PRESCRIPTION DRUG ADVERTISING AND PATIENT COMPLIANCE: A PHYSICIAN AGENCY APPROACH. By Olivier Armantier and Soiliou Daw Namoroy July 2006 Abstract This paper proposes an analysis of both doctors and patients’ behavior in an agency model that accounts for the interplay between two highly debated health issues: drug advertising toward doctors and/or patients, and the serious problem of patients’noncompliance with their doctors’prescriptions. Due to the lack of individual data, we propose a structural approach inspired from the industrial organization literature. The model is estimated semiparametrically with product level data on the U.S. market for anti-glaucoma drugs. The results suggest that doctors’prescriptions are directly in‡uenced by the probability of noncompliance, as well as advertising aimed at both doctors and patients. Advertisement toward patients (respectively, doctors) appears to have contributed to (respectively, slowed down) the reduction of the estimated average noncompliance rate. Keywords: Direct-to-consumer advertising, prescription compliance, physician agency model, structural econometrics, semiparametric estimation. JEL Classi…cation: I10, L10, 14. Université de Montréal, CIRANO, CIREQ, CRT. Departement de sciences économiques, 3150 Jean-Brillant, Montréal, QC, H3T1N8. Email:
[email protected]. y Dept. of Economics, University of Pittsburgh, PA 15260, U.S.A;
[email protected]. We would like to thank Hugo Benitez-Silva, David DeJong, Debra Dwyer, John Hause, Mark Montgomery, Thomas Rawski, Jean-Francois Richard and Christopher Swann for helpful comments and suggestions, as well as seminars participants at the University of Pittsburgh, the University of Illinois at Urbana-Champaign, and the University of Saskatchewan. We would like to thank IMS Health and CMR for graciously providing the data. All remaining errors are ours.
1. INTRODUCTION In 1997, the Food and Drug Administration (FDA) simpli…ed the information requirements for direct-to-consumer advertising (DTCA) of prescription drugs. The FDA’s decision contributed to a sharp increase in the spending on DTCA (from $624 million in 1996 to $1.3 billion in 1998).1 This sudden intensi…cation of DTCA fueled the controversy pertaining to the e¤ects of advertising on the doctor-patient relationship. At the same time, concerns have grown in the medical profession about high rates of patient noncompliance with prescriptions drug regimens.2 As further explained, noncompliance is clearly a serious problem: a recent study indicates that 70% of patients do not comply with drug prescriptions, resulting in annual losses of $170 billions in the U.S. (Dezii 2000).3 As we shall see, although it has been recognized by health professionals, and in particular the FDA, the connection between advertising and prescription noncompliance has been ignored in the economics literature. The aim of this paper is to analyze the prescription and compliance behaviors of respectively doctors and patients, in an agency model that accounts for the interplay between patient noncompliance, direct-to-consumer advertising, and drug promotion toward doctors.4 More speci…cally, our goal is to address the following two questions: (i) How do advertising and the probability of noncompliance a¤ect the doctor’s prescription behavior? (ii) How does drug promotion to doctors and/or patients in‡uence the rate of noncompliance with medication prescription in a given therapeutic class? 1
These …gures are for the entire pharmaceutical industry. See Holmer (1999) and The National Institute for Health Care Management (2000). 2 Compliance is de…ned in the medical literature as “the extent to which a person’s behavior coincides with medical or health advice” (Bentley, Wilkin and McCa¤rey 1999). In this paper, we adopt the de…nition used in Ellikson, Stern and Trajtenberg (2000): a patient is said to be noncompliant with his doctor’s prescription if either he does not buy the drug (“purchase noncompliance”), or he does not consume the drug in accordance to the doctor’s prescription (“use noncompliance”). Noncompliance is, therefore, assumed to be a binary variable. 3 These losses are in particular generated by unnecessary medical expenses (e.g. additional hospitalizations, admissions in nursing home) and lost productivity. 4 An agency problem arises when a principal (the patient) hires an agent (the doctor) to perform a task on his behalf, but the goals of the two parties di¤er.
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The relevance and actuality of these issues may be demonstrated by the public inquiry launched in 2002 and 2005 by the FDA to determine the bene…ts and drawbacks of prescription advertising.5 Indeed, the FDA, which is contemplating whether or not to regulate further DTCA, speci…cally asked about the empirical e¤ect of DTCA on prescription habits, and patient noncompliance. In other words, the answers to the questions raised in the present paper may have important consequences, both from an economic and health perspective. In our attempt to answer the above two questions, we face two forms of data limitation. First, in none of the existing therapeutic classes of drug, does there exist noncompliance data on all (or a majority of) the drugs in the class. Moreover, the scattered existing data are not reliable because of the large variety of results obtained by di¤erent measurement methods. In fact, the measurement of noncompliance is still in the search of a …rm methodological basis. So, even though most experts agree that noncompliance is a serious health issue, there is only very limited data on this phenomenon. Second, our data set only contains product or market level information. In particular, we do not observe individual choices made by doctors and/or patients. These data limitations, therefore, preclude a purely descriptive reduced form approach. Instead, we adopt a structural approach, in which unobserved rates of noncompliance are treated as parameters to be estimated. In addition, to overcome the second form of data limitation, we follow the industrial organization literature in which techniques have been developed to estimate individual decision making models with product level data (Berry 1994, Berry, Levinsohn and Pakes 1995). Although the results produced by a structural model have the desirable property of being readily interpretable, their validity remains contingent on the acceptance of the underlying assumptions. In particular, as further explained in section 4, we will have to assume in order to identify the model, that the set of variables in‡uencing directly the doctors’utility, and the set of variables in‡uencing their patients’rate of non-compliance, do not overlap perfectly. It is important to stress from the beginning that our approach is an attempt to make sense of the alternative views on the interplay between noncompliance and drug advertising, within a coherent economic framework. Note, however, that by drawing extensively from the medical literature on the determinants on noncompliance, we strived to impose just enough structure to estimate the model semiparametrically from the available data. 5
See Docket No. 2002N-0209 and Docket http://www.fda.gov/ohrms/dockets/dockets/dockets.htm.
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No.
2005N-0354
at
To explain the doctor-patient relationship, we propose a two-period agency model in the setting of discrete choice theory. In period 1, the doctor prescribes a drug to treat the patient from a …nite set of alternative drugs. In period 2, the patient decides whether to comply with this prescription. The patient’s choice is assumed to be a rational trade-o¤ between health bene…ts, and monetary as well as non-monetary costs associated with drug consumption (e.g. side e¤ects, complexity of dosage schedule). The doctor’s decision to prescribe a given drug is in‡uenced, in particular, by his expectations of patient noncompliance. Finally, targeted advertisements toward doctors and/or patients in‡uence the decisions of both agents. We estimate this model by combining IMS and CMR product-level data on the U.S. market for anti-glaucoma drugs.6 The data set spans the period 1995 to 1999. It, therefore, covers the 1997 FDA decision on DTCA. The empirical analysis combines the techniques from semiparametric index models (Ichimura and Lee 1991, Ichimura 1993) and nonparametric models with endogenous variables (Newey, Powell and Vella 1999, Blundell and Powell 2003). We …nd that advertising for a given drug both toward doctors and patients increases the probability that it will be prescribed. Doctors are also sensitive to prices and anticipated noncompliance when they prescribe a drug. The results also suggest the possibility that the average noncompliance rate with anti-glaucoma drugs has been considerably reduced between 1995 and 1999. We argue that this reduction may well be the net e¤ect of two opposite forces: DTCA appears to have decreased noncompliance, whereas promotion to doctors may have contributed to increase the average noncompliance rate. In the next section, we provide a review of the related literature, along with a brief background on the relationship between advertising and noncompliance. In Section 3, we present the model and its theoretical implications. Section 4, describes the data and the estimation strategy. The empirical results are presented in Section 5. 6
IMS Health an CMR are two private market research companies, and major sources of information on the health care and advertising industries.
