass model parametersparametersparametersparameters - p, q and m - for each drugdrugdrugdrug is
based on historical annual sales datahistorical annual sales datahistorical annual sales datahistorical annual sales data since commercial launchcommercial launchcommercial launchcommercial launch till
2016201620162016
• ProcedureProcedureProcedureProcedure to estimateestimateestimateestimate Bass modelBass modelBass modelBass model parametersparametersparametersparameters is based on nnnnonononon
linear regression analysislinear regression analysislinear regression analysislinear regression analysis coupled with least squaresleast squaresleast squaresleast squares (NLS) method
using cumulative salescumulative salescumulative salescumulative sales as dependent variabledependent variabledependent variabledependent variable
• FittingFittingFittingFitting capability of Bass modelBass modelBass modelBass model is represented by the coefficientcoefficientcoefficientcoefficient of
determinationdeterminationdeterminationdetermination R,
calculated with respect to cumulative salescumulative salescumulative salescumulative sales
variable (also an implied R,
with respect to salessalessalessales variable is provided)
ApplicationApplicationApplicationApplication of Bass Modelof Bass Modelof Bass Modelof Bass Model –––– Machine Approach toMachine Approach toMachine Approach toMachine Approach to
TopTopTopTop 20 US Drugs within Pharmaceutical20 US Drugs within Pharmaceutical20 US Drugs within Pharmaceutical20 US Drugs within Pharmaceutical SectorSectorSectorSector
26
fdrose14@gmail.com
List of Top 20 USList of Top 20 USList of Top 20 USList of Top 20 US
Drugs in 2016Drugs in 2016Drugs in 2016Drugs in 2016
List of Top 20 USList of Top 20 USList of Top 20 USList of Top 20 US
Drugs in 2016Drugs in 2016Drugs in 2016Drugs in 2016
• Bass ModelBass ModelBass ModelBass Model is used to forecastforecastforecastforecast the annual salesannual salesannual salesannual sales of a listlistlistlist of top 20top 20top 20top 20
US drugsUS drugsUS drugsUS drugs within pharmaceuticalpharmaceuticalpharmaceuticalpharmaceutical sector
• The above salesabove salesabove salesabove sales are relativerelativerelativerelative to a specific combinationspecific combinationspecific combinationspecific combination of one
manufacturermanufacturermanufacturermanufacturer and one drugdrugdrugdrug (i.e. there are cases in which a drug is
distributed by more than one manufacturer)
Bass Model Application with Machine ApproachBass Model Application with Machine ApproachBass Model Application with Machine ApproachBass Model Application with Machine Approach ----
HypothesisHypothesisHypothesisHypothesis
Bass Model Application with Machine ApproachBass Model Application with Machine ApproachBass Model Application with Machine ApproachBass Model Application with Machine Approach ----
HypothesisHypothesisHypothesisHypothesis
Humi Abb
Enbr Amg
Harv Gil
Remi Joh
Ritu Roc
Neul Amg
Lant San
Copa Tev
Eyle Reg
Tecf Bio
Lyri Pfi
Avas Roc
Opdi Bri
Herc Roc
Adva Gla
Truv Gil
Xare Joh
Stel Joh
Ibra Pfi
Eliq Bri
DrugDrugDrugDrug Manufac.Manufac.Manufac.Manufac.
JanuJanuJanuJanu, RevlRevlRevlRevl,
SpirSpirSpirSpir and
VictVictVictVict
are likely to
be in Top
20 US drugs
list but
figuresfiguresfiguresfigures are
notnotnotnot
availableavailableavailableavailable

Focus of Next SlidesFocus of Next SlidesFocus of Next SlidesFocus of Next Slides
Aggregated AnnualAggregated AnnualAggregated AnnualAggregated Annual SSSSales Trend 2016ales Trend 2016ales Trend 2016ales Trend 2016----2025202520252025 ofofofof TopTopTopTop
20 US20 US20 US20 US DrugsDrugsDrugsDrugs withinwithinwithinwithin Bass ModelBass ModelBass ModelBass Model----Machine ApproachMachine ApproachMachine ApproachMachine Approach
27
fdrose14@gmail.com
Aggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US Drugs
(KUSD; 2016-2025)
% Growth
16-25
CAGR
16-25
72'466'610
67'934'081
51'666'482
0
10'000'000
20'000'000
30'000'000
40'000'000
50'000'000
60'000'000
70'000'000
80'000'000
Sales 2016 Sales 2022 Sales 2025
-28.7% -3.7%

