Response Modeling with Non-Random Marketing Mix Variables

Response Modeling with Non-Random Marketing Mix Variables



Puneet Manchanda
Peter E. Rossi
Pradeep K. Chintagunta

January 2003
This version: October 2003
















Puneet Manchanda is Associate Professor, Peter E. Rossi is Joseph T. Lewis Professor of Marketing and
Statistics and Pradeep K. Chintagunta is Robert Law Professor of Marketing at the University of Chicago. The
authors would like to thank Arun Shastri and Andy Zoltners for industry insights; Devi Antony, Rahul Bhatia
and Sridhar Narayanan for help with the data and ZS Associates and an anonymous firm for providing the data.
Participants at the Marketing Science conference in Edmonton, seminar participants at Berkeley, Kellogg,
UCLA, UC Riverside, UC Irvine, Xavier Dreze and Rob McCulloch provided valuable comments on earlier
drafts. Manchanda would like to thank the Kilts Center for Marketing and the Beatrice Foods Company Faculty
Research Fund at the Graduate School of Business, University of Chicago, for research support. All
correspondence may be addressed to Manchanda at the University of Chicago, Graduate School of Business,
1101 East 58th Street, Chicago, IL 60637 or via e-mail at puneet.manchanda@gsb.uchicago.edu.

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Response Modeling with Non-Random Marketing Mix Variables

Abstract

Sales response models are widely used as the basis for optimizing the marketing mix or for allocation of
the sales force. Response models condition on the observed marketing mix variables and focus on the
specification of the distribution of observed sales given marketing mix activities. These models usually
fail to recognize that the levels of the marketing mix variables are often chosen with at least partial
knowledge of the response parameters in the conditional model. This means that, contrary to standard
assumptions, the marginal distribution of the marketing mix variables is not independent of response
parameters. We expand on the standard conditional model to include a model for the determination of
the marketing mix variables. We apply this modeling approach to the problem of gauging the
effectiveness of sales calls (details) to induce greater prescribing of drugs by individual physicians. We
do not assume, a priori, that details are set optimally but, instead, infer the extent to which sales force
managers have knowledge of responsiveness and use this knowledge to set the level of sales force
contact. We find that physicians are not detailed optimally; high volume physicians are detailed to a
greater extent than low volume physicians without regard to responsiveness to detailing. In fact, it
appears that unresponsive but high volume physicians are detailed the most.

Keywords: Response Models, Salesforce Effectiveness, Micromarketing, Pharmaceutical Industry, Hierarchical Bayes
Models, Metropolis-Hastings Algorithm, Gibbs Sampler, Markov Chain Monte Carlo Methods


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Introduction

Marketing mix decisions are based on the responsiveness of sales to each of the possible marketing mix
activities. In a data-rich environment, responsiveness to marketing variables can be obtained by
estimation of various sales response models. These models are based on the conditional distribution of
sales given marketing mix variables and other covariates. However, the levels of the marketing mix
variables are determined by marketing or sales force managers in a non-random fashion. In particular,
the manager may have partial knowledge of sales response parameters and use this knowledge in setting
the level of the marketing mix variables. This creates a simultaneity problem in which both sales and
the marketing mix variables are determined jointly. The contribution of this work is to develop a
modeling approach for this class of problems and apply this approach to data from the pharmaceutical
industry on the marketing of prescription drugs.

There are many elements in the marketing mix for prescription drugs including direct sales calls
(termed “detailing”), direct to consumer advertising, advertising in professional medical journals, and
various physician meetings and events. The single largest expenditure is on direct sales calls with over
$6 billion expended in 2000 (see Wittink 2002). Expenditures on detailing are almost three times that
of direct-to-consumer advertising, the second largest marketing mix activity. Detailing is a
decentralized activity that requires the sales force manager to allocate sales force effort over more than
100,000 physicians nationwide.

