Measuring the Informative and Persuasive Roles of
`Detailing on Prescribing Decisions∗
`
`Andrew Ching†
`Masakazu Ishihara
`Rotman School of Management
`University of Toronto
`
`First draft: May 5, 2008
`
`This draft: April 27, 2010
`
`∗We thank Abe Dunn, Avi Goldfarb, Nitin Mehta, and seminar participants at the University of Toronto,
`Conference on Health Economics and the Pharmaceutical Industry in Toulouse, 2008 IIOC Conference, 2008
`North American Econometric Society Summer Meeting, 2009 AEA Annual Meeting, 2009 CEA Annual Confer-
`ence, and 2009 Marketing Science Conference for their helpful comments. All remaining errors are ours. We are
`grateful to CurrentPartnering for sharing their report on co-marketing agreement with us. We also acknowledge
`the financial support provided by the Michael Lee-Chin Family Institute for Corporate Citizenship at Rotman
`School of Management.
`†Please direct all correspondence to: Andrew Ching, Rotman School of Management, University of Toronto,
`105 St. George Street, Toronto, ON, CANADA M5S 3E6. Phone: 416-946-0728. Fax: 416-978-5433. Email:
`andrew.ching@rotman.utoronto.ca.
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`Measuring the Informative and Persuasive Roles of Detailing on
`
`Prescribing Decisions
`
`Abstract
`
`In the pharmaceutical industry, measuring the importance of informative and persuasive
`
`roles of detailing is crucial for both drug manufacturers and policy makers. However, little
`
`progress has been made in disentangling the informative and persuasive roles of detailing in
`
`empirical research. In this paper, we provide a new identification strategy to separately identify
`
`these two roles. Our key identification assumption is that the informative component of detailing
`
`is chemical specific while the persuasive component is brand specific. Our strategy is to focus
`
`on markets where some drug manufacturers engage in a co-marketing agreement. Under a
`
`co-marketing agreement, two companies market the same chemical using two different brand-
`
`names. With our identification assumption, the variations in the relative market share of these
`
`two brands, together with their brand specific detailing efforts, would allow us to measure the
`
`persuasive component of detailing. The variations in the market share of chemicals, and the
`
`detailing efforts summed across brands made of the same chemical, would allow us to measure
`
`the informative component of detailing. Using the data from the Canadian market for ACE-
`
`inhibitor with diuretic, we find evidence that our identification strategy could outperform the
`
`traditional way of identifying these two effects. We find that both the informative and persuasive
`
`components are strong in this market. We also find that patients could be worse off if the
`
`government bans detailing for ACE-inhibitor with diuretic.
`
`Keywords: Detailing, Informative Role, Persuasive Role, Prescription Drugs, Decisions Under
`
`Uncertainty, Diffusion
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`1
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`Introduction
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`In the pharmaceutical industry, measuring the importance of informative and persuasive roles of
`
`detailing is crucial for both drug manufacturers and policy makers. Understanding the relative
`
`importance of these two roles could help drug manufacturers allocate resources to detailing more
`
`efficiently. If the persuasive role is important, firms could create artificial product differentiation
`
`by increasing their detailing efforts. On the contrary, if detailing is mainly informative and its
`
`persuasive role is weak, the effectiveness of detailing intensity will highly depend on the actual
`
`quality of drugs (i.e., side-effects and efficacy profiles). Among policy debates, many people
`
`believe that detailing is mainly persuasive and consumers will be better off if the industry
`
`reduces their detailing budget. Consequently, there are frequent calls for the industry to restrict
`
`detailing activities. However, if detailing is mainly informative in nature, putting restrictions
`
`on it might slow down the adoption rate of new innovative drugs. Consequently, this would
`
`not only hurt manufacturers’ profits and their incentives to innovate, but also lower consumer
`
`welfare.
