Promotion Response Modeling - PMSA

1 Promotion Response ModelingDavid Wood, PhD, Senior PrincipalRajnish Kumar, Senior ManagerCopyright 2015 Axtria, Inc. All Rights today s discussion we will discuss following questions:What is Promotion Response Modelling ? Why bother ?What are the building blocks to do Promotion Response modelling?What decisions are involved ? .. what does it look like ?Where can I apply the results?Copyright 2015 Axtria, Inc. All Rights Response : OverviewPromotion Response : ApplicationsPromotion Response : ApproachCopyright 2015 Axtria, Inc. All Rights build Response models?To make trade-off decisions Whether I need to increase / reduce effort What effort is required to hit my brand forecast Which segments should I target more or less?

2 Which channels should I spend more or less? ..In a nutshell, to optimize promotional effortsCopyright 2015 Axtria, Inc. All Rights concepts of Response modelingLaw of diminishing returnsResponse curveMarginal and Overall ROIP rofit MaximizationBase and incremental salesCopyright 2015 Axtria, Inc. All Rights of diminishing returnsLaw of diminishing returnsIf you keep adding more of one unit of production to a productive process while keeping all others units constant, you will at some point produce lower per unit returnsAssisting marketing channelsThere are multiple channels of Promotion no one channel is completely responsible for all salesExample: Beyond a point, a particular channel Promotion cannot make any difference to brand sales as other channels too have an impact on brand salesCopyright 2015 Axtria, Inc.

3 All Rights Curve: A Response curve is a graphical (and/or mathematical) expression of the relationship between Promotion and returnsResponse Curve0204060801001200102030 Promotionimpactable Sales40 Marginal Revenue = Marginal Cost( Optimal )1. Response curve starts from origin. Therefore, zero Promotion would lead to zero impactable sales2. Response curve is not sales curve; sales curve will not start from origin Even at zero Promotion brand sales are (usually) not zero3. Response curves typically have two distinguishing parameters: Asymptote CurvatureCopyright 2015 Axtria, Inc. All Rights Standard Response model formsDependent variable = f ( Independent variables ) Left Hand Side (LHS) = f ( Right Hand Side variables )Typical ly:Some measure of sales = f( Promotion , practice size, (or share) history, etc.)

4 But .. what variables should we use?.. what model form should we use?Copyright 2015 Axtria, Inc. All Rights Model Construct LHS some measure of Sales (NRx, TRx, Units, Share) Volume change (NRx, TRx, Units, Share) RHS Constant Prior volume ( auto-regressive terms) Current Promotion (possibly transformed) Lagged Promotion (similarly transformed) Seasonality indicators Specialty groups .. Level of data granularity Time: Weekly, monthly, annual Entity: Physician, segment, geography9 Copyright 2015 Axtria, Inc. All Rights Model FormsMost commonly used(Negative Exponential, Log)Simple, can calculate historical avgROI but not optimal Sometimes seen, not usefulAccounts for threshold effectTypically only when data is limited.

5 Possibly realistic, but hard to model or to act onIn all models:X axis: EffortY axis: Return10051015200 2 4 6 8 1012141618202224262830 Linear0510150 2 4 6 8 1012141618202224262830 Diminishing Return0510150 2 4 6 8 1012141618202224262830S Shaped Return0510150 2 4 6 8 1012141618202224262830 Stepwise02040608010002468101214161820222 4262830 Piecewise Linear010203040500 2 4 6 8 1012141618202224262830 Non Dimishing ReturnCopyright 2015 Axtria, Inc. All Rights common forms for diminishing returns modelsNegative exponentialLHS (share or sales in monthi) =Constant + Asymptote* (1 exp( -(Scale* promotioni))+ Parameters* other terms (covariates)LogarithmicLHS (share or sales in monthi) =Constant+ Slope* ln(Scale* promotioni))+ Parameters* other terms (covariates)Copyright 2015 Axtria, Inc.