10'375
8'796'932
1'532'537
50'207
1'446'820
858'942
1'213'817
6'351'007
801'263
3'296'359
47'379
416'895
1'461'919
1'185'002
2'668'771
1'531'823
7'209'598
1'672
5'061'969
23’990’795
Annual Sales of Top 20 US Drugs 2016Annual Sales of Top 20 US Drugs 2016Annual Sales of Top 20 US Drugs 2016Annual Sales of Top 20 US Drugs 2016----2022 within2022 within2022 within2022 within
Bass ModelBass ModelBass ModelBass Model----Machine ApproachMachine ApproachMachine ApproachMachine Approach
28
fdrose14@gmail.com
Sales Bass ModelSales Bass ModelSales Bass ModelSales Bass ModelSales Bass ModelSales Bass ModelSales Bass ModelSales Bass Model
(KUSD; 2016)
(KUSD; 2022)
-1'952'625
6'728'932
-730'463
-2'237'793
-937'180
-1'602'261
-1'320'527
3'687'007
-2'192'676
157'359
-3'122'021
-2'906'105
-2'038'081
-2'721'218
-1'256'229
-2'418'682
2'367'598
-4'939'328
-657'031
13’558’795
%g%g%g%g%g%g%g%g
VariationVariationVariationVariationVariationVariationVariationVariation (KUSD; 2016-2022)
Delta SalesDelta SalesDelta SalesDelta SalesDelta SalesDelta SalesDelta SalesDelta Sales
Tot.Tot.Tot.Tot. 72’466’61072’466’61072’466’61072’466’61072’466’61072’466’61072’466’61072’466’610 ----4’532’5294’532’5294’532’5294’532’529----4’532’5294’532’5294’532’5294’532’529 ----6.3%6.3%6.3%6.3%----6.3%6.3%6.3%6.3% 67’934’08167’934’08167’934’08167’934’08167’934’08167’934’08167’934’08167’934’081
1'963'000
2'068'000
2'263'000
2'288'000
2'384'000
2'461'203
2'534'343
2'664'000
2'993'939
3'139'000
3'169'400
3'323'000
3'500'000
3'906'220
3'925'000
3'950'505
4'842'000
4'941'000
5'719'000
10’432’000
Eliq - Bri
Ibra - Pfi
Stel - Joh
Xare - Joh
Truv - Gil
Adva - Gla
Herc - Roc
Opdi - Bri
Avas - Roc
Lyri - Pfi
Tecf - Bio
Eyle - Reg
Copa - Tev
Lant - San
Neul - Amg
Ritu - Roc
Remi - Joh
Harv - Gil
Enbr - Amg
Humi - Abb
-99%
325%
-32%
-98%
-39%
-65%
-52%
138%
-73%
5%
-99%
-87%
-58%
-70%
-32%
-61%
49%
-100%
-11%
130%

1'446'820
-127'656
420'063
167'245
216'719
2'023'109
63'584
-261'522
5'061'598
510'771
-1'789'737
-1'639'463
-3'262'621
-3'555'793
-3'720'625
4'830'932
-4'597'105
-3'031
-870'993
13’261’795
0
129'327
438'879
1'017'757
1'245'200
1'273'250
1'468'239
1'475'339
2'148'000
2'158'000
2'591'000
3'172'000
3'310'000
3'606'000
3'731'000
3'966'000
5'014'000
5'065'000
7'222'000
10’729’000
Truv - Gil
Harv - Gil
Adva - Gla
Lant - San
Copa - Tev
Lyri - Pfi
Ritu - Roc
Herc - Roc
Remi - Joh
Neul - Amg
Avas - Roc
Stel - Joh
Tecf - Bio
Xare - Joh
Eliq - Bri
Ibra - Pfi
Eyle - Reg
Enbr - Amg
Opdi - Bri
Humi - Abb
na
-99%
96%
16%
17%
159%
4%
-18%
236%
24%
-69%
-52%
-99%
-99%
-100%
122%
-92%
0%
-12%
124%
1'446'820
1'672
858'942
1'185'002
1'461'919
3'296'359
1'531'823
1'213'817
7'209'598
2'668'771
801'263
1'532'537
47'379
50'207
10'375
8'796'932
416'895
5'061'969
6'351'007
23‘990‘795
ConsensusConsensusConsensusConsensus vs Bass Modelvs Bass Modelvs Bass Modelvs Bass Model –––– MachineMachineMachineMachine Approach onApproach onApproach onApproach on
AnnualAnnualAnnualAnnual Sales of Top 20 US DrugsSales of Top 20 US DrugsSales of Top 20 US DrugsSales of Top 20 US Drugs in 2022in 2022in 2022in 2022
29
fdrose14@gmail.com
Sales ConsensusSales ConsensusSales ConsensusSales ConsensusSales ConsensusSales ConsensusSales ConsensusSales Consensus
(KUSD; 2022)
(KUSD; 2022)%g%g%g%g%g%g%g%g
VariationVariationVariationVariationVariationVariationVariationVariation (KUSD; 2016-2022)
Delta SalesDelta SalesDelta SalesDelta SalesDelta SalesDelta SalesDelta SalesDelta Sales
Tot.Tot.Tot.Tot. 59’759’99259’759’99259’759’99259’759’99259’759’99259’759’99259’759’99259’759’992 8’174’0898’174’0898’174’0898’174’0898’174’0898’174’0898’174’0898’174’089 12%12%12%12%12%12%12%12% 67’934’08167’934’08167’934’08167’934’08167’934’08167’934’08167’934’08167’934’081