`
`Despite its importance, little progress has been made in disentangling the informative and
`
`persuasive roles of detailing. The main difficulty is that both effects would likely have positive
`
`impacts on the demand for prescription drugs. If one only observes sales and detailing efforts
`
`over time, it is hard to disentangle these two roles. In this paper, we provide a new identification
`
`strategy to separately identify the persuasive and informative roles of detailing. Our key identi-
`
`fication assumption is that the informative component of detailing is chemical specific while the
`
`persuasive component is brand specific. Our strategy is to focus on a market where some drug
`
`manufacturers engage in a co-marketing agreement. Under such an agreement, two companies
`
`market the same chemical under two different brand-names. With our identification assump-
`
`tion, the variation in the relative market share of these two brands, together with their brand
`
`specific detailing efforts, would allow us to measure the persuasive component of detailing. After
`
`controlling for the persuasive effect, the variation in the market share of chemicals, and the cor-
`
`responding chemical specific detailing efforts summed across brands made of the same chemical,
`
`would allow us to measure the informative component of detailing. For instance, if detailing
`
`does not play any persuasive role at all, our assumptions would imply that the market shares
`
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`for two brand-name drugs made of the same chemical should be roughly the same over time
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`even if the detailing efforts are different across these two brands (assuming other marketing-mix
`
`variables are about the same across brands).
`
`More specifically, to model persuasive detailing, we follow the previous literature (e.g.,
`
`Nerlove and Arrow 1962) and allow a brand specific persuasive detailing goodwill stock to enter
`
`physicians’ utility functions. To model informative detailing, we consider two alternative models
`
`of informative detailing that have been used in the literature. The first model follows Ching and
`
`Ishihara (2010), which models informative detailing as a means to build/maintain the measure
`
`of physicians who know the most updated information about drugs. The second model follows
`
`Narayanan et al. (2005), in which detailing conveys noisy signals about the true quality of drugs
`
`to physicians.
`
`Our identification strategy applies to both product level data and individual level data.
`
`As an application, we apply it to the product level data from the market of ACE-inhibitor
`
`with diuretic in Canada.1 This market has three brand-name drugs: Vaseretic, Zestoretic, and
`
`Prinzide. Zestoretic and Prinzide are made of the same chemicals, but are co-marketed by two
`
`different companies. To demonstrate the usefulness of our identification strategy, in addition
`
`to estimating the full model with all three brands, we also estimate two versions with only
`
`two brands: Zestoretic and Prinzide, assuming that in one version, we treat the two brands as
`
`the same 1 chemical (i.e., we use our co-marketing identification argument), and in the other
`
`version, we treat the two brands as different two chemicals (i.e., we do not use the co-marketing
`
`identification argument). We argue that the identification of the informative and persuasive
`
`effects in the 2-chemical version relies more heavily on the functional form assumption.
`
`In
`
`particular, we find that the estimation results are counterintuitive in the 2-chemical version –
`
`the persuasive effect of detailing is negative and insignificant. On the contrary, the estimation
`
`results from the 1-chemical version are much more sensible – the persuasive effect is positive
`
`and significant, regardless of the way we model the informative detailing.
`
`1Although we use product level data to illustrate our identification strategy, it should be emphasized that
`the argument applies to individual level data as well. The basic identification ideas are the same except that we
`will need to set up individual level likelihood when estimating the parameters.
`
`2
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`Based on the parameter estimates from the full model with three brands, we investigate
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`the importance of informative and persuasive detailing by simulating our model in the case
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`of ACE-inhibitor with diuretic. We find that both informative and persuasive components
`
`are important. In particular, the informative component is mainly responsible for the growth
`
`of the demand for chemicals, and the persuasive component mainly influences brand choice.
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`Furthermore, to examine the overall impact of detailing on patient welfare, we use compensating
`
`variation to measure changes in the patient’s welfare over time from banning detailing activities.
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`Our simulation results suggest that banning detailing could cost a patient as large as $160 per
`
`prescription during our sample period in the Canadian ACE-inhibitor with diuretic market.