6 All Rights , these models are inherently non-linear (unless we resort to trickery)Negative exponentialLHS (share or sales in monthi) =Constant + Asymptote* (1 exp( -(Scale* promotioni))+ Parameters* other terms (covariates)LogarithmicLHS (share or sales in monthi) =Constant+ Slope* ln(Scale* promotioni))+ Parameters* other terms (covariates)Presence of Scale parameter makes model non-linearCopyright 2015 Axtria, Inc. All Rights can pre-set the Scale parameter, and apply a transformation to the RHS variable .. and then use linear regressionNegative exponentialLHS (share or sales in monthi) =Constant + Asymptote* (1 exp( -( * promotioni))+ Parameters* other terms (covariates)LogarithmicLHS (share or sales in monthi) =Constant+ Slope* ln( * promotioni))+ Parameters* other terms (covariates)In this approach, you must either try multiple values of Scale to find best fit.

7 Or just use non-linear estimation methods to find the value of that parameter (and others) directlyPre-set variable If Scaleis pre-set, this entire structure can be pre-calculated Copyright 2015 Axtria, Inc. All Rights are limits to the use of diminishing returns models Diminishing returns models really only make sense if the promotional program you are measuring can be applied at varying levels of intensity Example: sales rep detailing .. You can reasonably think of having any level of Promotion between 0 and 4 (or even 5) calls / month But, a program that can really only be done once a year (speaker / dinner meeting?) or a program where you have only a binary in/out status indicator can t be modeled as curve.

8 Only a straight line051015024681012141618202224262830 Diminishing Return051015200 2 4 6 8 1012141618202224262830 LinearCopyright 2015 Axtria, Inc. All Rights transformations need to be applied to get a robust modelSimple, can calculate historical avg ROI but not optimal Sometimes seen, not useful051015200 2 4 6 8 1012141618202224262830 Linear010203040500246810 12 14 16 18 20 22 24 26 Non Diminishing ReturnMost commonly used(Negative Exponential, Log)Possibly realistic, but hard to model or to act on0510150 2 4 6 8 101214161820222426 Stepwise0510150 2 4 6 8 1012141618202224262830 Diminishing ReturnAccounts for threshold effectGood approximation for diminishing returns curve02040608010002468101214161820222426 2830 Piecewise LinearIn all graphs:X axis: Effort Y axis.

9 ReturnCopyright 2015 Axtria, Inc. All Rights Exponential model framework Equation form: NRx = a0 + a1*NRx1 + a2*NRx2 + a3*NRx3 + a4*NRx4+ A*(1 - Exp(-C*(PDE + c1*PDE1 + c2*PDE2 + c3*PDE3 + c4*PDE4)))ParametersMeaninga0 Constant (Base); pure Brand EquityAAsymptoterepresents maximum impactable sales at infinite level of efforta1 Impact of previous month sales on current month salesa2, a3, a4 Impact of current month-2, current month-3, current month-4 on current month salesc1 Promotionalactivity lag coefficients for current month-1c2, c3, c4 Promotionalactivity lag coefficients for current month-2, current month-3, current month-4 Overall curvature= C*(1+c1+c2+c3+c4)Rate at which impactable sales vary with Promotion , higher curvature values imply a more arched Response curve (will reach asymptote faster) and lower curvature implies flatter Response curve (will reach asymptote slowly)Copyright 2015 Axtria, Inc.

10 All Rights more advanced considerations (1 of 4) A bit out-of-scope for today s discussion, but: Consider choice of LHS variable: sales, Rx, share, or month-to-month change of Rx volume Use of auto-regressive terms on RHS is conceptually similar to using LHS as month-to-month change in Rx. This also de-emphasizes cross-sectional ( between doctors ) variation in your model and increases the importance of within doctor, over time variation (generally, a good thing)Equation form: NRx = a0 + a1*NRx1 + a2*NRx2 + a3*NRx3 + a4*NRx4+ A*(1 - Exp(-C*(PDE + c1*PDE1 + c2*PDE2 + c3*PDE3 + c4*PDE4)))Copyright 2015 Axtria, Inc. All Rights A bit out-of-scope for today s discussion, but: The structure of how to represent Promotion (including lagged Promotion (effort in previous time periods)) is open to a lot of debate.