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2. Background and Related literature 2.1. Compliance Behavior Although the precise measurement of noncompliance remains a controversial topic, noncompliance is widely recognized to be a serious public health problem. Ellickson, Stern and Trajtenberg (2000) (hereafter, EST) report an average rate of noncompliance with drug prescription of 70% (20% purchase noncompliance and 50% use non compliance). Dezii (2000) reports the rate of use noncompliance for the following classes of medication: medications for diabetes (31%), tuberculosis medications (45%), antihypertensives (47%), antipsychotics and schizophrenics (58%), and penicillin for rheumatic fever (67%). As mentioned in the introduction, the annual cost of noncompliance in 2000 was estimated at $170 billions in the U.S., thereby exceeding the expenses in prescription medications during that year. Noncompliance also have serious health implications: it has been estimated that 11.4% of admissions to hospital resulted from failure to comply with drug regimen (Col, Fanale and Kronholm 1990). A Study by Sullivan, Krelig and Hazlet (1990) also suggests that 125,000 cardiovascular deaths should be blamed annually in the U.S. on noncompliance. In fact, the American Hearth Association has recently stated that “the cost of noncompliance in terms of human life and money is shocking”, and has made prescription drug compliance one of the association key issue.7 To the best of our knowledge, EST (2000) are the …rst economists to explicitly analyze noncompliance with drug prescriptions. According with the approach adopted in the present paper, they develop a physician agency model in which agents play a sequential game: the doctor chooses …rst the treatment and its intensity, and the patient then decides whether to adhere to the treatment recommendation.8 EST, however do not consider the interplay between advertising and noncompliance, and their theoretic model could be estimated only with detailed data on noncompliance. As noted by the authors, these data do not exist so far. In contrast, we propose a model that may be estimated with available product level data, and without requiring the observation of noncompliance rates. Recently, several studies in the marketing literature have attempted to understand better the determinants of patients’consumption behavior (see Manchanda et al. 2005 for a review). In particular, Bowman, Heilman, Seetharaman (2004), 7
See the 1999 American Heart Association statement, “American Hidden Health Threat”. For a general overview of the literature on physician agency models, see McGuire (2000). For speci…c applications to drug selection, see Rochaix (1988), as well as Mott et al. (1998). 8
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and Wosinska (2005) …nd that by signi…cantly lowering the number and the duration of unclaimed re…ll prescriptions, DTCA curbs down re-purchase noncompliance. The reduced form approach adopted by these authors does not account, however, for (i) the doctor/patient interaction, (ii) drug promotion toward doctors, and (iii) the separate e¤ects of both forms of advertising on the doctors’ prescription behavior. 2.2. Prescription Drug Promotion Prescription drug promotion by pharmaceutical …rms takes two forms: the promotion aimed at doctors, and advertisements directed to consumers. Advertisements toward doctors include visits by pharmaceutical representatives, free samples, advertisements in medical journals, displays and presentations at professional meetings. Such promotions were the only form of advertising for prescription drugs until 1981, when drug companies expanded their marketing strategies to include direct advertising to patients. Although the most familiar form of promotion toward consumers targets the general population via popular media, such as television or magazines, DTCA is also commonly conveyed directly to patients through web sites, help-lines, personalized mailings, targeted web-advertisement, and indoctor-o¢ ce or in-pharmacy information pamphlets. After a brief moratorium in 1983, the FDA permitted DTCA to resume in 1985 under stringent requirements on the informational content of advertisements. DTCA has grown signi…cantly, especially since 1997 when the FDA simpli…ed considerably the information requirements.9 The recent increase in advertising spending, combined with the relative shift in the structure of advertising (from promotion to doctors, to DTCA) has intensi…ed the controversy pertaining to the e¤ects of advertising on both doctors and consumers. Most of the controversy concerning promotion toward doctors is related to the informative or the persuasive nature of advertising. Drug makers insist that promotions are informative, but others (including some health practitioners and public health policy makers) are concerned by the possibility that advertising inappropriately in‡uences doctors’ prescription behavior.10 DTCA is by far the 9 The information constraints related to drug advertising require the advertiser to provide a brief summary relating to the side e¤ects, contraindications and e¤ectiveness of the advertised drug. In the late 1997, the FDA issued a document, the Draft Guidance for Industry: ConsumerDirected Broadcast Advertisements , which makes it much easier for the drug advertisers to meet these requirements (Reeves 1998). 10 A sampling of the arguments in this debate may be found in Hurwitz and Caves (1988), and
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most controversial issue related to drug promotion. Opponents of DTCA argue that advertising intrudes upon the doctor-patient relationship. For instance, patients may request from their doctor drugs that have been advertised, even when these drugs are more expensive or are not the most appropriate for their condition (see e.g. Peters 2001). Supporters of DTCA, on the other hand, suggest that the information provided through DTCA may educate the public to make more informed medical choices. For instance, it has been recently shown that DTCA encourages untreated patients to consult their doctor (see Wosinska 2002 and Izuka and Jin 2005).11 A potentially important social bene…t, mentioned in Wosinska (2002) and explicitly studied here, is the in‡uence of DTCA on compliance. Responses to the FDA public inquiry mentioned in the introduction, indicate that a wide majority of health professionals (including the National Health Council, the National Institutes for Health Care Management, and representants of the FDA) believe that DTCA may help curb down prescription noncompliance. The arguments most frequently advanced are that DTCA acts as a reminder to take the drug, it comforts the patient, and makes him feel better about the drug. These factors have been known for years to in‡uence positively compliance (Marinker et al. 1997). Other respondents to the FDA inquiry, however, expressed skepticism, some even suggesting that the long recitation of side e¤ects imposed by the FDA on DTCA, may in fact reduce the likelihood that a patient complies to his doctor’s prescription. To summarize, although DTCA and its e¤ects on compliance are important issues, they are still relatively poorly understood. This may be explained by the fact that detailed data on DTCA are only starting to be available.
3. A Model of Drug Product Selection It is assumed that an initial examination of the patient by the doctor has led to the diagnosis of a disease, which is common knowledge. The disease may Berndt et al. (1997). 11 Due to the lack of speci…c information on doctor’s visits, we are unable to address this issue in the present paper. As further explained in section 4.1, however, DTCA for glaucoma drugs are essentially targeted toward already diagnosed patients, rather than the general population. In other words, DTCA for glaucoma drugs does not directly in‡uence an individual’s decision to consult. DTCA for glaucoma drugs essentially targets already diagnosed patients, however. This may suggest that the above issue is not important in the speci…c case that we examine here.
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be treated either by one of J alternative drugs in a given therapeutic class, or by an “outside” J + 1-th method (e.g. surgery). The game takes place in two periods. In period one, the doctor prescribes the best available drug (according to the doctor) for the patient, conditional on her information set.12 In period 2, the patient chooses to comply or not with the prescription.13 This choice is assumed to be a rational trade-o¤ between anticipated health bene…ts, and both monetary and non-monetary costs associated with compliance with the prescribed drug regimen. A patient is characterized by a vector p 2 Rq , representing, e.g., some aspects of his health history, his anti-drug attitude, his exposure to DTCA. This vector of characteristics is unobserved by the doctor, but its probability distribution is assumed to be common knowledge, although unknown to the econometrician. The patient’s preference is represented by a utility function which depends on the prescribed alternative j (j = 0; : : : ; J), the patient’s privately known idiosyncratic characteristics, p, and the decision variable nc, which can take two possible values 1 (do not comply) and 0 (comply). More precisely, when drug j is prescribed, patient p’s utility function over the alternatives “do not comply” and “comply,” is speci…ed as follows: U P (nc; j; p) =
if nc = 1 (do not comply) + ! if nc = 0 (comply) jp 2
up + ! 1 jp
;
where up 0, jp 0, jp 0 and ! i (i = 1; 2) is a random shock satisfying E[! i jp; j] = 0. up and jp represents the health outcome associated to respectively noncompliance, and compliance with the prescription of drug j. The term jp may be interpreted as the inconvenience (or cost) experienced by patient p when complying to drug j. As previously mentioned, this cost represents in particular the price of drug j and/or the side e¤ects associated with the consumption of this drug. The patient’s decision will be based upon the expected utility E!1 ;!2 [U P (nc; j; p)jp; j; nc], where E!1 ;!2 [ : j : ] is the conditional expectation operator taken with respect to ! i (i = 1; 2). Patient p’s expected utility is then given by P
U (nc; j; p) = E!1 ;!2 [U P (nc; j; p)jp; j; nc] = 12
up jp
jp
if nc = 1 (do not comply) if nc = 0 (comply)
We refer to the doctor as “she” and to the patient as “he.” Any dynamic consideration, such as learning, or reputation building, is beyond the scope of the present paper. 13
8
:
We shall assume that jp can be written as jp = j + jp , where j 0 may be interpreted as the average costs (over the set of patients) associated with compliance. The average cost j is assumed to be common knowledge.14 The deviation from this average, jp , still accounts for the interaction patient-drug. Patient p’s optimal decision when prescribed drug j is the indicator function nc (j; p) = 1fwjp
jg
(p) ;
where wjp = jp up jp . In other words, patient p chooses not to comply with the prescription if the net expected costs incurred by complying is higher than the average costs associated with noncompliance. The probability of noncompliance, P r(nc (j; p) = 1) = P r(wjp j ) = F ( j ), is the rate of noncompliance with the prescription of drug j, relatively to the probability distribution of the vector p. We now turn to the doctor’s decision. As it is done in the discrete-choice literature, we assume that from the doctor’s perspective, drugs are ranked according to an indirect and random utility function U D (j; nc; d; p) = Xj0
nc +
j
+
jdp
;
where the index d refers to the doctor, nc is the patient’s decision and j represents the characteristics of drug j that are observed by the doctor, but unobservable to the econometrician. The components of the vector Xj are the observable characteristics (known to the econometrician) of drug j, and jdp is a random shock. The negative sign preceding the patient’s decision (nc) indicates that the doctor gets disutility from noncompliance. In other words, the doctor takes into consideration her patient’s utility in two ways: directly through the health bene…ts provided by the drug’s characteristics Xj , and indirectly through her patient’s decision to comply with her prescription. The equilibrium for this game is found by backward induction. Therefore, anticipating the patient’s decision, the physician substitutes nc (j; p) for nc in her utility function. However, since the doctor still has incomplete information about her patient’s characteristics, she will average out her utility over the set of unobserved patients’characteristics. This leads to the following expression of the doctor’s expected utility: D
U (j; d; p) = Ep [U D (j; nc (j; p); d; p)jj; d] = Xj 14
F ( j) +
j
+
jd
;
(3.1)
Doctors are assumed to know the average costs associated with compliance through the channel of scienti…c meetings, publications, and various medical communications.