Next Slides OrderNext Slides OrderNext Slides OrderNext Slides Order
Positioning of Top 20 US Drugs in terms of ModelPositioning of Top 20 US Drugs in terms of ModelPositioning of Top 20 US Drugs in terms of ModelPositioning of Top 20 US Drugs in terms of Model
Deviation vs Consensus and Model ReliabilityDeviation vs Consensus and Model ReliabilityDeviation vs Consensus and Model ReliabilityDeviation vs Consensus and Model Reliability
30
fdrose14@gmail.com
Matrix crossing Delta Consensus vs Bass ModelMatrix crossing Delta Consensus vs Bass ModelMatrix crossing Delta Consensus vs Bass ModelMatrix crossing Delta Consensus vs Bass Model----MachineMachineMachineMachine Approach withApproach withApproach withApproach withMatrix crossing Delta Consensus vs Bass ModelMatrix crossing Delta Consensus vs Bass ModelMatrix crossing Delta Consensus vs Bass ModelMatrix crossing Delta Consensus vs Bass Model----MachineMachineMachineMachine Approach withApproach withApproach withApproach with
BassBassBassBass Model Reliability in terms of N.Model Reliability in terms of N.Model Reliability in terms of N.Model Reliability in terms of N.°°°° observationsobservationsobservationsobservations
Delta Consensus vs Bass ModelDelta Consensus vs Bass ModelDelta Consensus vs Bass ModelDelta Consensus vs Bass Model----Machine ApproachMachine ApproachMachine ApproachMachine Approach
High Medium-High Medium Low Very low
BassModelReliabilityintermsBassModelReliabilityintermsBassModelReliabilityintermsBassModelReliabilityinterms
ofnumberofobservationsofnumberofobservationsofnumberofobservationsofnumberofobservations
High
Medium
Low
Enbr - Amg
Ritu - Roc
Lant - San
Herc - Roc
Opdi - Bri
Harv - Gil
Neul - Amg
Adva - Gla
Copa - Tev
Tecf - Bio
Lyri - Pfi
Avas - Roc
Stel - Joh
Truv - Gil
Eyle - Reg
Eliq - Bri
Xare - Joh
Humi - Abb
Remi - Joh
Ibra - Pfi
1111
2222
3333
4444
5555
6666
7777
8888
9999
10101010
11111111
12121212
13131313
14141414
1515151517171717
16161616
18181818
19191919
20202020
………… = Ranking valuation
N.N.N.N.°°°° of observationsobservationsobservationsobservations means N.N.N.N.°°°° of
annual salesannual salesannual salesannual sales figures for a given drugdrugdrugdrug
N.N.N.N.°°°° of observationsobservationsobservationsobservations means N.N.N.N.°°°° of
annual salesannual salesannual salesannual sales figures for a given drugdrugdrugdrug
VariationVariationVariationVariation of salessalessalessales between
ConsensusConsensusConsensusConsensus and Bass Model at 20’22Bass Model at 20’22Bass Model at 20’22Bass Model at 20’22
VariationVariationVariationVariation of salessalessalessales between
ConsensusConsensusConsensusConsensus and Bass Model at 20’22Bass Model at 20’22Bass Model at 20’22Bass Model at 20’22
Drug positioning within
Bass Model – Mach. / App.

EnbrEnbrEnbrEnbr----AmgAmgAmgAmg Sales and Cumulative SalesSales and Cumulative SalesSales and Cumulative SalesSales and Cumulative Sales
31
fdrose14@gmail.com
Cumulative SalesCumulative SalesCumulative SalesCumulative SalesCumulative SalesCumulative SalesCumulative SalesCumulative Sales
(KUSD; 1998-2025)
SalesSalesSalesSalesSalesSalesSalesSales
(KUSD; 1998-2025)
m 129'781'653
p 0.603%
q 15.660%
Peak time in # years 21.0
Peak time in date 2'019
Peak point 5'468'857
^
^
^
Reg. date:
Nov 1998Nov 1998Nov 1998Nov 1998
Reg. date:
Nov 1998Nov 1998Nov 1998Nov 1998
2’022
1111
0
20'000'000
40'000'000
60'000'000
80'000'000
100'000'000
120'000'000
1'998 2'012 2'025
0
1'000'000
2'000'000
3'000'000
4'000'000
5'000'000
6'000'000
1'998 2'012 2'025
R, implied
94.273%
R, 99.652%
5’065’000
Consensus
5’061’969
Bass Model –
Machine Approach
Sales data
Actual Sales data
Bass Model – Machine Approach
Cumulative Sales data
Actual Cumulative Sales data