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`The rest of the paper is organized as follows. Section 2 reviews the literature and discusses
`
`the background of the co-marketing agreement. Section 3 describes the demand models. Section
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`4 describes the data. Section 5 discusses the results. Section 6 is the conclusion.
`
`2 Literature Review and Co-marketing Agreement
`
`2.1 Previous Literature on Persuasive Detailing
`
`How does detailing affect physicians’ prescribing decisions? Leffler (1981) argues that detailing
`
`plays both informative and persuasive roles. He finds that newly introduced drugs tend to
`
`receive more detailing than older drugs, and interprets this as evidence that supports informative
`
`detailing. He argues that physicians are relatively unfamiliar with new drugs and hence if
`
`detailing provides information about drug’s benefits and side-effects, drug manufacturers would
`
`spend more detailing efforts for newer drugs. However, he also finds that drug companies
`
`still spend significant amount of detailing efforts on old drugs and target older physicians. He
`
`interprets this as evidence for its persuasive role, assuming that older physicians have already
`
`known the older drugs’ efficacy and side-effect profiles.
`
`Hurwitz and Caves (1988) find that pre-patent expiration cumulative detailing efforts slow
`
`down the decline in post-patent expiry market shares of brand-name drugs. They interpret
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`this as evidence for its persuasive role. Rizzo (1999) also finds evidence that detailing lowers
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`the price elasticity of demand and argues that it supports persuasive detailing. However, it
`
`should be pointed out that the results from Hurwitz and Caves (1988) and Rizzo (1999) are
`
`also consistent with informative detailing. As argued by Leffler (1981), informative detailing
`
`reduces the uncertainty about drug qualities, and hence could also achieve similar empirical
`
`implications.
`
`Narayanan et al. (2005) is the first paper that structurally estimates the informative and
`
`persuasive roles of detailing in the pharmaceutical market. They extend the framework of Erdem
`
`and Keane (1996). Their identification argument builds on Leffler (1981) - they assume that
`
`drug companies know the true quality of their products when launching them, and informative
`
`detailing provides physicians with noisy signals about their products’ true qualities. With this
`
`assumption, physicians will eventually learn the true quality of the drugs and detailing no longer
`
`plays any informative role in the long-run. As a result, the long-run correlation between sales
`
`and cumulative detailing efforts will identify the parameters that capture the persuasive role of
`
`detailing. The product diffusion paths then identify the parameters that capture the informative
`
`role.
`
`It should be emphasized that in their framework, in order to separately identify the
`
`informative and persuasive roles of detailing, it is crucial that: (i) one assumes detailing does
`
`not play any informative role in the long-run; (ii) the data set needs to be long enough so that
`
`it captures part of the product lifecycle after learning is complete.2 In contrast, this modeling
`
`assumption and data requirement are not necessary for our identification strategy.
`
`Another related paper is by Ackerberg (2001). He argues that one can empirically dis-
`
`tinguish informative and persuasive effects of advertising by examining consumers’ purchase
`
`behavior conditional on whether they have tried the product before. His insight is that ad-
`
`vertisements that give consumers product information should primarily affect consumers who
`
`have never tried the brand, whereas persuasive advertisements should affect both inexperienced
`
`and experienced consumers. His identification argument requires one to observe individual level
`
`2Anand and Shachar (2005), Byzalov and Shachar (2004), Chan et al. (2007), Mehta et al. (2008), Narayanan
`and Manchanda (2009) rely on similar identification arguments to estimate the informative and persuasive roles
`of advertising using individual level data.
`
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`panel data, while our identification strategy applies as long as one observes product level panel
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`data.