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where, as explained earlier, F ( j ) represents the rate of patient noncompliance with the prescription of drug j, and jd = E( jdp jj; d) . The doctor then chooses the alternative j that yields the highest expected utility, given the anticipated choice of the patient and the doctor’s beliefs. To obtain closed form solutions, we assume that the random shocks jd are i.i.d. extreme value distributed, as it is usually done in the discrete choice literature. In addition, the average costs j associated with compliance is assumed to depend linearly on a vector Zj of observable characteristics of product j ( j = Zj0 ). The probability Pj that drug j is prescribed is then of the logistic form 0
Pj =
1+
eXj PJ
r=1
F (Zj0 )+
eXr
j
F (Zr0 )+
: r
From the above equality, we obtain the following relation: Yj
ln(Pj )
ln(P0 ) = Xj0
F (Zj0 ) +
j
;
(3.2)
where P0 is the choice probability of the outside alternative. Before proceeding with the estimation of equation (3.2), we make the following observation on its interpretation.15 By construction, the components of Z a¤ect the physician behavior only by shifting the expected noncompliance rate. This is true in particular for DTCA in the benchmark model we estimate in section 5.1. Physicians, however, may also seek to develop a long-term relationship with their patients by adopting a prescription policy that, beside medical needs, attempts as much as possible to meet their patients subjective expectations regarding (e.g.) price, brand image, or dosage.16 In this more general setting, the components of Z would a¤ect the doctors’ utility both directly and indirectly, through the noncompliance rate. In particular, the in‡uence of DTCA on the doctor-patient relationship would be twofold: …rst, doctors may seek to promote medication compliance by prescribing drugs that have been intensely advertised toward their patients; and second, doctors may also seek to strengthen their patients loyalty by trying not to stand against their preferences, which might be partly shaped by DTCA. In such a model, the vector Z would be a sub-vector of X. This alternative speci…cation is estimated in section 5.2. 15
We would like to thank the anonymous referee who brought this point to our attention. Observe, however, that the introduction of patients’ loyalty considerations would not be consistent with our model as it is purely static. 16
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4. Data and Estimation 4.1. Description of the Data We use a data set, mainly provided by IMS America and CMR, on the U.S. market for anti-glaucoma drugs. The remaining part of the sample was collected from di¤erent sources to be mentioned along with the description of the variables that appear in the structural econometric model. Glaucoma is an eye disease characterized by a high intra-ocular pressure (IOP). It is a common disease a¤ecting almost four million people in the United States. Health practitioners are well aware of the signi…cant noncompliance problem with anti-glaucoma drugs. Indeed, these drugs have several side e¤ects (e.g. decreased vision, eye discoloration, redness), their usage is often inconvenient, and there is no immediate relationship between the use of the drug and the prevention of the most important consequence of the disease (blindness). As explained in the introduction, however, there is currently a glaring lack of data on noncompliance. In fact, after an extensive search, we were only able to …nd a couple of noncompliance rates for glaucoma drugs. These observations are not su¢ cient to estimate our model, but they will be used to check whether the noncompliance rates we estimate are sensible.17 Our data have a panel structure, each of the 48 observed drugs being observed over the period 1995-1999. Note that the sample includes seven drugs that were introduced between 1995-1999. Although a drug company may market several anti-glaucoma drugs, we assume that the set of characteristics are independent across products. To be consistent with the theoretical model, we distinguish between two sets of explanatory variables, X and Z. Recall that the components of X in‡uence directly the doctor’s preference, while the components of Z in‡uence her patient’s rate of noncompliance. As further explained in section 4.2, the model (3.2) is identi…ed only when X and Z do not overlap perfectly. We describe below the components of X, and Z as they appear in the estimation of our benchmark model. In section 5.2, we test an alternative speci…cation in which X is composed of all the explanatory variables presented in this section. The components of the vector X are initially assumed to be the following: 17
Unclaimed prescriptions have been suggested as a possible proxy for noncompliance. Unclaimed prescriptions,however, only describe repeated purchase noncompliance. So, even if they were available for glaucoma drugs (which, to the best of our knowledge, is not the case), unclaimed prescriptions would be of little use in our analysis since we consider both purchase and use noncompliance.
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Type of chemical structure (Class). Glaucoma drugs are usually classi…ed according to their type of chemical structure. we consider, the following seven classes.18 Class 0 : Beta-adrenergic blocking agents (or beta blockers). Class 1 : Carbonic anhydrase inhibitors. Class 2 : Parasympathomimetic agents (or miotics). Class 3 : Sympathomimetic agents. Class 4 : Alpha 2-adrenergic agonists. Class 5 : Prostaglandins analogs. Class 6 : Multiple ingredients drugs. This classi…cation is motivated by the medical literature in which side e¤ects pro…les and the relative e¤ectiveness of glaucoma drugs are usually presented using a similar classi…cation. Class is represented by six dummy variables, with “Class 0”as the reference class. Mode of action (Action). Anti-glaucoma drugs fall in two broad categories: some lower the intra-ocular pressure by increasing the out‡ow of the aqueous humor (category 1); others lower the IOP by reducing the formation of the aqueous humor. These two categories of drugs also di¤er by their side e¤ects (category 2). Hence, Action is a binary variable with the value 1 denoting the …rst category of drugs. Age (Drug_Age). This variable represents the number of months separating the current date from the date the drug was launched on the market. Following Rizzo (1999), this variable is assumed to capture life cycle patterns typically observed for pharmaceutical products. Detailing costs (Dcosts). This variable represents the largest part (roughly 75%) of advertising toward doctors. It includes the annual expenses for keeping representatives in the …eld. However, it does not contain the other expenses involved in support of the detailing e¤ort, such as free samples. 18 The classi…cation is based on Munger (2006), Robinson (2000), and Lewis et al. (1999). In addition, we have separated single from multiple ingredients drugs. The latter are put in a separated class (class 6).
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The variable is a de‡ated version of the corresponding IMS variable, using the producer price index for pharmaceutical preparations. Although we subsequently test this hypothesis, advertising will initially be considered as a ‡ow. This assumption …nds support in Rizzo (1999) who found that current detailing ‡ows have stronger e¤ects than detailing stocks on the elasticity of demand. We now describe the components of Z in‡uencing the patient’s total costs (i.e. monetary and non-monetary) of compliance. Price (Dayprice) is the wholesale price de‡ated by the consumer price index for pharmaceutical preparations.19 Each price is computed by dividing the wholesale price of a drug by the number of days of treatment. The latter is estimated from the recommended dosage found in the Physician’s Desk Reference. Direct-to-consumer advertising (Dtca). This variable represents the de‡ated annual amount of DTCA spent by the pharmaceutical companies on each drug in our sample. Although some drug companies advertise in popular media, most of the DTCA for glaucoma drugs is targeted toward already diagnosed patients through (e.g.) specialized magazines, medical websites, direct-mailing, or informative pamphlets. Dosage schedule (Howfreq). This variable shows the frequency of use of the drug as recommended in the Physician’s Desk Reference. When the frequency is a range, we choose the upper bound of the range. Form of presentation (Form). This is a dummy variable that indicates whether the drug has other forms of presentation than drops, the value 1 standing for “drops only”. The dependent variable corresponds to the annual market share for each drug. To construct these shares, we …rst homogenize the products by expressing the quantities in terms of days of treatment. These quantities are, therefore, computed as the ratio between sales and the price of a day of treatment. Finally, to determine the market share of the outside good, we assume that the size of the market is one day of treatment per glaucoma patient, where the total number of glaucoma 19
The price data are collected from the Red Book, Drug Topics, Montvale, NJ.