0
500'000
1'000'000
1'500'000
2'000'000
2'500'000
3'000'000
3'500'000
4'000'000
4'500'000
1'996 2'011 2'025
RituRituRituRitu----Roc Sales and Cumulative SalesRoc Sales and Cumulative SalesRoc Sales and Cumulative SalesRoc Sales and Cumulative Sales
32
fdrose14@gmail.com
(KUSD; 1996-2025)
(KUSD; 1996-2025)
m 61‘450‘744
p 0.439%
q 22.935%
Peak point 3'646‘768
^
^
^
Reg. date:
Nov 1997Nov 1997Nov 1997Nov 1997
Reg. date:
Nov 1997Nov 1997Nov 1997Nov 1997
1’468’239
1’531’823
2’022
Consensus
2222
0
10'000'000
20'000'000
30'000'000
40'000'000
50'000'000
60'000'000
70'000'000
1'996 2'011 2'025
R, implied
96.189%
R, 99.872%
Note: Consensus is derived from major equity investment banking analyst estimates released in June
2015 and author estimate
Bass Model – Machine
Approach Sales data
Actual Sales data

LantLantLantLant----San Sales and Cumulative SalesSan Sales and Cumulative SalesSan Sales and Cumulative SalesSan Sales and Cumulative Sales
33
fdrose14@gmail.com
(KUSD; 2000-2025)
(KUSD; 2000-2025)
m 56‘839‘904
p 0.340%
q 33.379%
Peak point 4‘827‘211
^
^
^
Reg. date:
Apr 2000Apr 2000Apr 2000Apr 2000
Reg. date:
Apr 2000Apr 2000Apr 2000Apr 2000
2’022
0
10'000'000
20'000'000
30'000'000
40'000'000
50'000'000
60'000'000
2'000 2'013 2'025
0
1'000'000
2'000'000
3'000'000
4'000'000
5'000'000
6'000'000
2'000 2'013 2'025
R, implied
96.883%
R, 99.942%
1’185’002Consensus
1’017’757
3333
Note: Consensus is derived from a punctual equity investment banking analyst estimate released in
February 2017 (for time interval from 2017 to 2021) and author estimate (for 2022)
Approach Cumulative
Sales data
Actual Cumulative Sales
data
Bass Model –
Machine Approach
Sales data
Actual Sales
data

0
10'000'000
20'000'000
30'000'000
40'000'000
50'000'000
1'996 2'011 2'025
0
500'000
1'000'000
1'500'000
2'000'000
2'500'000
3'000'000
3'500'000
4'000'000
1'996 2'011 2'025
CopaCopaCopaCopa----TevTevTevTev Sales and Cumulative SalesSales and Cumulative SalesSales and Cumulative SalesSales and Cumulative Sales
34
fdrose14@gmail.com
(KUSD; 1996-2025)
(KUSD; 1996-2025)
m 48'661'622
p 0.176%
q 27.270%
^
^
^
Reg. date:
Dec 1996Dec 1996Dec 1996Dec 1996
Reg. date:
Dec 1996Dec 1996Dec 1996Dec 1996
1’461’919
2’022
Consensus 1’245’200
4444
R, implied
99.075%
R, 99.981%
Note: Sales data figure in 1997 is not retrieved from financial statement / press release by Tev but it is
an estimate by an equity investment banking analyst; Consensus is derived from major equity
investment banking analyst estimates released in August 2016, June 2015 and author estimate
Approach Sales data
Actual Sales
data

HercHercHercHerc----Roc Sales and Cumulative SalesRoc Sales and Cumulative SalesRoc Sales and Cumulative SalesRoc Sales and Cumulative Sales
35
fdrose14@gmail.com
(KUSD; 1997-2025)
(KUSD; 1997-2025)
m 37‘543‘159
p 0.403%
q 22.673%
Peak point 2‘201‘851
^
^
^
Reg. date:
Sep 1998Sep 1998Sep 1998Sep 1998
Reg. date:
Sep 1998Sep 1998Sep 1998Sep 1998
2’022
5555
0
8'000'000
16'000'000
24'000'000
32'000'000
40'000'000
1'997 2'011 2'025
0
500'000
1'000'000
1'500'000
2'000'000
2'500'000
3'000'000
1'997 2'011 2'025
R, implied
95.013%
R, 99.874%1’213’817
Consensus
1’475’339
Note: Consensus is derived from major equity investment banking analyst estimates released in
August 2016, June 2015 and author estimate
Approach Sales data
Actual Sales data

AdvaAdvaAdvaAdva----GlaGlaGlaGla Sales and Cumulative SalesSales and Cumulative SalesSales and Cumulative SalesSales and Cumulative Sales
36
fdrose14@gmail.com
(KUSD; 2000-2025)
(KUSD; 2000-2025)
0
10'000'000
20'000'000
30'000'000
40'000'000
50'000'000
60'000'000
70'000'000
2'000 2'013 2'025
0
1'000'000
2'000'000
3'000'000
4'000'000
5'000'000
2'000 2'013 2'025
R, implied
87.971%
R, 99.981%
m 63'856'456
p 2.185%
q 21.888%
^
^
^
Reg. date:
Dec 2000Dec 2000Dec 2000Dec 2000
Reg. date:
Dec 2000Dec 2000Dec 2000Dec 2000
858’942
2’022
Consensus 438’879
6666
Note: Consensus is derived from a punctual major equity investment banking analyst estimate
released in March 2017
Actual Cumulative
Sales data
Approach Sales data
Actual Sales data