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`2.2 Co-marketing Agreement
`
`Co-marketing in the pharmaceutical industry is a marketing practice where a company in ad-
`
`dition to its own, uses another company’s sales force to promote the same product, and allow
`
`another company to use a different brand name.3 According to CurrentPartnering (2009), the
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`total number of co-marketing deals announced in the United States between 2000 and 2008 is
`
`208, and the yearly number has remained at fairly steady levels. One reason why a company
`
`that develops the drug is willing to partner with another company could be because it requires
`
`high fixed costs to build a sales force. The sales force in the pharmaceutical industry requires
`
`extensive training because they are required to know the clinical trials results of not only the
`
`drug being promoted, but also their rivals’ drugs. Instead of paying such a high fixed cost, a
`
`company which is short in their sales force of promoting a certain category of drugs (say a high
`
`blood pressure drug) might find it worthwhile to sign a co-marketing agreement with another
`
`company, and charge its partner a royalty fee.
`
`This type of marketing agreement has also appeared in the automobile industry (Sullivan
`
`1998; Lado et al. 2003). Furthermore, for industrial products, it is common that different firms
`
`market essentially identical products using their own brand-names (Saunders and Watt 1979;
`
`Bernitz 1981). In some countries, firms also market generic drugs with a brand name (Birkett
`
`2003). Under these environments, we expect that our identification arguments could also be
`
`applied.
`
`3There is another type of related arrangement which is called co-promotion agreement where two or more
`firms market the same drug under one brand-name.
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`3 Model
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`We now turn to describe the models that will be used to implement our new identification
`
`strategy for informative and persuasive detailing. We consider two structural models that have
`
`been developed in the literature. They differ in terms of how to model the role of informative
`
`detailing. The first model (Model CI) extends Ching and Ishihara (2010). They model infor-
`
`mative detailing as a means to build/maintain the measure of physicians who know the most
`
`updated information about drugs. The second model (Model NMC) follows Narayanan et al.
`
`(2005), who model detailing as a way of conveying noisy signals about the true quality of drugs
`
`to physicians. In both models, we model the persuasive role of detailing by including a detailing
`
`goodwill stock in the utility function for physicians. These two models allow us to capture the
`
`role of informative detailing under different environments. For example, when manufacturers
`
`know the true quality of their drugs from the beginning of the product lifecycle, Model NMC
`
`is particularly relevant. When manufacturers do not know the true quality and use detailing
`
`to inform or remind physicians of the most updated information, Model CI is more appropri-
`
`ate. Since these two models generate different empirical implications, it is of our interest to
`
`investigate how our identification strategy performs regardless of the way we model informative
`
`detailing.
`
`The following basic setup is common in both models. We consider a set of brand-name
`
`drugs, which treat the same illness using similar chemical mechanisms. Let j = 1, . . . , J indexes
`
`brands, j = 0 denotes an outside alternative, which represents other close substitutes. Some
`
`of the brands may be marketed under a co-marketing agreement and are made of the same
`chemical. Let k = 1, . . . , K indexes for chemicals, where K ≤ J. Let Ak be the set of brands
`that are made of chemical k. We assume that each brand is made of one of K chemicals. The
`characteristics of brand j ∈ Ak are given by pj and qk, where pj is the price of product j, and qk
`is the mean quality level of chemical k. Physicians are imperfectly informed about the chemical’s
`
`mean quality level, qk. Let I(t) = (I1(t), . . . , IK(t)) be a vector of public information sets that
`
`describe the most updated belief about q = (q1, . . . , qK) at time t.
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`As we mentioned, CI and NMC differ in terms of how they model informative detailing.
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`Model CI assumes that I(t) is updated by a representative opinion leader based on past patients’
`
`experiences with the chemical.4 This is the only role that he/she plays. For each chemical k, a
`
`physician either knows Ik(t), or I k, which is the initial prior that physicians have when a drug
`made of chemical k is first introduced.5 Let Mkt be the measure of physicians who know Ik(t).
`
`In CI, Mkt depends on the cumulative detailing efforts at time t. The learning process for I(t)
`
`is similar in NMC; however, they assume that detailing does not influence Mkt. More precisely,
`they assume Mkt = 1,∀k, t. Moreover, other than consumption experience signals, detailing also
`provides noisy signals about the true quality of the chemicals for updating the I(t).