In theory, the sales force manager should optimize allocation of effort across physicians.
Assuming that the marginal cost of detailing is equal across physicians, the sales force manager should
allocate details so that the marginal effect of a detail is equal across physicians. The sales force manager
must be able to reliably estimate the effect of a detailing visit for each of over 100,000 doctors active in
the drug category. Syndicated suppliers of data such as IMS and Scott-Levin provide information on
the prescription writing of individual physicians. This should enable the sales force manager to make

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allocations of detailing on the basis of some hard data. However, it has only recently been possible to
estimate models that provide estimates at the individual level for large cross-sections and these
developments are only now reaching marketing practice. This means that the sales force manager must
use some more approximate method to allocate sales force effort. In particular, it is a rather simple
matter to calculate the volume of prescriptions in the drug category and allocate proportionately more
detailing to physicians who write a high-volume of prescriptions in the drug class. This allocation
scheme can be justified by the standard efficiency argument for all promotional activities. Any given
promotional activity will be more effective on average at a higher volume operation. If the detail raises
the probability that the physician will prescribe the company’s drug for each patient, then physicians
with more patients will show greater total detailing effects. This volume-based allocation of detailing
effort assumes that the marginal effect of detailing on the probability of prescribing the company’s
drug is the same across physicians.

Given the difficulties in estimating individual level response models for a huge number of
physicians, it is not surprising that volume-based detailing allocation is commonplace. However, even
if it is not possible to implement individual level models, managers can form some impressions of the
responsiveness of physicians. For example, observable characteristics of physicians such as specialty,
geographic location or the medical insurance provisions for their patients (see Gonul et al 2001 for
evidence on the role of insurance) might be used in a segmentation strategy. Informal sources of
information such as the judgment of the sales force could also be used. This means that the detailing
allocation could be based not only on volume of prescriptions in the category but also with partial
knowledge of the responsiveness of an individual physician.

Most modeling of sales force responsiveness is based on some sort of pooling of physicians.
Modelers in the pharmaceutical industry are aware that individual physician level models fit with
standard methods such as linear regression or logit models have unstable and imprecise parameter

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estimates. For this reason, modelers will typically pool the individual level data in to large groups (e.g.,
Gonul et al 2001 do this with a 3 segment latent class model). There is a real danger that even partial
pooling will result in biased estimates of the effects of detailing. If sales force managers have a policy
of detailing high volume more than low volume physicians, then this will induce a spurious correlation
between detailing and number of prescriptions written. As a result, pooled analyses will have an
upward bias in the effectiveness of detailing. If only time series variation in detailing levels for the
same physicians is used, then this upward bias in detailing effectiveness can be avoided. Thus,
development of practical methods for determining the effectiveness of detailing at the physician level
will help in the allocation of detailing resources as well as avoid potentially substantial biases in the
coefficient estimates.

Our approach to developing individual physician level models is to use a hierarchical Bayes
model. This involves a model for the distribution of prescriptions written given the monthly number of
details at the physician level and a model for the distribution of the coefficients from this model across
physicians. The number of prescriptions written is fundamentally a count variable with a substantial
number of zeroes and a relatively small number of frequently occurring outcomes. We postulate a
negative binomial (NBD) regression model for the distribution of prescriptions conditional on the
number of details, coupled with a normal distribution of response coefficients.

If detailing levels are set based on partial knowledge of physician responsiveness to detailing,
then the standard hierarchical Bayes approach can provide systematically misleading estimates at the
physician level. Chamberlain (1982, 1984) shows that there can be asymptotic bias or inconsistency in
standard likelihood approaches which fail to control for the situation in which the independent
variables are correlated with random intercepts. The same reasoning applies to the more general
situation in which there are both random intercepts and slopes. In any conditional model or regression
style approach, it is typically assumed that the marginal distribution of the independent variable (in this