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patients is estimated by combining the patients treated with drugs and the patients treated by surgery.20 The main features of the sample are summarized in Table 1. The market for glaucoma drugs consists of a relatively large number of products (42.2 on average). Although the average market share of a drug is relatively small (2.76%), the partition of the market between products is highly unequal. In particular, 8 out of 36 drugs had roughly 73% of the market in 1999. This result may be explained by the introduction in 1996 of Xalantan, the only once-a-day drug at the time, whose market share rapidly grew to approximately 35% by 1999.21 In Table 1, we also decompose the descriptive statistics by chemical structure (i.e. Class). On average, the drugs in Class 3 are the oldest, while the drugs in Class 4 and 5 (the latter being composed of a single drug, Xalatan) are the newest and the most advertised. Note also that drug promotion to doctors is (on average) more than six time larger than DTCA. This ratio is slightly above the pharmaceutical industry average, since glaucoma drugs do not belong to the small class of highly advertised drugs. The correlation between advertising and sales may be appreciated in Graphs 1 and 2. At the market level, we can see that while total advertisements (i.e. DTCA and promotion to doctors) grew by 28.3% (see Graph 2), sales increased steadily by roughly 65.1% between 1995 and 1999 (see Graph 1). The latter e¤ect may be explained by the combination of (i) a price increase essentially generated by the introduction of newer drugs (see Graph 3), and (ii) a market expansion resulting from an accrued awareness in the population of the dangers of glaucoma. At the product level, anti-glaucoma drugs may be broadly divided in two groups: the …rst includes highly advertised products with increasing sales (see Graph 1); the second includes less advertised drugs with decreasing sales (see Graph 2). Note also that although Xalatan and Alphagan are equally advertised, and their price ratio remains constant over time, the sales of Xalatan have increased considerably compared to Alphagan. As we shall see later on, this empirical observation may be explained by the di¤erence in noncompliance rate between the two products. Finally, Graph 3 indicates a clear 20
Our approach to de…ne quantities and market size is, therefore, very similar in spirit to Nevo (2001) who studies the U.S. ready-to-eat cereal industry. Indeed, Nevo (2001) …rst homogenizes the di¤erent cereals in the market by expressing them in terms of “servings”; he then converts sales into a number of servings per day; and …nally, he assumes the market size to be one serving of cereals per capita per day. 21 The glaucoma market was more equally divided across drugs in the years prior to 1999. For instance, in 1996, the year of the introduction of Xalatan, the same eight drugs accounted for “only” 46.3% of the market.
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increase in price over time, but the advertising to sales ratio does not exhibit any obvious trend. 4.2. Estimation Strategy As mentioned in the introduction, our empirical approach builds on the structural econometric literature to deal with the unavailability of consumer level data and the latent variable problem of noncompliance. More speci…cally, following recent developments in applied industrial organization, we have developed in section 3, an individual decision making model that only requires market shares and product level data to be estimated. Likewise, we take advantage of the structure of the game played between the doctor and the patient to estimate the distribution of noncompliance from the sole observation of sales and product characteristics. Such an approach has now become standard in the structural econometric literature. For instance, in structural empirical auctions, the distribution of privates types is estimated while only bids are observed.22 Likewise, in industrial organization, the distribution of …rms’costs is structurally estimated from the sole observation of prices and quantity sold.23 Comparable structural approaches, in which the variable of interest (in our case, noncompliance) is not observed, have been used to estimate, e.g., the extent of the shadow economy, tax evasion, corruption, potential output, or productions frontiers.24 Equation (3.2) is the basic equation to be estimated. More precisely, we wish to estimate the parameters vectors ; , and the unknown cdf F (:). Since F (:) does not have a known analytical form, and since we want to impose the least possible structure, we are led to perform a semiparametric estimation of the unknowns in our model. For the model to be identi…ed, however, we must assume that the set of variables entering the model linearly (i.e. X), and the set of variables entering the model non-linearly (i.e. Z) do not overlap perfectly. Before proceeding to the estimation of the model, we …rst need to address a sample selection and an endogeneity problem. 22
See e.g. Donald and Paarsch (1993), La¤ont, Ossart and Vuong (1995), or Guerre Perrigne and Vuong (2000). 23 See e.g. Berry (1994), Berry, Levinsohn and Pakes (1995), or Nevo (2001). 24 See e.g. Blanchard and Quah (1989), Lemieux, Fortin and Frechette (1994), Wolak (1994), Giles (1999), Alañón and Gómez-Antonio (2005), or Dreher, Kotsogiannis and McCorriston (2005).
15
4.2.1. Sample Selection The prescription probabilities, on the left-hand-side of equation (3.2) are not observed in our sample. The only information available to us is the sales in dollars for each drug. The sales and prescriptions are not equivalent, however, since many prescriptions are not turned into sales due to purchase noncompliance, which is believed to a¤ect around 20% of all prescriptions. Failure to distinguish between prescriptions and sales, would lead to severely biased estimates in the present study. Indeed, the unobserved purchase noncompliance is generally believed to be in‡uenced by variables entering the right-hand-side of equation (3.2), such as the price or the drug reputation generated in part by DTCA. The drug sales, however, are su¢ cient to estimate the model in our case. Indeed, let us denote P (jjB) the probability that alternative j = 0; :::; J is prescribed, conditional on the fact that one of the J + 1 alternatives has been bought. From the drug sales, we can compute, P (jjB), the share (in quantity) of drug j = 1; :::J, where B stands for “An alternative is Bought.” Recall that we denoted by Pj the corresponding unconditional probability. By Bayes rule, we have P (jjB) =
Pj P (Bjj) P (B)
;
where P (Bjj) is the probability of purchase if alternative j is prescribed and P (B) is the unconditional probability of purchase (the proportion of purchased alternatives among prescribed alternatives). Dividing both sides of the preceding equality by the analogous expressions for the outside good and taking logarithms, we obtain, ln
P (jjB) Pj P (Bjj) = ln + ln P (0jB) P0 P (Bj0) = Xj0
F (Zj0 ) +
j
+ ln
P (Bjj) ; P (Bj0)
where the last equation is obtained from (3.2). As noted above, we observe only the probability P (jjB). Therefore, if we de…ne a new unobservable variable ~j as ~j =
j
+ ln
16
P (Bjj) ; P (Bj0)
(4.1)
we can rewrite the original model as Yj = ln
P (jjB) = Xj0 P (0jB)
F (Zj0 ) + ~j :
(4.2)
Equation (4.2) may then be estimated from the available data, provided that the purchase probability of a drug is driven by its price and its reputation generated by its level of DTCA.25 One should note that this approach will not allow us to estimate the magnitude of the parameters, but only their signs, and these will be enough to answer the questions raised in the introduction. 4.2.2. Endogeneity As it is traditionally the case with discrete choice models, j , the characteristic that is unobserved to the econometrician, is likely to be correlated with the price and advertising variables. In addition, purchase noncompliance has been shown to be essentially in‡uenced by the price of a drug and the intensity of its advertising.26 In other words, one should also expect the ratio of purchase probabilities P (Bjj)=P (Bj0) to be essentially driven by prices and advertisements. Therefore, aggregated error term ~j de…ned in (4.1) is likely to be correlated with the price and advertising variables. We handle this endogeneity problem by applying the “control function method” (see e.g., Newey, Powell and Vella 1999, or Blundell and Powell 2000). The method consists in including as additional regressors in the right-hand-side of equation (4.2), the residuals of the nonparametric regressions of the endogenous variables on a set of instruments. Endogeneity is therefore treated in that approach as an omitted variable problem. In the present context, the endogenous variables are the detailing costs (Dcosts), the prices (Dayprice) and DTCA (Dtca). Let us denote the vector of endogenous variables by N and the remaining exogenous variables as e. Equation (4.2) may then be written as Yj = (Nj ; ej )+ ~j , in which E(Yj jNj ; ej ) 6= (Nj ; ej ) because of the endogeneity problem. Consider now the nonparametric regression equations Ni;j = mi (Wj )+ui;j where i = 1; 2; 3 denotes one of the three endogenous variables, Wj is an appropriate vector of instruments (including in particular the exogenous variables ej ), mi ( : ) are 25
This assumption appears reasonable since prices and reputation are the principal information available to patients at the time of purchase. 26 See e.g. the conclusions of the recent study conducted by Barrett (2005).