`
`Our key identification assumptions are: 1) informative detailing is chemical-specific; and
`
`2) persuasive detailing is brand-specific. The first assumption implies: (a) Ik(t) is updated based
`
`on past patients’ experiences for all products made of chemical k; (b) in Model CI, Mkt depends
`
`on the sum of the cumulative detailing efforts for all drugs made of chemical k; and (c) in Model
`
`NMC, in addition to past patients’ drug experiences, Ik(t) are also updated based on the sum
`
`of the detailing signals for all drugs made of chemical k. The second assumption implies that
`
`the persuasive detailing goodwill stock for brand j is built based only on the detailing efforts
`
`for brand j. In what follows, we will describe Model CI first, and then Model NMC.
`
`3.1 Model CI (Ching and Ishihara 2010)
`
`3.1.1 Updating of the Information Set
`
`A drug is an experienced good. Consumption of a drug provides information about its quality.
`
`It is assumed that physicians and patients in the model can measure drug qualities according to
`
`4A representative opinion leader captures the following intuition. The medical continuing education litera-
`ture finds that opinion leaders are an important source of information for general physicians (e.g., Haug 1997,
`Thompson 1997). In Medicine, opinion leaders are physicians who specialize in doing research in a particular
`field (e.g., cardiovascular). The research focus of their career requires them to be much more updated about the
`current evidence about the drugs used in the field.
`5For simplicity, we assume that physicians and the representative opinion leader share the same initial prior
`belief. In general, we can allow them to be different.
`
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`a fixed scale. For example, a patient can measure quality in terms of how long he/she needs to
`
`wait before the drug becomes effective to relieve his/her symptoms, how long his/her symptoms
`
`would be suppressed after taking the drug, or how long the side-effects would last.6
`
`Each patient i’s experience with the quality of a drug made of chemical k at time t (˜qikt)
`
`may differ from its mean quality level qk. As argued in Ching (2000; 2010; 2011), the difference
`
`between ˜qikt and qk could be due to the idiosyncratic differences of human bodies in reacting to
`
`drugs. An experience signal may be expressed as,
`
`˜qikt = qk + δikt,
`
`(1)
`
`where δikt is the signal noise. We assume that δikt is an i.i.d. normally distributed random
`
`variable with zero mean, and the representative opinion leader’s initial prior on qk (I k) is also
`
`normally distributed:
`
`δikt ∼ N (0, σ2
`δ ),
`
`and
`
`qk ∼ N (q
`
`, σ2
`k).
`
`k
`
`(2)
`
`The representative opinion leader updates the public information set at the end of each period
`
`using the experience signals that are revealed to the public. The updating is done in a Bayesian
`
`fashion. In each period, we assume that the number of experience signals revealed is a random
`
`subsample of the entire set of experience signals. This captures the idea that not every patient
`
`revisits and discusses his/her experiences with physicians, and not every physician shares his/her
`
`patients’ experiences with others.
`
`According to the Bayesian rule (DeGroot 1970), the expected quality is updated as follows:
`
`E[qk|I(t + 1)] = E[qk|I(t)] + ιk(t)(¯qkt − E[qk|I(t)]),
`
`(3)
`
`where ¯qkt is the sample mean of all the experience signals that are revealed in period t; ιk(t) is a
`
`Kalman gain coefficient, which assigns the updating weight to ¯qkt. Note that both ιk(t) and the
`
`
`perception variance, σ2k(t + 1), are functions of the variance of the signal noise (σ2δ ), perceived
`
`
`
`6Obviously, drug qualities are multi-dimensional. Following Ching (2010), we implicitly assume patients are
`able to use a scoring rule to map all measurable qualities to a one-dimensional index. It is the value of this
`one-dimensional index that enters the utility function.