0
500'000
1'000'000
1'500'000
2'000'000
2'500'000
3'000'000
3'500'000
4'000'000
4'500'000
2'001 2'013 2'025
NeulNeulNeulNeul----AmgAmgAmgAmg Sales and Cumulative SalesSales and Cumulative SalesSales and Cumulative SalesSales and Cumulative Sales
37
fdrose14@gmail.com
(KUSD; 2001-2025)
(KUSD; 2001-2025)
m 75‘219'697
p 1.287%
q 17.110%
^
^
^
Reg. date:
Jan 2002Jan 2002Jan 2002Jan 2002
Reg. date:
Jan 2002Jan 2002Jan 2002Jan 2002
2’668’771
2’022
Consensus
2’158’000
7777
0
10'000'000
20'000'000
30'000'000
40'000'000
50'000'000
60'000'000
70'000'000
2'001 2'013 2'025
R, implied
94.575%
R, 99.923%
Approach Sales data
Actual Sales data

0
4'000'000
8'000'000
12'000'000
16'000'000
20'000'000
24'000'000
28'000'000
32'000'000
2'013 2'019 2'025
0
2'000'000
4'000'000
6'000'000
8'000'000
10'000'000
12'000'000
2'013 2'019 2'025
HarvHarvHarvHarv----Gil Sales and Cumulative SalesGil Sales and Cumulative SalesGil Sales and Cumulative SalesGil Sales and Cumulative Sales
38
fdrose14@gmail.com
(KUSD; 2013-2025)
(KUSD; 2013-2025)
R, implied
100.000%
R, 100.000%
m 26‘740‘356
p 25.953%
q 112.352%
^
^
^
Reg. date:
Oct 2014Oct 2014Oct 2014Oct 2014
Reg. date:
Oct 2014Oct 2014Oct 2014Oct 2014
129’327
1’672
2’022
Consensus
8888
Approach Sales data
Actual Sales data

0
10'000'000
20'000'000
30'000'000
40'000'000
50'000'000
60'000'000
70'000'000
80'000'000
2'014 2'020 2'025
0
4'000'000
8'000'000
12'000'000
16'000'000
20'000'000
2'014 2'020 2'025
OpdiOpdiOpdiOpdi----BriBriBriBri Sales and Cumulative SalesSales and Cumulative SalesSales and Cumulative SalesSales and Cumulative Sales
39
fdrose14@gmail.com
(KUSD; 2014-2025)
(KUSD; 2014-2025)
m 74’405’964
p 0.988%
q 87.269%
Peak point 15’808’578
^
^
^
Reg. date:
Dec 2014Dec 2014Dec 2014Dec 2014
Reg. date:
Dec 2014Dec 2014Dec 2014Dec 2014
7’222’000
6’351’007
2’022
Consensus
R, 100.000%
R, implied
100.000%
9999
Note: Sales for 1M USD in December 2014 are not acknowledged and 2015 sales are
proposed on a like-for-like basis embedding a 4 month lag in commercialization inception
Approach Cumulative
Sales data
Actual Cumulative
Sales data
Approach Sales data
Actual Sales data

0
5'000'000
10'000'000
15'000'000
20'000'000
25'000'000
30'000'000
35'000'000
2'003 2'014 2'025
0
500'000
1'000'000
1'500'000
2'000'000
2'500'000
3'000'000
2'003 2'014 2'025
TruvTruvTruvTruv----Gil Sales and Cumulative SalesGil Sales and Cumulative SalesGil Sales and Cumulative SalesGil Sales and Cumulative Sales
40
fdrose14@gmail.com
(KUSD; 2003-2025)
(KUSD; 2003-2025)
R, implied
94.297%
R, 99.906%
m 34‘717‘118
p 1.109%
q 21.649%
^
^
^
Reg. date:
Aug 2004Aug 2004Aug 2004Aug 2004
Reg. date:
Aug 2004Aug 2004Aug 2004Aug 2004
1’446’820
2’022
Consensus 0
10101010
Note: Consensus is derived from a punctual estimate by an equity investment banking analyst
delivered in February 2017
Approach Sales data
Actual Sales data

0
4'000'000
8'000'000
12'000'000
16'000'000
20'000'000
24'000'000
28'000'000
2'008 2'017 2'025
0
500'000
1'000'000
1'500'000
2'000'000
2'500'000
3'000'000
2'008 2'017 2'025
StelStelStelStel----Joh Sales and Cumulative SalesJoh Sales and Cumulative SalesJoh Sales and Cumulative SalesJoh Sales and Cumulative Sales
41
fdrose14@gmail.com
(KUSD; 2008-2025)
(KUSD; 2008-2025)
R, implied
99.665%
R, 99.991%
m 25‘288‘559
p 0.597%
q 43.293%
Peak point 2‘792’643
^
^
^
Reg. date:
Sep 2009Sep 2009Sep 2009Sep 2009
Reg. date:
Sep 2009Sep 2009Sep 2009Sep 2009
3’172’000
1’532’537
2’022
Consensus
11111111
Note: Sales data figure in 2009 is not retrieved from financial statement / press release by
Joh but it is an author estimate
Approach Sales data
Actual Sales data