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case, detailing) is independent of the conditional distribution. In our case, we want to consider the
situation in which the level of detailing can be set with knowledge of the response parameters from the
conditional model. This will require a model for the joint distribution of prescriptions and detailing.
The problem we consider here is a special case of the more general setting in which the
marginal distribution of the independent variable is not independent of the conditional distribution of
the dependent variable given the independent. This general class of problems can be characterized by
the situation in which the independent variables are set strategically or where the independent variables
are “endogeneous.” It should be emphasized that our problem is different from the problem of price
endogeneity as in Villas-Boas and Winer (1999) or Nevo (2001). In the case of price endogeneity,
prices are set strategically as a function of a common demand shock. In our case, the detailing levels are
set a function of physician-specific response parameters. Standard instrumental variable or
simultaneous equations methods do not apply to our problem. We employ a full information
likelihood-based approach designed for this problem. Our approach is closer to that of Bronnenberg
and Mahajan (2001) who postulate that marketing mix variables are set as a function of the baseline
level of sales.

The paper is organized as follows. We begin with a brief review of the literature on detailing
effects. We then describe our data and the stated policy for determination of detailing. Our
hierarchical modeling approach is outlined next, followed by our approach to the joint or simultaneous
determination of both prescriptions and detailing. The next section provides the results of our
modeling and contrasts the more standard conditional approach with the joint or simultaneous
approach. The specific parametric models introduced here are special cases of a general framework for
situations in which the marketing mix variables are set with some knowledge of individual response
parameters. We discuss this general framework next. Finally, we provide concluding remarks.


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Data
Data on prescriptions and sales force efforts at the physician level can be obtained from a variety of
syndicated suppliers and has been available for at least ten years. Prior to the advent of these physician
level data sources, sales force allocation and evaluation was done at a more aggregate level and with
judgmental methods (e.g. Lodish (1971) outlines a procedure termed “CALLPLAN” which uses sales-
force estimates of effectiveness rather than behavioral data for territory level decisions). Although
physician level data is commonly available in the pharmaceutical industry, few academic researchers
have had access to it. Kamakura and Kossar (1998), Manchanda and Chintagunta (2000), Gonul et al
(2001) are the exceptions. The focus of these papers is solely on the sales response model.
A major U.S. pharmaceutical firm made available to us data on physician prescription behavior
and sales-force effort for a drug in a mature product category. 1 The data represent a detailed record of
physicians' prescription behavior for the drug in question (which we refer to as drug X) over the period
June, 1999 to June, 2001. This drug belongs to a mature product category and was under patent during
the time our data was collected. The number of affected individuals in this therapeutic category is
estimated to be about 19 million. This makes it one of the top three prescription categories in the
Unites States.
The number of new prescriptions written by each physician for drug X is available monthly.
These data have been compiled from pharmacy records and contains data on prescriptions for drug X
and prescriptions for the drug X category. We have twenty-four months of prescription behavior for
each physician. The specialty of each physician is also available in the data.
Data on details by the firm's sales force for each of these physicians for each month has been
compiled from internal firm records. The number of calls made to each physician per month as well as

1 The firm has requested that we do not identify the drug category or the specific drug.

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the number of free samples of drug X given out to each physician during this time period is available in
the data.
The distinction between a “detail” and a sales “call” is important. In general, the practice in the
pharmaceutical industry has been that more than one drug is detailed during a call to a physician.
Recent trends however indicate that the number of drugs detailed during a call is one or two (Medical
Marketing and Media 2000). However, in our data, a call is recorded only if drug X has been detailed in
that call. We, therefore, treat each calls and details synonymously.
In our analysis, we use a sample of 1000 physicians drawn from a restricted population of
regularly prescribing physicians (there are 142,680 regularly prescribing physicians). We eliminate all
physicians with more than 10,000 total prescriptions for drug X on the grounds that these are probably
data entry errors. We consider only regular prescribing physicians who have received at least two
details in one of the 24 months of observation. We impose this restriction to insure that there is
sufficient variability in detailing to estimate detailing effects This results in a sample frame of 112,088
physicians from which we draw random sample of 1000. We have a total of 24,000 observations - 24
months of data for 1000 physicians. On average, a physician in our sample writes approximately 5 new
prescriptions for drug X and receives 1.8 details and 5.6 (product) samples per month.
In terms of specialty, there are three types of physicians across which we expect to see
differences in prescription behavior based on our discussions with the industry specialists. These are
the specialty directly related to the drug benefit or patient problem (labeled SPE),2 Primary
Care/Family physicians (PCP) and all other specialties (OTH). 18.5 per cent of our sample of
physicians are specialists in the specialty most closely related to drug X’s benefit and 60.1 per cent are
primary care physicians. The composition, detailing and prescription-writing behavior of our sample
matches closely to the full population of regularly prescribing physicians.