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`k(t)), the quantities sold at time t for all drugs made of chemical k (nkt ),7 and the
`
`variance (σ2
`proportion of experience signals revealed to the public (κ). They can be expressed as:
`
`ιk(t) =
`
`σ2
`k(t)
`k(t) + σ2
`σ2
`
`δ
`κnk
`t
`
`,
`
`and
`
`σ2
`k(t + 1) =
`
`1
`k(t) + κnk
`
`t
`σ2
`δ
`
`1
`σ2
`
`.
`
`(4)
`
`The above expressions imply: (i) ιk(t) increases with σ2
`k(t); (ii) after observing a sufficiently
`
`large number of experience signals for a product, the representative opinion leader will learn
`about qk, at any arbitrarily precise way (i.e., σk(t) → 0 and E[qk|I(t)] → qk as the number of
`signals received grows large).
`
`3.1.2 Detailing and Measure of Well-Informed Physicians
`
`There is a continuum of physicians with measure one. They are heterogeneous in their informa-
`
`tion sets. A physician is either well-informed or uninformed about chemical k. A well-informed
`
`physician knows the current information set maintained by the representative opinion leader,
`
`i.e., Ik(t). An uninformed physician only knows the initial prior, i.e., I k. This implies that the
`number of physician types is 2K.8
`
`The measure of well-informed physicians for chemical k at time t, Mkt, is a function of
`
`(cid:80)
`
`Mkt−1 and D1t, ..., DJt. For simplicity, we assume that this function only depends on Mkt−1
`
`Djt, i.e., Mkt = f (Mkt−1, Dk
`and Dk
`t ). We assume that f (Mkt−1, .) is monotonically
`t =
`j∈Ak
`t . To capture the idea that physicians may forget, we assume that f (M, 0) ≤
`increasing in Dk
`M,∀M .
`
`Following Ching and Ishihara (2010), in our econometric model, we capture the relationship
`
`
`
`between Mkt and (Mkt−1, Dkt ) by introducing a detailing goodwill stock, GI
`kt, which accumulates
`
`as follows:
`
`
`GI
`
`kt = (1 − φI)GIkt−1 + Dk
`t ,
`
`(5)
`
`t is the total quantity prescribed for chemical k at time t, including free samples measured in number of
`7nk
`prescriptions.
`8For justifications of this modeling assumption, see Ching and Ishihara (2010).
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`where φI ∈ [0, 1] is the depreciation rate. We specify the relationship between Mkt and GI
`kt as:
`
`Mkt =
`
`exp(β0 + β1GI
`kt)
`1 + exp(β0 + β1GI
`kt)
`
`.
`
`(6)
`
`3.1.3 Prescribing Decisions
`
`Now we turn to discuss how physicians make their prescribing decisions. Each physician takes
`
`the current expected utility of his/her patients into account when making prescribing decisions.
`
`Physician h’s objective is to choose dhij(t) to maximize the current period expected utility for
`
`his/her patients:
`
`(cid:88)
`
`E[
`j∈{0,1,...,J}
`
`uijt · dhij(t)|I h(t)],
`
`(7)
`
`where dhij(t) = 1 indicates that alternative j is chosen by physician h for patient i at time t,
`
`and dhij(t) = 0 indicates otherwise. We assume that
`
`j dhij(t) = 1. The demand system is
`obtained by aggregating this discrete choice model of an individual physician’s behavior.
`
`(cid:80)
`
`We assume that a patient’s utility of consuming a drug can be adequately approximated
`
`by a quasilinear utility specification, additively separable in a concave subutility function of
`
`drug return, and a linear term in price. The utility of patient i who consumes drug j made of
`
`chemical k at time t is given by the following expression:
`
`uijt = αj − exp(−r˜qikt) − πppjt + ςilt + ζikt + eijt,
`
`(8)
`
`where αj is a brand-specific intercept; r is the risk aversion parameter; πp is the utility weight
`
`for price; (ςilt + ζikt + eijt) represents the distribution of patient heterogeneity; and k, l indexes
`
`nests.9 ςilt, ζikt, and eijt are unobserved to the econometrician but observed to the physicians
`
`when they make their prescribing decisions. We assume that ςilt, ζikt and eijt are i.i.d. extreme
`
`value distributed.