0
8'000'000
16'000'000
24'000'000
32'000'000
40'000'000
48'000'000
2'003 2'014 2'025
0
500'000
1'000'000
1'500'000
2'000'000
2'500'000
3'000'000
3'500'000
2'003 2'014 2'025
AvasAvasAvasAvas----Roc Sales and Cumulative SalesRoc Sales and Cumulative SalesRoc Sales and Cumulative SalesRoc Sales and Cumulative Sales
42
fdrose14@gmail.com
(KUSD; 2003-2025)
(KUSD; 2003-2025)
R, implied
77.234%
R, 99.789%
m 42‘532’552
p 2.318%
q 24.521%
^
^
^
Reg. date:
Feb 2004Feb 2004Feb 2004Feb 2004
Reg. date:
Feb 2004Feb 2004Feb 2004Feb 2004
2’591’000
801’263
2’022
Consensus
12121212
Approach Sales data
Actual Sales data

0
10'000'000
20'000'000
30'000'000
40'000'000
50'000'000
60'000'000
2'004 2'015 2'025
0
500'000
1'000'000
1'500'000
2'000'000
2'500'000
3'000'000
3'500'000
4'000'000
2'004 2'015 2'025
LyriLyriLyriLyri----PfiPfiPfiPfi Sales and Cumulative SalesSales and Cumulative SalesSales and Cumulative SalesSales and Cumulative Sales
43
fdrose14@gmail.com
(KUSD; 2004-2025)
(KUSD; 2004-2025)
R, implied
90.483%
R, 99.757%
m 66'920‘422
p 0.859%
q 18.440%
^
^
^
Reg. date:
Dec 2004Dec 2004Dec 2004Dec 2004
Reg. date:
Dec 2004Dec 2004Dec 2004Dec 2004
1’273’250
3’296’359
2’022
Consensus
13131313
Note: Consensus is derived from major equity investment banking analyst estimates released in
August 2016 and author estimate
Approach Sales data
Actual Sales data

TecfTecfTecfTecf----Bio Sales and Cumulative SalesBio Sales and Cumulative SalesBio Sales and Cumulative SalesBio Sales and Cumulative Sales
44
fdrose14@gmail.com
(KUSD; 2012-2025)
(KUSD; 2012-2025)
14141414
0
2'000'000
4'000'000
6'000'000
8'000'000
10'000'000
12'000'000
14'000'000
16'000'000
2'012 2'019 2'025
0
500'000
1'000'000
1'500'000
2'000'000
2'500'000
3'000'000
3'500'000
2'012 2'019 2'025
R, implied
95.865%
R, 99.922%
m 14’059’639
p 5.914%
q 81.098%
Peak point 3‘093’956
^
^
^
Reg. date:
Mar 2013Mar 2013Mar 2013Mar 2013
Reg. date:
Mar 2013Mar 2013Mar 2013Mar 2013
3’310’000
47’379
2’022
Consensus
Bass Model –
Machine Approach
Sales data
Actual Sales data

0
2'000'000
4'000'000
6'000'000
8'000'000
10'000'000
12'000'000
2'010 2'018 2'025
0
500'000
1'000'000
1'500'000
2'000'000
2'500'000
2'010 2'018 2'025
XareXareXareXare----Joh Sales and Cumulative SalesJoh Sales and Cumulative SalesJoh Sales and Cumulative SalesJoh Sales and Cumulative Sales
45
fdrose14@gmail.com
(KUSD; 2010-2025)
(KUSD; 2010-2025)
R, 99.922%
m 10’729’855
p 1.067%
q 81.973%
Peak point 2'197’669
^
^
^
Reg. date:
Jul 2011Jul 2011Jul 2011Jul 2011
Reg. date:
Jul 2011Jul 2011Jul 2011Jul 2011
3’606’000
50’207
2’022
Consensus
R, implied
97.826%
15151515
Note: Sales data figure in 2011 is not retrieved from financial statement / press release but it
is an author estimate
Approach Cumulative
Sales data
Actual Cumulative
Sales data
Approach Sales data
Actual Sales data

EliqEliqEliqEliq----BriBriBriBri Sales and Cumulative SalesSales and Cumulative SalesSales and Cumulative SalesSales and Cumulative Sales
46
fdrose14@gmail.com
0
1'000'000
2'000'000
3'000'000
4'000'000
5'000'000
6'000'000
7'000'000
8'000'000
2'012 2'019 2'025
0
500'000
1'000'000
1'500'000
2'000'000
2'500'000
2'012 2'019 2'025
(KUSD; 2012-2025)
(KUSD; 2012-2025)
R, 99.993%
m 7'095'833
p 0.839%
q 123.403%
^
^
^
Reg. date:
Dec 2012Dec 2012Dec 2012Dec 2012
Reg. date:
Dec 2012Dec 2012Dec 2012Dec 2012
3’731’000
10’375
2’022
Consensus
R, implied
99.931%
16161616
Approach Cumulative
Sales data
Actual Cumulative
Sales data
Approach Sales data
Actual Sales data