17
unknown functions, and ui;j are uncorrelated error terms. Our application of the method relies on the assumption that in the presence of both u and W , the variable e is correlated only with u = (u1 ; u2 ; u3 )0 : E(eju; W ) = E(eju);
and
E(ujW ) = 0 :
(4.3)
These assumptions imply
E(Y jN; W ) = (N; e) + E(ejN; W ) = (N; e) + E(eju) = (N; e) + '(u) ;
where '(u) = E(eju). The method, therefore, has two steps: in step 1, we perform a nonparametric regression of each of the endogenous on the instruments. In other words, we estimate the equations Ni;j = mi (Wj0 ) + ui;j (i = 1; : : : ; 3) ;
(4.4)
which yields the residuals u bi;j . In step 2, we estimate a modi…ed version of equation (4.2): Yj = ln P (jjB)
ln P (0jB) = E[ln P (jjB) ln P (0jB)jX; Z; u^] = Xj0 F (Zj0 ) + '(b u0j ) + j ;
(4.5)
where u^ = (b u1 ; u b2 ; u b3 )0 is the vector of residuals obtained in step 1. As previously mentioned, the vector of instruments includes all exogenous variables (i.e., every variable listed in section 4.1, except for the market share, price, detailing cost, and DTCA). In addition, following the industrial organization literature on the estimation of discrete choice model with market level data (see e.g. Berry et al. 1995, or Nevo 2001), the vector of instruments Wj also includes the annual average of the variables Drug_Age, Howfreq, and Class calculated across all drugs, other than the drugs produced by the manufacturer of drug j. The underlying identifying assumption, is that the location of the di¤erent drugs in the space of these product’s characteristics is exogenous (see e.g. Nevo 2001). This assumption may be considered reasonable in the present context, since it is unlikely that the product’s characteristics under consideration be modi…ed in response to random shocks on the market shares. To verify whether our model’s hypotheses may be considered reasonable, we also estimate nonparametrically the more general model Yj = (Nj ; Wj ) + vj 18
;
(4.6)
in which E(Y jNj ; Wj ) = (Nj ; Wj ). If our model is correctly speci…ed, then (Nj ; Wj ) = (Nj ; ej ) + '(uj ), or equivalently j = vj . The informal veri…cation technique will, therefore, consist in comparing the estimated residuals of the two econometric models in equations (4.5) and (4.6).27 4.2.3. Practical Considerations To avoid the curse of dimensionality, we have assumed that the nonparametric multiple regressions in steps 1 and 2 are index models (Ichimura and Lee 1991, Ichimura 1993). To ensure the identi…cation of the parameter , we further assume, without loss of generality for the purpose of the analysis, that k k = 1. Although, the nuisance parameters ( , ) are identi…ed only up to a multiplicative factor, the expressions '(u0 ) and m(W 0 ), if regarded as parameters, are identi…ed. This identi…cation issue is not a serious problem here, since and are nuisance parameters, and we are only interested in the signs of and . The cdf F (:) is estimated nonparametrically as follows, Zj0 Zr0 1X F^ (Zj0 ) = K( ) ; n r6=j hK n
where n is the sample size, is a vector of parameters to be estimated, K(x) is a cdf associated with a kernel derivative k(:), and hK is a bandwidth controlling the smoothness of the kernel estimates. In practice, we select K(x) = (1 + e x ) 1 , the cdf of a logistic distribution. Similarly, the functions mi (:) (i = 1; 2; 3) and '(:) are estimated nonparametrically by m ^ i (Wj0 ) =
Pn
r6=j
Pn
Ni;r g(
r6=j g(
Wj0
Wj0
Wr0 hmi Wr0
hmi
)
)
and ' b (^ u0j ) =
Pn
r6=j [Yr
Xr0 ^ + F^ (Zr0 ^ )]g( Pn u ^0r u ^0j ) r6=j g( h'
u ^0r
u ^0j h'
where g(:) is a Gaussian kernel, hmi and h' are bandwidths, and ; ; ; are parameter vectors to be estimated. Following Pagan and Ullah (1999), the optimal bandwidths in all nonparametric estimations are approximated by least squares cross-validation. 27
More traditional tests, such as the Hausman test, cannot be applied in the present context due to the semiparametric structure of the model.
19
)
;
To estimate the parameters problems:
in step 1, we solve the following minimization
1X min Rn ( ^ ) = !(Wk )[Nk ^ n k=1 n
m ^ i (Wk0 ^ )]2 i = 1; : : : ; 3 ;
(4.7)
where !(:) is a standard weighting function that may be chosen optimally in order to minimize the variance of the estimator. In step 2, the parameters ( ; ; ) are estimated by solving 1X !(Xi ; Zi )[Yi min Sn ( ^ ; ^ ; ^) = ^ ;^ ;^ n i=1 n
Xi0 ^ + F^ (Zi0 ^ )
' b (^ u0 ^)]2
:
(4.8)
The optimal weighting functions !(:) are approximated sequentially by estimating the covariance matrix of the estimates in equations (4.7) and (4.8). Under standard regularity conditions on the kernel functions and the bandwidths, Ichimura (1993) shows that the parameters are consistent and asymptotically Gaussian.
5. Results 5.1. The Benchmark Model The results are interpreted in this section within the context of our structural model. This interpretation is therefore contingent on the validity of the structural model. In the following section, we will see that the estimated parameters are still informative when our model is re-interpreted as purely reduced form. We report in the second column of Table 2 the results of the estimations conducted in step 2.28 Recall that the magnitude of the e¤ects of the explanatory variables on the prescription probabilities and the average noncompliance rate cannot be evaluated from the values of the estimated parameters.29 Therefore, we will only discuss here the economic interpretation that may be given to the signs of the parameters. Before describing the results, we note that Graph 4 suggests 28
For the sake of brevity, the estimates of the nuisance parameters, and , are not reported here since (i) they are identi…ed only up to a multiplicative parameter, and (ii) they have no economic interpretation. These estimation results may be found on the web-site: http://www.sceco.umontreal.ca/liste_personnel/armantier/index.htm. 29 This also implies that we will not be able to conduct some ex-post simulations to predict how a change in variables may a¤ect doctors’and/or patients’behavior.
20
that the residuals estimated with our model (i.e. equation (4.5)), and the residuals estimated with the general model (i.e. equation (4.6)), are very similar.30 This result suggests that the hypotheses imposed to derive our structural model may be considered reasonable. All the components of the vectors and but two (the parameters associated with the variables Class 1 and Form) are signi…cantly di¤erent from zero. Note also that all the statistically signi…cant parameters have the expected signs. In particular, 3 to 7 are all negative, which indicates that the drugs in class 0 (the beta blockers) are prescribed more often. This was expected, since beta blockers have remained over time the mainstay therapy for glaucoma. 9 is positive, which suggests that there is a …rst mover advantage, in the sense that a drug introduced earlier is more prescribed than a newer drug with similar characteristics. In other words, the sample tends to indicate the presence of learning and/or habit formation on the part of doctors. Finally, 1 is signi…cant and positive, which indicates that doctors are sensitive to price changes. This result con…rms several empirical studies that demonstrate that when patients pay less for a drug, doctors write more prescriptions for that drug, as a response to increased requests by patients (see for instance Lavizzo-Mourrey and Eisenberg 1990). The estimated parameters 1 and 1 are both positive, while 2 is negative. Therefore, we are now in position to answer the two questions raised in the introduction. We …nd that advertising toward doctors and/or patients for a given anti-glaucoma drug increases the number of prescriptions for that drug. In other words, contrary to the opinion expressed by many doctors, advertisements toward doctors appear to a¤ect their prescription behavior, independently of the characteristics of the advertised drug. In addition, although not directly exposed to DTCA, doctors appear to be indirectly in‡uenced by DTCA through their patients’expected noncompliance. We …nd that DTCA unambiguously lowers the average rate of noncompliance with anti-glaucoma drugs. This result tends to support the opinions of proponents of DTCA recently expressed before the FDA. However, we cannot assess from our analysis, whether the reduction in noncompliance is due to the information content of DTCA, or to the fact that doctors tend to prescribe drugs with a high DTCA intensity, which are likely to be preferred by patients. In contrast, the estimation More speci…cally, the null hypothesis that b and vb, the estimates of and v, have the same distribution cannot be rejected by a Kolmogorov-Smirnov test (P -value=0.135). In addition, the null hypothesis that the slope parameter is equal to 1 in the regression of vb on b cannot be 30
rejected (P -value=0.162).