`
`In this specification, r represents the coefficient of absolute risk aversion.
`
`Also, we allow a brand-specific intercept to capture time-invariant differences among drugs.
`
`9This is equivalent to modeling physicians’ choice as a three-stage nested process, where they choose between
`the inside goods and the outside good in the first stage, choose one of the chemicals in the second stage, and an
`alternative made of the chemical chosen in the second stage.
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`Note that ˜qikt is observed neither by physicians nor patients when prescribing decisions
`
`are made. It is observed by physicians/patients only after patients have consumed the drug,
`
`but it remains unobserved by the econometrician. Physicians make their decisions based on the
`
`expected utility of their patients. Let I(t) and I h(t) denote the representative opinion leader’s
`information set and physician h’s information set at time t, respectively. For drug j ∈ Ak, if
`physician h is well-informed about chemical k at time t, his/her expected utility will be:
`E[uijt|I h(t)] = E[uijt|Ik(t)] + γP GP
`jt + γSF Sjt
`= αj − exp(−rE[qk|I(t)] +
`+γP GP
`jt + γSF Sjt + ςilt + ζikt + eijt,
`
`δ )) − πppjt
`r2(σ2
`k(t) + σ2
`
`1 2
`
`(9)
`
`where GP
`jt is a detailing goodwill stock for drug j at time t, and γP captures the effect of
`
`persuasive detailing; F Sjt is the amount of free samples given for drug j at time t, and γS
`
`captures the effect of free samples. Similar to GIkt, we assume that GP
`jt accumulates as follows:
`jt = (1 − φP )GP
`GP
`jt−1 + Djt,
`
`(10)
`
`We emphasize that GP
`jt is drug j specific rather than chemical k specific. Furthermore, we allow
`
`the depreciation rates to be different for GIkt and GP
`jt. We should also note that Ching and
`Ishihara (2010) just focus on modeling the informative role of detailing, and they do not allow
`
`for GP
`jt in the utility function. They also do not control for free samples.
`
`If physician h is uninformed about chemical k at time t, his/her expected utility of choosing
`drug j ∈ Ak becomes:
`E[uijt|I h(t)] = E[uijt|I k] + γP GP
`jt + γSF Sjt
`k + σ2δ )) − πppjt
`= αj − exp(−rq
`+
`+γP GP
`jt + γSF Sjt + ςilt + ζikt + eijt.
`
`
`r2(σ2
`
`1 2
`
`k
`
`(11)
`
`It should be noted that patient heterogeneity components of the utility function (ςilt, ζikt, eijt)
`
`reappear in the expected utility equation because they are stochastic only from the econometri-
`
`cian’s point of view.
`
`Equations (8)-(11) apply only to the inside goods. In each period, physicians may also
`
`choose an outside alternative that is not included in our analysis (i.e., other non-bioequivalent
`
`11
`
`IMMUNOGEN 2275, pg. 13
`Phigenx v. Immunogen
`IPR2014-00676
`
`

`
`drugs). We assume the expected utility associated with the outside alternative takes the follow-
`
`ing functional form:
`
`E[ui0t|I h(t)] = α0 + πtt + ςi0t + ζi0t + ei0t.
`
`(12)
`
`The time trend of the outside alternative allows the model to explain why the total demand for
`
`inside goods may increase or decrease over time.
`
`The quantity demand for drug j ∈ Ak, njt, can be expressed as,
`
`njt = Sizet · S(j|Dt, (E[qk|I(t)], σk(t), Mkt−1)K
`k=1; θd) + jt,
`where Sizet is the size of the market, S(j|·) is the market share of drug j, jt represents a
`measurement error, and θd is a set of demand side parameters.
`
`(13)
`
`3.2 Model NMC (Narayanan et al. 2005)
`
`Many elements in Model NMC are similar to Model CI. Therefore, we will only discuss the
`
`elements that are specific to Model NMC. All the variables introduced in the previous section
`
`will be used here without repeating the descriptions.
