# Promotion Response Modeling. David Wood, PhD, Senior Principal Rajnish Kumar, Senior Manager

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1 Promotion Response Modeling David Wood, PhD, Senior Principal Rajnish Kumar, Senior Manager

2 In 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? 2

3 Agenda Promotion Response: Overview Promotion Response: Approach Promotion Response: Applications 3

4 Why 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? Which channels should I spend more or less?.. In a nutshell, to optimize promotional efforts 4

5 Basic concepts of response modeling Law of diminishing returns Response curve Marginal and Overall ROI Profit Maximization Base and incremental sales 5

6 Law of diminishing returns Law of diminishing returns If 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 returns Assisting marketing channels There are multiple channels of promotion no one channel is completely responsible for all sales Example: Beyond a point, a particular channel promotion cannot make any difference to brand sales as other channels too have an impact on brand sales 6

7 Response Curve: A response curve is a graphical (and/or mathematical) expression of the relationship between promotion and returns impactable Sales Response Curve Marginal Revenue = Marginal Cost ( Optimal ) Promotion Response curve starts from origin. Therefore, zero promotion would lead to zero impactable sales 2. Response curve is not sales curve; sales curve will not start from origin Even at zero promotion brand sales are (usually) not zero 3. Response curves typically have two distinguishing parameters: Asymptote Curvature 7

8 Standard Response model forms Dependent variable = f ( Independent variables ) Left Hand Side (LHS) = f ( Right Hand Side variables ) Typically: Some measure of sales = f( promotion, practice size, (or share) history, etc.) But... what variables should we use?... what model form should we use? 8

9 Response Model Construct LHS some measure of RHS Sales (NRx, TRx, Units, Share) Volume change (NRx, TRx, Units, Share) 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, geography 9 9

10 Response Model Forms Simple, can calculate historical avg ROI but not optimal Linear Non Dimishing Return Sometimes seen, not useful Most commonly used (Negative Exponential, Log) Diminishing Return Stepwise Possibly realistic, but hard to model or to act on Accounts for threshold effect S Shaped Return Piecewise Linear Typically only when data is limited In all models: X axis: Effort Y axis: Return 10 10

11 Most common forms for diminishing returns models Negative exponential LHS (share or sales in month i ) = Constant + Asymptote * (1 exp( -(Scale * promotion i )) + Parameters * other terms (covariates) Logarithmic LHS (share or sales in month i ) = Constant + Slope * ln(scale * promotion i )) + Parameters * other terms (covariates) 11

12 Unfortunately, these models are inherently non-linear (unless we resort to trickery) Negative exponential LHS (share or sales in month i ) = Constant Logarithmic + Asymptote * (1 exp( -(Scale * promotion i )) + Parameters * other terms (covariates) LHS (share or sales in month i ) = Constant + Slope * ln(scale * promotion i )) + Parameters * other terms (covariates) Presence of Scale parameter makes model non-linear 12

13 We can pre-set the Scale parameter, and apply a transformation to the RHS variable... and then use linear regression Negative exponential LHS (share or sales in month i ) = Constant + Asymptote * (1 exp( -(1.5 * promotion i )) + Parameters * other terms (covariates) If Scale is pre-set, this entire structure can be pre-calculated Logarithmic LHS (share or sales in month i ) = Constant + Slope * ln(1.0 * promotion i )) + Parameters * other terms (covariates) Pre-set variable In this approach, you must either try multiple values of Scale to find best fit... Or just use non-linear estimation methods to find the value of that parameter (and others) directly 13

14 There 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... only a straight line Diminishing Return Linear

15 Appropriate transformations need to be applied to get a robust model Simple, can calculate historical avg ROI but not optimal Linear Non Diminishing Return Sometimes seen, not useful Most commonly used (Negative Exponential, Log) Diminishing Return Stepwise Possibly realistic, but hard to model or to act on Accounts for threshold effect Piecewise Linear Good approximation for diminishing returns curve In all graphs: X axis: Effort Y axis: Return 15