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Conditional Modeling Approach
A conditional model for the distribution of prescriptions written given detailing and sampling is the
starting point for our analysis. Our data are count data with most observations at less than 10
prescriptions in a given month. The standard count model is the Poisson regression model. As is well
known, the Poisson model specifies that the conditional mean and variance are identical. Figure 1 plots
the mean and variance (computed over the 24 monthly observations) for each of the 1000 physicians.
There is clear evidence that the variance often exceeds the mean. This does not conclusively prove that
the conditional distribution of prescriptions given detailing is over-dispersed but it is consistent with
this. If there are significant differences between physicians in the parameters of the conditional
distribution, then we are observing a mixture of conditional distributions that could appear to be over-
dispersed. We will adopt the Negative Binomial (NBD) as the base model for the conditional
distribution and couple this model with a model of the distribution of coefficients over physicians.
The NBD model is flexible in the sense that it can exhibit a wide range of degrees of over-dispersion,
allowing the data to resolve this issue. An NBD distribution with mean ? and over-dispersion
it
parameter ? is given by equation 1.
?
k
Pr (y = k ? )
?(? + k) ? ? ? ? ?
?
=
it
it
it
( ) (

(1)
k 1) ?
? ?
?
? ? ? +
? + ?
? + ?
?
it ? ?
it ?
y is the number of new prescriptions written by physician i in month t. As ? goes to infinity, the NBD
it
distribution approaches the Poisson distribution.

The specification of the conditional mean is determined by the nature of detailing effects.
Many analyses of aggregate sales and detailing use cumulative detailing measures that are the cumulative
discounted number of details (c.f. Neslin 2001 or Wittink 2002). The notion here is that the effects of
detailing are felt not only in the current month but also carry-over to future months. Rather than use

2 As an example, for Anti-Ulcer drugs, this specialty would be gastroenterology.

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cumulative detailing measures which involve somewhat ad hoc choices of the discount or smoothing
parameters, we will include a lagged prescriptions term in the conditional mean function to allow for
carry-over effects as in much of the time series literature on advertising effects (Clarke 1976). The
literature on detailing effects has emphasized of diminishing returns to detailing as in Manchanda and
Chintagunta (2000) and Gonul et al (2001). This can be accomplished by addition of a detailing-
squared term to the regression function. We did consider a model with physician-specific squared
terms but found that we could not estimate these coefficients reliably. Given that detailing rarely varies
outside a range of 0-4 details per month, it may be too much to ask of this dataset to estimate physician
level diminishing returns. For this reason, we did not include squared terms in the models reported
below.
We adopt the standard log-link function and specify that the log of the mean of the conditional
distribution is linear in the parameters.
? = E ?y x ? =
'
it
? it it ? exp(x ?
it i )






(2)
ln (? ) = ? + ? Det + ? ln(y ? +
it
0,i
1,i
it
2,i
it 1
d)




(3)
The lagged log-prescriptions term, ln (yit 1
? + d) , in equation 3 allows the effect of detailing to be felt
not only in the current period, but in subsequent periods. We add d to the lagged level of prescriptions
to remove problems with zeroes in the prescription data. Certainly any positive number will “remove”
the zeroes in the data so there is some arbitrariness in the selection of d. In some sense, the smaller
the number added the more accurate the Koyck solution is as an approximation. This might argue for
using very small values such as .1 or .001. The problem here is that the log of these small numbers can
be a very large in magnitude which would have the effect of giving the zeroes in the data undue
influence on the carry-over coefficients. We choose d=1 as the smallest number which will not create
large outliers in the distribution of ln (y +
it
d) .

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