`
`3.2.1 Updating of the Information Set
`
`In Model NMC, in addition to consumption experience signals, detailing provides physicians
`
`with noisy signals about the true quality of drugs. Let ˜qd
`hkt be the detailing signal about the
`
`quality of chemical k that physician h receives at time t. Similar to consumption experience
`
`signals, it may be expressed as,
`
`˜qd
`hkt = qk + ϑhkt,
`
`(14)
`
`where ϑhkt is the signal noise. We assume that ϑhkt is an i.i.d. normally distributed random
`
`variable with zero mean:
`
`ϑhkt ∼ N (0, σ2
`ϑ).
`
`12
`
`(15)
`
`IMMUNOGEN 2275, pg. 14
`Phigenx v. Immunogen
`IPR2014-00676
`
`

`
`Signals from patients’ experiences and detailing are used to update I(t + 1) in a Bayesian
`
`fashion. According to the Bayesian rule (DeGroot 1970), the expected quality is updated as
`
`follows:
`
`E[qk|I(t + 1)] = E[qk|I(t)] + ιk(t)(¯qkt − E[qk|I(t)]) + ωk(t)(¯qd
`kt − E[qk|I(t)]),
`
`(16)
`
`
`
`where ¯qdkt is the sample mean of all the detailing signals for chemical k in period t.10 Note that
`unlike Model CI, the expected quality is updated based on consumption signals and detailing
`
`signals. ιk(t) and ωk(t) are expressed as
`
`ιk(t) =
`
`1
`σ2
`
`κnk
`t
`σ2
`δ
`
`t
`σ2
`δ
`
`+ κdDk
`σ2
`ϑ
`
`t
`
`k(t) + κnk
`k(t) + κnk
`where κd is a scaling parameter similar to κ. ιk and ωk can be interpreted as the weights that
`
`,
`
`and ωk(t) =
`
`κdDk
`t
`σ2
`ϑ
`
`1
`σ2
`
`t
`σ2
`δ
`
`+ κdDk
`σ2
`ϑ
`
`t
`
`,
`
`(17)
`
`physicians attach to consumption experiences and detailing efforts in updating its expectation
`
`about the level of qk.
`
`The perception variance at the beginning of time t + 1 is given by (DeGroot 1970):
`
`σ2
`k(t + 1) =
`
`1
`k(t) + κnk
`
`t
`σ2
`δ
`
`1
`σ2
`
`.
`
`+ κdDk
`σ2
`ϑ
`
`t
`
`(18)
`
`Physicians’ prescribing decisions are identical to those of Model CI except that all physi-
`cians are informed of I(t), i.e., Mkt = 1 ∀k, t.
`
`4 Background and Data Description
`
`4.1 Background
`
`Now we turn to discuss the Canadian market of ACE-inhibitor with diuretic in Canada. ACE-
`
`inhibitor works by limiting production of a substance that promotes salt and water retention in
`
`the body. Diuretic prompts the body to produce and eliminate more urine. This helps in lowering
`
`kt|(κdDkt , I(t)) ∼ N(qk, σ2
`10 ¯qd
`
`).
`
`ϑ
`κdDk
`t
`
`13
`
`IMMUNOGEN 2275, pg. 15
`Phigenx v. Immunogen
`IPR2014-00676
`
`

`
`blood pressure. This class of combination drugs are usually not prescribed until therapy is
`
`already underway. The majority of Canadian have some form of coverage for prescription drugs.
`
`In 1995, it is estimated that 88% of Canadian had coverage: 62% were covered under private
`
`plans, 19% under provincial plans, and 7% were covered under both.11 Provinces subsidize
`
`the cost of prescription drugs for at least some sectors of the population, most notably seniors
`
`and social assistance recipients. Patented drug prices are regulated in Canada by the Patented
`
`Medicine Prices Review Board (PMPRB). There are two components to this price regulation.
`
`One is the limit