16 Negative 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))) Parameters a0 A Meaning Constant (Base); pure Brand Equity Asymptote represents maximum impactable sales at infinite level of effort a1 Impact of previous month sales on current month sales a2, a3, a4 Impact of current month-2, current month-3, current month-4 on current month sales c1 Promotional activity lag coefficients for current month-1 c2, c3, c4 Promotional activity 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) 16

17 Slightly 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. 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))) 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) 17

18 Slightly more advanced considerations (2 of 4) 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... there is not one universally correct structure The particular form used here has certain features (i.e., it treats lagged promotion as something that can be traded off against current promotion at an exchange rate dictated by the c1, c2, etc. coefficients)... but that may or may not be an advantage) 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))) 18

19 Slightly more advanced considerations (3 of 4) A bit out-of-scope for today s discussion, but: Consider normalizing each individual doctor s (or account s) values relative to seasonally-adjusted average over the time period, i.e.: LHS becomes Rx current_month Rx avg RHS can be similarly normalized, or remain as original As with using auto-regressive elements on the RHS, this approach also reduces the cross-sectional ( between doctors ) component of the model and increases its dependence on within doctor variation over time However, it makes creating projections from the model more difficult (possibly, much more difficult) 19

20 Slightly more advanced considerations (4 of 4) A bit out-of-scope for today s discussion, but: Introduction of S-shaped curves will (probably) represent reality a little better... but will significantly increase the complexity of both estimation, and optimization on the results. 20

21 Parameter Estimation Techniques Estimate those parameters which minimize overall sum of square errors in the model Parameters need to make business sense Different methods of estimating parameters include linear/non linear regression Tools generally used: SAS / SPSS / R / Excel / (almost anything) 21

22 Marginal and Overall ROI Overall RoI = Overall Return Overall Cost Marginal Return Marginal RoI = Marginal Cost Impact Optimal Promotion Promotion 0 Overall Return (primary axis) Marginal Return (secondary axis) Marginal Cost (secondary axis) 22

23 Profit is maximized where marginal revenue is equal to marginal cost Impact Optimal Promotion Profit Maximized Marginal Return and Cost Promotion 0 Overall Return (primary axis) Profit Curve Marginal Return (secondary axis) Marginal Cost (secondary axis) 23

24 Promotion Response Modeling helps in identifying the impact of promotional activity on physician prescribing behavior Physician prescribing can be thought of as being influenced by 3 broad effects: Direct Detailing, Short-term Trends, and Long-term Trends. Promotion response modeling can use historical data to model the three component and identify contribution of promotional activity in sales results Long-term Trends: Effects attributable to factors with longer term persistence (e.g., brand equity, patient preference, market positioning) Total prescription written by a physician Short-term Trends: A component that measures how the value obtained by promotion and brand equity play out over time. That is, if the effects will vanish quickly or if they will persist over many months Direct Detailing Effect: Direct impact of detailing received in the current month and recent months 24

25 Sales generated from effort in current year has a lingering effect into future periods, referred to as carryover Carryover from 2015 Promotion effort Base 2015 promotion 2016 Promotion 2017 Promotion During the launch phase direct impact of promotional activity on revenue is higher (50-70%) as compared to mature and stable brand (7-8 years after launch) Carryover increases as brand matures and its equity/long term persistence value increase 25

26 Promotion Response Modeling helps in identifying the impact of promotional activity on physician prescribing behavior Physician prescribing can be thought of as being influenced by 3 broad effects: Direct Detailing, Short-term Trends, and Long-term Trends. Promotion response modeling can use historical data to model the three component and identify contribution of promotional activity in sales results Long-term Trends: Effects attributable to factors with longer term persistence (e.g., brand equity, patient preference, market positioning) Total prescription written by a physician Short-term Trends: A component that measures how the value obtained by promotion and brand equity play out over time. That is, if the effects will vanish quickly or if they will persist over many months Direct Detailing Effect: Direct impact of detailing received in the current month and recent months Example promotion response equation : Rx Current = Rx Previous month + f (Promotional activity) + Constant Captures short-term trends by using prescribing behavior in previous months Captures direct detailing effect by calculation estimates for promotional activity Coefficients to establish the base level of prescribing for each doctor 26