EyleEyleEyleEyle----RegRegRegReg Sales and Cumulative SalesSales and Cumulative SalesSales and Cumulative SalesSales and Cumulative Sales
47
fdrose14@gmail.com
(KUSD; 2010-2025)
(KUSD; 2010-2025)
17171717
0
5'000'000
10'000'000
15'000'000
20'000'000
25'000'000
2'010 2'018 2'025
0
500'000
1'000'000
1'500'000
2'000'000
2'500'000
3'000'000
3'500'000
2'010 2'018 2'025
R, 99.908%
m 21’104’920
p 1.373%
q 61.548%
Peak point 3’299’449
5’014’000
416’895
2’022
Consensus
R, implied
98.040%
Reg. date:
Nov 2011Nov 2011Nov 2011Nov 2011
Reg. date:
Nov 2011Nov 2011Nov 2011Nov 2011
^
^
^
Approach Cumulative
Sales data
Actual Cumulative
Sales data
Bass Model –
Machine
Approach
Sales data
Actual Sales data

0
10'000'000
20'000'000
30'000'000
40'000'000
50'000'000
60'000'000
70'000'000
80'000'000
90'000'000
2'014 2'020 2'025
0
5'000'000
10'000'000
15'000'000
20'000'000
25'000'000
2'014 2'020 2'025
IbraIbraIbraIbra----PfiPfiPfiPfi Sales and Cumulative SalesSales and Cumulative SalesSales and Cumulative SalesSales and Cumulative Sales
48
fdrose14@gmail.com
(KUSD; 2014-2025)
(KUSD; 2014-2025)
m 88’544’730
p 0.558%
q 95.192%
Peak point 20’842‘140
R, implied
100.000%
R, 100.000%
^
^
^
Reg. date:
Feb 2015Feb 2015Feb 2015Feb 2015
Reg. date:
Feb 2015Feb 2015Feb 2015Feb 2015
3’966’000
8’796’932
2’022
Consensus
18181818
Note: Consensus is calculated as a weighted average of consensus – derived from major equity
investment banking analyst estimates released in August 2016 – and a punctual estimate by an equity
investment banking analyst delivered in January 2017
Actual Cumulative
Sales data
Bass Model –
Machine Approach
Sales data
Actual Sales
data

0
2'000'000
4'000'000
6'000'000
8'000'000
10'000'000
1997 2011 2025
RemiRemiRemiRemi----Joh SalesJoh SalesJoh SalesJoh Sales
49
fdrose14@gmail.com
(KUSD; 1997-2025)
R, implied
100.000%
m 4'969'330'443
p 0.0481%
q 7.0339%
Peak time in # years > 42.0
Peak time in date > 2'039
Peak point na
^
^
^
Reg. date:
Aug 1998Aug 1998Aug 1998Aug 1998
Reg. date:
Aug 1998Aug 1998Aug 1998Aug 1998
7’209’598
2’022
Consensus 2’148’000
19191919
No Data AvailableNo Data Available
Given no availabilityno availabilityno availabilityno availability
of datadatadatadata till 2006,
equationequationequationequation - referring to
derivative timederivative timederivative timederivative time
evolutionevolutionevolutionevolution with
translationtranslationtranslationtranslation of cccc years
– is used
zŒ
BŸ
Š m†
p• p• q• ,e #†!$† BŸ •
p• q•e #†!$† BŸ • ,
Sales data given by:
Actual Sales data

HumiHumiHumiHumi----AbbAbbAbbAbb Sales and Cumulative SalesSales and Cumulative SalesSales and Cumulative SalesSales and Cumulative Sales
50
fdrose14@gmail.com
(KUSD; 2002-2025)
(KUSD; 2002-2025)
0
50'000'000
100'000'000
150'000'000
200'000'000
250'000'000
300'000'000
2'002 2'014 2'025
0
5'000'000
10'000'000
15'000'000
20'000'000
25'000'000
30'000'000
2'002 2'014 2'025
R, implied
99.461%
R, 99.956%
m 463'388'517
p 0.108%
q 23.647%
^
^
^
Reg. date:
Dec 2002Dec 2002Dec 2002Dec 2002
Reg. date:
Dec 2002Dec 2002Dec 2002Dec 2002
23’990’795
2’022
Consensus
10’729’000
20202020
Approach Sales data
Actual Sales data

• Application of Bass Model to Top 20 US Drug SalesApplication of Bass Model to Top 20 US Drug SalesApplication of Bass Model to Top 20 US Drug SalesApplication of Bass Model to Top 20 US Drug Sales
ProjectionsProjectionsProjectionsProjections
- A Full 100% Machine Approach
- A Managerial ApproachA Managerial ApproachA Managerial ApproachA Managerial Approach
- Delta Consensus vs Bass Model within Machine and
Managerial Approach
• Annex
51
fdrose14@gmail.com