21
results suggest that promotion to doctors has an ambiguous in‡uence on the average noncompliance rate. Indeed, the average noncompliance rate increases in our model when the advertised drug has initially a higher than average rate of noncompliance. In other words, if the average compliance rate is taken as a component of health care quality, then advertising toward doctors would have a negative impact on patients when the drugs advertised to doctors have a high noncompliance rate. To determine whether this was the case on the market for anti-glaucoma drugs, we now turn to the estimates of the noncompliance rates. We report in Table 3 the estimated probability of noncompliance for each product and each year. In addition, the annual average noncompliance rates are shown in Table 4. It is somewhat di¢ cult to compare these …gures with rates estimated elsewhere. Indeed, studies of noncompliance at the patient or drug levels are almost non-existent in the medical literature, and this holds true in particular for Glaucoma. In addition, a direct comparison may not be appropriate since, depending on the methodology adopted, the rates found in the medical literature may be inaccurate and/or may not explicitly combine purchase and use noncompliance. Although the comparisons that follow should be taken with caution, they tend to suggest that the magnitude of our results is reasonable. In particular, note that the average, as well as the individual rates of noncompliance are consistent with the corresponding rates found in the literature for anti-glaucoma drugs (Wick and Zanni 2000) and for di¤erent therapeutic classes (Dezii 2000). More speci…cally, Rotchford and Murphy (1998) evaluate the noncompliance rate of the Drug Timolol in 1998 at around 51%, while we estimate the corresponding rate at 54%. Finally, the pharmaceutical group Akorn provided us with their own estimates of noncompliance in 1997 and 1999 for the four drugs they were supplying at the time. A regression of our estimates on these noncompliance rates suggests a slight overestimation of our model.31 A signed-ranks test, however, indicates that the ordering of the estimated noncompliance rates is consistent with the data provided by the pharmaceutical group.32 These results suggest that the 31
The constant is estimated at 0.085 with a standard deviation of 0.027, while the slope is estimated at 1.087 with a standard deviation of 0.039. The overestimation, however, may simply re‡ect a slight overcon…dence of the pharmaceutical group in the compliance with the prescription of their products. Note also that these observations of the noncompliance rate were too few to be used in a meaningful way in the estimation of F (:). 32 The object of the test is to verify whether the noncompliance rates for each drug are ranked in the same order in the sample provided by the pharmaceutical group (sample 1) and in our sample of estimated noncompliance rates (sample 2). To do so, we create two samples consisting of the ranks of each drug in sample 1 and sample 2. We then use a Wilcoxon matched-pairs
22
model and the estimates are sensible, and they support our interpretation of F (:) as a noncompliance rate. Graph 5 indicates that the annual distributions of noncompliance rates across products are rather concentrated around their modes and slightly asymmetric with a predominance of rates above the mean. Table 4 and Graph 5, also clearly show a decline in noncompliance (both at the average and individual level) between 1995 and 1999. In particular, the noncompliance mode in 1995 (slightly above 0.7) has become highly improbable in 1999. Note also that the average noncompliance rate decreases sharply after the 1997 FDA decision on DTCA (see Table 4). This result may be explained by the fact that, as previously noted, DTCA unambiguously reduces the average rate of noncompliance. We should not exclude, however, that the growing concerns among doctors also played a role in the reduction of average noncompliance. However, recall that advertising toward doctors has an ambiguous e¤ect on the average noncompliance rate. Graph 6, actually shows that most of the highly advertised drugs toward doctors have a noncompliance rate above average. In other words, advertising toward doctors had a negative impact on the average noncompliance rate with anti-glaucoma drugs between 1995 and 1999. Let us now concentrate on two of the most popular products (Xalatan and Alphagan). First, note that every year between 1996 and 1999, Xalatan has the smallest noncompliance rate among all products in our sample. This is an interesting result for our structural model, since, although it does not necessarily have the best observable characteristics, Xalatan is known to be one of the drugs with the highest compliance rate. Indeed, Xalatan is a once a day eye drop, while its competitors (except Cosopt, a recently introduced multiple-ingredient drugs) require at least two applications per day. This result may also partially explain why, although Alphagan and Xalatan are equally advertised, and their price ratio remained constant over time, the markets share for Xalatan grew at a faster rate than that of Alphagan. Indeed, we have seen that, caeteris paribus, doctors prefer to prescribe a drug with a higher compliance rate. 5.2. Alternative Speci…cations and Alternative Interpretations In this section, we test the robustness of our structural model by considering alternative speci…cations. We start by relaxing the assumption that the variables signed-ranks test to verify whether the di¤erence between the ranks for each drug has median value zero. The p-value is 0.285 and therefore, we fail to reject the null hypothesis that the two samples are ranked in the same order.
23
in Zj a¤ect only the patient decision to comply with drug j. Instead, we now consider that the doctor’s utility may be in‡uenced directly by Zj , and not only through the noncompliance rate F (:). This speci…cation therefore allows us to test whether variables such as the price or the DTCA a¤ect doctors independently of concerns regarding their patient compliance. To do so, we generalize our model by including in the vector Xj the four variables in Zj (i.e. the price, the DTCA, the dosage schedule, and the form of presentation). In other words, Xj now includes all the explanatory variables, while Zj still consists of the variables controlling a patient’s decision to comply.33 As a result, we are also in a position to test whether a linear speci…cation …ts the data better than our partially linear model. Indeed, if the correct speci…cation is linear, then the parameter in the nonlinear function F (:) should be insigni…cant. The estimated parameters for this alternative model are reported in the third column of Table 2. Observe that the components of the vector do not vary signi…cantly compared to our benchmark model. In contrast, none of the linear parameters associated with Zj (i.e. 10 to 13 ) are signi…cantly di¤erent from zero. In fact, an F -test indicates that one cannot reject the null hypothesis that the parameters 10 to 13 are jointly equal to zero (the p-value is 0:247). A purely linear speci…cation may therefore be rejected, as it appears that Zj only enters the model through the nonlinear function F (:). In other words, the drug’s characteristics in‡uencing a patient’s behavior such as the price or the DTCA, only seem to enter the doctor’s utility indirectly through the noncompliance rate.34 As previously mentioned, the product set may be divided in a small group of heavily advertised drugs with high markets shares, and a larger groups of drugs with substantially smaller market shares. To test whether the presence of asymmetries across products a¤ect our results, we …rst relax the assumption that the drugs are uniformly distributed in the space of characteristics. To do so, we adopt a nested logit speci…cation (see e.g. Train 2003), with a nest for the …ve most heavily advertised drugs (i.e. Alphagan, Xalatan, Timoptic-XE, Trusopt, and 33
Observe that although the variables entering the model nonlinearly (Zj ) are common to the variables entering the model linearly (Xj ), we can still identify the noncompliance cumulative distribution F (:) independently of the linear coe¢ cient , since Zj is not a subset of Xj . 34 To explore the consequences of potential multicollinearity problems between the linear and nonlinear part of the alternative model, we also estimated a purely linear model (i.e. without the noncompliance rate F (:)). Among the four variables in Zj , only the parameter associated with the price was found to be signi…cantly di¤erent from zero. In other words, the fact that the parameters 10 to 13 are insigni…cant in the alternative model cannot be explained by the presence of the noncompliance rate F (:).
24
Ocupress). This speci…cation recognizes that heavily advertised glaucoma drugs may be better substitutes to one another, compared to the group of less advertised drugs. As a result of creating a correlation between the utilities for di¤erent drugs, the nested logit model allows a richer set of possible substitution patterns between drugs. In particular, the independence from irrelevant alternatives does not hold for products in di¤erent nests. Table 2 indicates that the additional parameter is not signi…cantly di¤erent from 1, thereby rejecting the presence of a nest for the …ve most heavily advertised drugs. In addition, the remaining estimated parameters do not vary substantially from our benchmark model. In other words, a richer discrete choice speci…cation does not appear to …t the data signi…cantly better.35 Moreover, to test whether the presence of drugs with small markets share a¤ects our results, we re-estimated the benchmark model under a di¤erent de…nition of a product. Since the main therapeutic component of a drug is its chemical structure, the new de…nition of a product is based on the variable Class. More speci…cally, within each of the six Class categories, we consolidated into a single product the drugs with a market share below 0.5% that year. In doing so, we reduced the number of products from 48 to 39. A comparison of the second and …fth columns in Table 2, indicates that an alternative de…nition of the products yields slightly di¤erent results. Note, however, that with the exception of 9 and 4 , the di¤erences between the parameters are not statistically signi…cant across models. In addition, observe that the principal structural parameters, e.g., 1 , 1 , 2 , remain statistically signi…cant under the new de…nition of the product. In fact, the main di¤erence between the two models may be found in the estimated standard deviations. Indeed, because of the reduction in the sample size, the estimated standard deviations are signi…cantly larger in column …ve than in column two. In other words, changing the de…nition of a product does not change the nature of the estimated parameters. The benchmark model was estimated under the assumption that advertising may be considered a ‡ow. We now relax this assumption and test whether advertising may be better represented as a stock. To do so, we assume that DTCA 35
We have also estimated two additional nested logit models, one with a nest for the outside good, and one with a nest for drugs with a once-a-day dosage. Again, both of these speci…cations were rejected in favor of our benchmark model.