27 Base and incremental sales Base vs. incremental volume Base: volume that would be generated in absence of any marketing activity Incremental: volume generated by marketing activities in short run Base can grow or decline over long run and is also impacted by marketing activities 35% 40% Variation in base volume is good indicator of brand equity Base can be further sub-divided into historical sales carryover and pure constant Historical sales carryover: Historical sales which are driving current sales Constant: Pure Brand equity i.e. volume which is irrespective of any promotion 25% Base volume: Constant Base volume: Historical Sales Carryover Incremental volume: Promotion 27

28 Agenda Promotion Response: Overview Promotion Response: Approach Promotion Response: Applications 28

29 Approach Strategic Data Assessment Model Estimation Optimization Forecasting / Projection Data collection, review and preparation Aggregate brand level trends Segment level trends Overlaps Key metrics: Reach Frequency Brand sales / customer Segmentation / Clustering Estimation of key parameters using Generalized Linear or Non Linear methods Model Validation Creation of response curves Based upon financials and response curve parameters, estimate optimal effort for each segment Steady state optimal or discounted cash flow Based upon model diagnostics and response curves, estimate forecast for base vs. incremental volume At historical and optimal targeting Layer in future market events Potential sales / customer 29

30 Strategic Data Assessment Collect Process Analyze Data Prescription data Call data Market Definition Current Price, anticipated price increases, Gross-to- Net discounting Rep cost and Financials Any other physician segmentation Demographic Information Forecast (Gross / Net / Unit) Market Events (if relevant) (typically: major competitive launches or major competitor goes generic) Any other Promotional Data (Samples,Copay Cards ) Managed Care Data Granularity Physician x Month (24M) Physician x Month (24M) Brand Brand Sales Force Physician Brand Physician Brand Brand Physician x Month Brand x State Once the data is collected, process, clean and integrate all datasets to create preliminary summaries & perform a comprehensive Data Health Check, in order to: 1. Ensure completeness and accuracy of the data collected 2. Understand historical trends & relationships 3. Confirm your interpretation of the preliminary insights 4. Identify additional data gaps / plans to bridge the data gaps 30

31 Segmentation Next, we need to identify clusters of customers (physicians) which could ultimately warrant different levels of sales rep promotion (calls) 1. Different customers react differently to promotion 2. Resource allocation decisions based on the response estimation typically need to be made at a segment level. 3. Estimating the promotional response of a single customer using his data alone is (typically) not possible Segmentation Scheme Market Potential Brand Share Behavioral Clusters Specialty Groups Managed Care 31

32 Optimal results by segment can be aggregated up to estimate total promotional needs NRx / writer TRx / writer TRx / NRx Ratio Market NRx / Doctor % of Brand NRx 32

33 Promotion response models enable analysts to understand the split of base volume vs. incremental volume in projecting sales forward in time Trend at Historical Targeting Impact Breakout Current % Sales Unit ( 000) Carryover + Baseline + Promotion Carryover + Baseline only 77% Promotion Carryover + Baseline 33

34 Agenda Promotion Response: Overview Promotion Response: Approach Promotion Response: Applications 34

35 Many applications in life sciences for promotion response modeling Sales Force Size and Structure Optimal promotion required by the entire portfolio how many sales team? What size? What structure? Territory Alignments How to deploy those sales teams / sales reps geographically? Call Planning Who all to promote? How frequently? Which products? 35

36 Response models allow marketers to optimize spend across marketing channels this technique is widely used across industries Marketing Mix Optimization 36

37 Thank you Presenter: David Wood Rajnish Kumar Contact No.:

38 Backup 38

39 Standard Transformations types Transformation Parameters Equation Negative Exponential A,C A * [1 Exp(-C*X)] Log A A*LN(1+X) S Shaped A,C A*[1/{1+Exp(-C*(X- ))}] 39

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