Application of Bass ModelApplication of Bass ModelApplication of Bass ModelApplication of Bass Model –––– ManagerialManagerialManagerialManagerial ApproachApproachApproachApproach
to Top 20 US Drugs within Pharmaceutical Sectorto Top 20 US Drugs within Pharmaceutical Sectorto Top 20 US Drugs within Pharmaceutical Sectorto Top 20 US Drugs within Pharmaceutical Sector
52
fdrose14@gmail.com
• HypothesisHypothesisHypothesisHypothesis underlying application of Bass ModelBass ModelBass ModelBass Model adopting a Managerial ApproachManagerial ApproachManagerial ApproachManagerial Approach are the
samesamesamesame ones used for the Machine ApproachMachine ApproachMachine ApproachMachine Approach with some exceptionsexceptionsexceptionsexceptions outlined below
• In those casesthose casesthose casesthose cases for which quantitativequantitativequantitativequantitative estimationestimationestimationestimation of Bass model parameterparameterparameterparameter m (see 2nd column
of the below table) - accomplished through Machine ApproachMachine ApproachMachine ApproachMachine Approach - is not realisticnot realisticnot realisticnot realistic or not optimalnot optimalnot optimalnot optimal
from a “business sense ““business sense ““business sense ““business sense “ perspective, following steps have to be put in place:
- definitiondefinitiondefinitiondefinition of a minminminmin or max thresholdmax thresholdmax thresholdmax threshold for m – according to the specific case – through a
simplifiedsimplifiedsimplifiedsimplified qualitative judgementqualitative judgementqualitative judgementqualitative judgement (see 3rd column of the below table)
- rererere----workworkworkwork of the procedureprocedureprocedureprocedure to estimateestimateestimateestimate parametersparametersparametersparameters p, q and m (see 4th column of the below
table) - based on non linear regression analysisnon linear regression analysisnon linear regression analysisnon linear regression analysis coupled with least squaresleast squaresleast squaresleast squares (NLS) method
using cumulative salescumulative salescumulative salescumulative sales as dependentdependentdependentdependent variablevariablevariablevariable ---- conditionedconditionedconditionedconditioned to the above thresholdthresholdthresholdthreshold
imposed on parameterparameterparameterparameter m
• The above casesabove casesabove casesabove cases are properly detected and outlined in the below listbelow listbelow listbelow list:
Bass Model Application with Managerial ApproachBass Model Application with Managerial ApproachBass Model Application with Managerial ApproachBass Model Application with Managerial Approach ---- HypothesisHypothesisHypothesisHypothesis
Remi - Joh 4'969'330'443 <= 100’000’000 67'902'172
Humi - Abb 463'388'517 <= 200’000’000 200'000'000
Eliq - Bri 7'095‘833 >= 50’000’000 50'000'000
Xare – Joh 10'729'855 >= 50’000’000 50'000'000
Ibra - Pfi 88'544'730 <= 50’000’000 50'000'000
Tecf - Bio 14'059'639 >= 50’000’000 50'000'000
Eyle - Reg 21'104'920 >= 50’000’000 50'000'000
DrugDrugDrugDrug –––– Manuf.Manuf.Manuf.Manuf. Quant.Quant.Quant.Quant. EstimatEstimatEstimatEstimat. of m. of m. of m. of m Threshold on mThreshold on mThreshold on mThreshold on m ManagManagManagManag.... EstimatEstimatEstimatEstimat.... oooof mf mf mf m
In USD
= Not realistic = Not optimal

Focus of Next Slides
Aggregated AnnualAggregated AnnualAggregated AnnualAggregated Annual SSSSales Trend 2016ales Trend 2016ales Trend 2016ales Trend 2016----2025202520252025 ofofofof TopTopTopTop
20 US20 US20 US20 US DrugsDrugsDrugsDrugs withinwithinwithinwithin Bass ModelBass ModelBass ModelBass Model----Manager. ApproachManager. ApproachManager. ApproachManager. Approach
53
fdrose14@gmail.com
Aggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US DrugsAggregated Annual Sales of Top 20 US Drugs
(KUSD; 2016-2025)
% Growth
16-25
CAGR
16-25
-57.0% -9.0%
72'466'610
62'294'023
31'156'143
0
10'000'000
20'000'000
30'000'000
40'000'000
50'000'000
60'000'000
70'000'000
80'000'000
Sales 2016 Sales 2022 Sales 2025

Innovation Diffusion and Pioneering Bass Model: Theory and Practical Applications

Innovation Diffusion and Pioneering Bass Model: Theory and Practical Applications

Recommended

Recommended

More Related Content

Similar to Innovation Diffusion and Pioneering Bass Model: Theory and Practical Applications

Similar to Innovation Diffusion and Pioneering Bass Model: Theory and Practical Applications (20)

Recently uploaded

Recently uploaded (20)

Innovation Diffusion and Pioneering Bass Model: Theory and Practical Applications