25
and detailing costs are stocks with respective rate of decays DT CA and Dcosts .36 The results in the sixth column of Table 2, indicate that the estimates of DT CA and Dcosts are not signi…cantly di¤erent from zero, thereby supporting our initial assumption that advertising may be considered a ‡ow. Note also that the estimation of the other structural parameters is not signi…cantly a¤ected if one treats advertising as a stock. As argued, e.g., by Nevo (2000), one should check the sensitivity of the results to the de…nition of the market size when estimating discrete choice models. Indeed, since it is often unobserved, the market size is typically imposed somewhat arbitrarily. One must therefore make sure that the results do not change drastically when alternative de…nitions are considered. To estimate the benchmark model, we assumed the market size, M , to be equal to the total estimated number of patients treated with either drugs or surgery. This number, however, is only an approximation, and the actual market size may in fact be larger (due for instance to purchase noncompliance), or smaller (for example, some patients may be treated with both surgery and drugs). Following Berry (1990) and Berry, Carnall and Spiller (2006), we now estimate the size of the market for glaucoma drugs. To do so, we assume the market size to be M , where is a parameter to be estimated. The results in the last column of Table 2 suggest that the market size is larger than assumed in the benchmark model, since the estimated value of is greater than one. The estimation of the other structural parameters, however, do not vary signi…cantly, thereby con…rming that our results are not sensitive to the de…nition of the market size. Finally, let us make a general comment on the interpretation of the results in section 5.1. As with any structural model, the interpretation of the estimation results is contingent on the structure imposed on the model. In particular, we recognize that our interpretation of F (:) as the noncompliance rate is only valid under our model’s assumption. As mentioned earlier, this interpretation …nds support in the fact that our estimates of F (:) seem to track fairly well the few known noncompliance rates. Alternatively, one could ignore our principal-agent structure, and simply view equation (3.2) as the demand function for di¤erentiated products resulting from a traditional discrete choice model as proposed by Berry 36
In other words, the two forms of advertising follow the following law of motions: StockDT CAt StockDcostst
= =
DT CA StockDT CAt 1
+ DT CAt ; Dcosts StockDcostst 1 + Dcostst ;
where t represents the current year.
26
(1994) and Berry, Levinsohn, and Pakes (1995). Instead of the interaction between the doctor and her patient, the demand function for glaucoma drugs would then re‡ect the individual decision problem faced by a doctor trying to select the drug that maximizes her own utility. As a result, and in contrast with our structural model, this discrete choice approach would not endogenize the decision of the patient to comply with his doctor’s prescription. In this discrete choice model, the variables a¤ecting the doctor’s utility in (3.1) would be decomposed in Xj , the drug’s characteristics that are medically relevant to the doctor’s decision, and Zj , the variables a¤ecting the patient’s utility but are not medically relevant. Instead of being viewed as the noncompliance rate, F (:) may be interpreted more generally in this model as the weight given by the doctor to the non-medical components a¤ecting her patients’utility. The interpretation of the estimation results in the previous sub-section would be the similar except that we would now conclude that (i) in addition to medically relevant drug’s characteristics, doctors are also sensitive to other variables in‡uencing their patients’ utility (for instance, the price, the DTCA); (ii) the weight given by doctors to characteristics that are not medically relevant increased signi…cantly over the sample period; and (iii) DTCA played an increasingly important role in the doctor’s prescription behavior.
6. Conclusion This paper is the …rst attempt to study patient noncompliance and drug advertising toward doctors and/or patients in a physician agency model. The object was to determine the in‡uence of noncompliance and advertising on doctors’prescription behavior, and the e¤ect of advertising on patients’noncompliance. To address these questions, we proposed, due to data limitations, a parsimonious discrete choice model inspired from the medical literature, with no more structure than was necessary to estimate the parameters with the data currently available. The model describes the prescription behavior of a doctor facing a patient who may fail to comply with the prescription. We apply semiparametric techniques to estimate the structural model using U.S. product level data on anti-glaucoma drugs. In particular, these econometric techniques allow us to estimate the individual, as well as the average annual noncompliance rates. The estimation results suggest that (i) doctors are sensitive to drug prices and noncompliance, and their prescription behavior is in‡uenced by both types of advertising; (ii) the average noncompliance rate on the market for anti-glaucoma drugs is estimated at around 57%, and it is shown to decrease signi…cantly between 1995 and 1999; (iii) DTCA 27
(respectively, promotion to doctors) contributed to (respectively, slowed down) the reduction of the average annual noncompliance rate observed in our sample. Note, however, that the estimation results generated by structural models may be in‡uenced by the restrictions, and the functional forms imposed. In the present paper, we strived to set the most neutral possible restrictions, and we avoided as much as possible to impose speci…c functional forms. As an illustration, the probabilities of noncompliance were estimated semiparametrically. The estimation results appear to be sensible, and the estimated noncompliance rates are in accordance with the few …gures available in the medical literature. Note also that some aspects of the glaucoma market and the doctor-patient relationship have not been fully taken into consideration in the paper. These include, on the theoretical side, long term care which allow the patient and the doctor to learn about each other as times goes by. On the empirical side, we did not consider heterogeneity among doctors and among patients. Finally, we did not account for other parties entering the agency problem such as HMOs or insurance companies. We are currently looking for data to investigate these extensions. It is important to note that the modeling of the interplay between noncompliance and advertising allows us to capture realistically the behaviors of both doctors and patients and their consequences on the glaucoma market. For instance, the relative performance of Xalatan compared to, for instance, Alphagan may be partially explained by the signi…cantly lower estimated noncompliance rate of Xalatan. Finally, the empirical relevance of the interaction between noncompliance and advertising may be illustrated by the introduction of the two newest drugs since 1999 (Lumigan and Travatan have been approved by the FDA in 2001). The launch of these two drugs was accompanied by an important advertising campaign (both to doctors and patients) and they are comparable to Xalatan with regard to the ease of use. In particular, just like Xalatan, Lumigan and Travatan are both once-a-day eye drops.37
References [1] Alañón A. and M. Gómez-Antonio (2005): “Estimating the Size of the Shadow Economy in Spain: a Structural Model with Latent Variables,”Applied Economics, vol. 37(9), pages 1011-1025. 37
Pharmacia & Upjohn, the marketer of Xalatan actually initiated a lawsuit against Allergan (the owner of Lumigan) and Alcon (the owner of Travatan ) for copyright infringement.
28
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32
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33
Table 1 Descriptive Statistics per Year and per Drug For Glaucoma Market between 1995 and 1999 (in $ thousand)
(in $ thousand)
(in $ thousand)
Number of Months since Drug Launch
Total
Mean Standard Deviation Median Min Max
15,961.55 35,280.04 7,552.47 3.00 303,036.00
36.48 88.56 27.93 0.00 1,616.38
226.91 521.72 162.73 0.00 5,973.00
154.76 112.23 118.92 3.00 405.00
1.63 1.27 1.29 0.32 5.98
2.76 5.98 2.37 0.16 34.81
42.20 2.52 43.00 36.00 48.00
Class 0
Mean Standard Deviation Median Min Max
29,736.33 4,977.23 29,279.10 22,462.27 34,971.09
195.27 44.38 203.79 124.32 233.13
1,069.76 319.98 1,105.36 574.09 1,418.80
120.44 38.28 117.45 8.00 169.45
1.62 0.11 1.65 1.45 1.74
5.43 1.62 4.72 2.75 7.17
10.8 0.4 11.0 10.0 11.0
Class 1
Mean Standard Deviation Median Min Max
13,958.86 5,941.58 16,840.13 5,270.11 20,027.00
79.40 26.92 77.68 49.98 119.59
438.31 159.96 516.33 190.22 571.63
98.22 61.65 87.00 3.00 177.50
2.83 0.46 2.82 2.28 3.36
3.68 1.27 3.63 0.76 6.09
8.4 0.5 8.0 8.0 9.0
Class 2
Mean Standard Deviation Median Min Max
2,008.28 510.39 1,737.79 1,504.20 2,655.27
1.52 0.83 1.82 0.21 2.41
8.62 4.93 8.80 1.60 14.80
160.31 99.51 148.60 68.13 314.14
1.06 0.12 1.08 0.32 1.18
1.63 0.87 1.23 0.32 2.84
14.8 0.4 15.0 14.0 15.0
Class 3
Mean Standard Deviation Median Min Max
3,213.51 2,345.21 2,424.33 581.00 6,777.40
3.41 2.86 4.15 0.00 7.26
24.05 22.70 21.00 0.00 50.20
148.35 111.84 101.50 10.20 306.67
1.62 0.57 1.43 1.07 2.49
0.94 0.45 0.67 0.16 1.61
4.4 0.9 5.0 3.0 5.0
Class 4
Mean Standard Deviation Median Min Max
24,681.00 17,032.90 19,568.00 3,928.00 42,592.00
274.52 357.00 158.87 39.02 895.81
1,561.80 1,672.63 1,446.00 118.00 4,240.00
159.40 91.94 201.00 53.00 262.00
4.08 1.91 4.75 2.04 5.98
3.52 1.18 3.03 0.70 5.85
1.8 0.4 2.0 1.0 2.0
Class 5
Mean Standard Deviation Median Min Max
175,325.00 121,242.31 185,494.50 27,275.00 303,036.00
1,012.49 697.64 945.81 241.96 1,616.38
3,990.75 1,887.97 4,248.00 1,494.00 5,973.00
226.25 135.22 201.50 8.00 392.00
0.62 0.05 0.60 0.59 0.70
25.92 11.01 22.75 7.36 34.81
1.0 0.0 1.0 1.0 1.0
Class 6
Mean Standard Deviation Median Min Max
6,101.09 11,182.48 332.60 219.60 25,921.00
125.93 210.93 15.23 0.00 486.62
427.03 665.74 83.18 12.53 1,517.67
141.33 106.016 105.88 27.81 297.67
0.68 0.11 0.62 0.59 0.82
2.78 1.28 2.12 0.66 5.05
4.4 0.9 5.0 3.0 5.0
Sales
DTCA
Promotion to Doctors
34
Price per day (in $)
Market share
Number of Products
TABLE 2 : Estimation Results Benchmark Model
Alternative Specification
Nested Logit Specification
Alternative Product Definition
Advertising as a Stock
Estimated Market Size
(Dcosts)
0.169** (0.071)
0.133** (0.058)
0.182** (0.068)
0.238* (0.117)
0.195** (0.082)
0.142** (0.063)
β 2 (Class_1)
1.102 (0.813)
1.524 (0.902)
1.236 (0.742)
0.731 (1.431)
0.956 (0.721)
1.224 (0.771)
Parameter
β1
β3
(Class_2)
-3.851** (1.228)
-3.172** (1.340)
-3.402** (1.143)
-2.973* (1.514)
-4.231** (1.341)
-3.540** (1.115)
β4
(Class_3)
-5.090** (1.320)
-4.629** (1.308)
-4.766** (1.380)
-5.631** (1.478)
-4.226** (1.618)
-5.216** (1.285)
β5
(Class_4)
-0.357** (0.103)
-0.281** (0.126)
-0.321** (0.095)
-0.425** (0.181)
-0.234** (0.133)
-0.379** (0.091)
β6
(Class_5)
-5.864** (1.637)
-6.307** (1.450)
-5.987** (1.702)
-3.974* (2.004)
-5.205** (1.971)
-6.145** (1.700)
β 7 (Class_6)
-3.555** (0.821)
-3.341** (0.916)
-3.479** (0.884)
-3.627** (0.898)
-3.427** (0.869)
-3.093** (0.846)
β 8 (Action)
2.751* (1.396)
2.682 (1.446)
2.700 (1.459)
1.642 (1.779)
2.471 (1.520)
2.788* (1.404)
β 9 (Drug_Age)
1.118** (0.394)
1.166** (0.402)
1.081** (0.416)
1.864** (0.468)
0.985** (0.429)
1.162** (0.372)
γ1
0.893** (0.326)
0.736* (0.375)
0.825 (0.286)
0.972** (0.381)
0.911** (0.363)
0.895** (0.344)
γ 2 (Dtca)
-0.126** (0.022)
-0.112** (0.034)
-0.098** (0.027)
-0.188** (0.052)
-0.094** (0.041)
-0.139** (0.028)
γ 3 (Form)
0.389 (0.324)
0.423 (0.540)
0.202 (0.398)
0.693 (0.463)
0.307 (0.365)
0.338 (0.302)
γ 4 (Howfreq)
0.188** (0.052)
0.246** (0.086)
0.205** (0.047)
0.271** (0.055)
0.220** (0.057)
0.197** (0.058)
___
-0.124 (0.082)
___
___
___
___
___
2.864E-4 (0.001)
___
___
___
___
1.423 (2.864)
___
___
___
___
___
0.024 (0.253)
___
___
___
___
___
___
0.737 (0.306)
___
___
___
___
___
___
___
0.098 (0.259)
___
___
___
___
___
0.221 (0.175)
___
___
___
___
___
___
1.285** (0.121)
(Dayprice)
β 10 (Dayprice) β 11 (Dtca) β 12 (Form) β 13 (Howfreq)
ρ
(Nest)
λ DTCA (DTCA Decay rate) λ D cos ts (Dcosts Decay rate) μ (Market size)
H m1 = 0.523
Bandwidths Step 1 Bandwidths Step 2
(
MinS n βˆ , γˆ, δˆ
)
H m 2 = 0.784
H m 3 = 0.407
H K = 0.415
H K = 0.385
H K = 0.419
H K = 0.561
H K = 0.437
HK = 0.400
H k = 0.460
H k = 0.442
H k = 0.479
H k = 0.410
H k = 0.484
H k = 0.513
H φ = 0.606
H φ = 0.639
H φ = 0.628
H φ = 0.546
H φ = 0.582
H φ = 0.570
1.612E-6
2.148E-6
1.203E-6
5.723E-6
3.4803E-6
2.004E-6
Numbers in parenthesis refer to standard deviations. Standard deviations have been estimated by a standard Bootstrap technique. ** (*) indicates parameters significantly different from 0 at a 5% (10%) level. Optimal Windows have been approximated by Least Squares Cross Validations.
35
TABLE 3 : Estimated Prescription and Noncompliance Rates per Drug and Year Noncompliance Drug Name
Rate ( F j )
Noncompliance
F j − Ft
F j − Ft
Drug Name
Rate ( F j )
MIOCHOL 1187 NSV
0.55762 0.48534 0.46835 0.57904 0.71602 0.56287 0.70058 0.66684 0.70270 0.58622 0.50563 0.48089 0.53660 0.56329 0.57233 0.60540 0.55832 0.55952 0.69161 0.52199 0.69733 0.61362
-0.06799 -0.14027 -0.15726 -0.04657 0.09041 -0.06274 0.07497 0.04123 0.07709 -0.03939 -0.11998 -0.14472 -0.08901 -0.06232 -0.05328 -0.02021 -0.06729 -0.06609 0.06600 -0.10362 0.07172 -0.01199
0.51492 0.50989 0.49846 0.75672 0.67425 0.63745 0.64754 0.77461 0.60246 0.48525 0.46833 0.44171 0.52940 0.63325 0.51813 0.60640 0.58083 0.59291 0.65658 0.63621
-0.07918 -0.08421 -0.09564 0.16262 0.08015 0.04335 0.05344 0.18051 0.00836 -0.10885 -0.12577 -0.15239 -0.06470 0.03915 -0.07597 0.01230 -0.01327 -0.00119 0.06248 0.04211
Year 1995 ACETAZOLAMIDE 0000 USA ADSORBOCARPINE 1187 ALC AKARPINE 0576 AKO AKBETA 0894 AKO BETAGAN 0386 ALL BETIMOL 0695 NSV BETOPTIC 0985 ALC BETOPTIC S 0290 ALC DARANIDE 0875 MSD DIAMOX 0362 SZO EPIFRIN 1269 ALL E-PILO 0566 NSV EPINAL 1187 ALC EPPY/N 1275 B.H GLAUCON 1187 ALC GLAUCTABS 0894 AKO HUMORSOL 1187 MSD IOPIDINE 0588 ALC ISOPTO CARBACHOL 1187 ALC ISOPTO CARPINE 0566 ALC LEVOBUNOLOL HCL 0000 USA METHAZOLAMIDE 0000 USA
0.57688 0.68307 0.66744 0.58842 0.58783 0.61514 0.68915 0.61864 0.78520 0.67720 0.51940 0.54111 0.66305 0.53029 0.56074 0.75142 0.70778 0.76385 0.51763 0.64484 0.73662 0.85876
-0.04873 0.05746 0.04183 -0.03719 -0.03778 -0.01047 0.06354 -0.00697 0.15959 0.04899 -0.10621 -0.08450 0.03744 -0.09532 -0.06487 0.12581 0.08217 0.13824 -0.10798 0.01923 0.11101 0.23315
MIOCHOL SY/PK PLUS 1288 NSV MIOCHOL SYSTEM PAK 1188 NSV MIOCHOL-E 0894 NSV MZM 1293 NSV NEPTAZANE 1187 SZO OCUPRESS 0492 NSV OCUSERT PILO-20 1187 ALZ OCUSERT PILO-40 1187 ALZ OPTIPRANOLOL 0790 BSP P1 E1 0466 ALC P2 E1 0466 ALC P4 E1 0466 ALC P6 E1 1187 ALC PHOSPHOLINE IODIDE 1187 WYE PILAGAN 0688 ALL PILOCAR OPHTH 0466 NSV PILOPTIC 1084 OTP PROPINE 0680 ALL TIMOPTIC 0978 MSD TIMOPTIC-XE 0194 MSD TRUSOPT 0595 MSD
Year 1996 ACETAZOLAMIDE 0000 USA ADSORBOCARPINE 1187 ALC AKARPINE 0576 AKO AKBETA 0894 AKO AKPRO 0296 AKO ALPHAGAN 1096 ALL BETAGAN 0386 ALL BETIMOL 0695 NSV BETOPTIC 0985 ALC BETOPTIC S 0290 ALC DARANIDE 0875 MSD DIAMOX 0362 SZO EPIFRIN 1269 ALL E-PILO 0566 NSV EPINAL 1187 ALC GLAUCON 1187 ALC GLAUCTABS 0894 AKO HUMORSOL 1187 MSD IOPIDINE 0588 ALC ISOPTO CARBACHOL 1187 ALC
0.61181 0.60140 0.54979 0.57483 0.69036 0.65301 0.51618 0.62973 0.57923 0.67661 0.69275 0.63640 0.67193 0.42763 0.58949 0.45500 0.70459 0.71124 0.58054 0.54810
0.01771 0.00730 -0.04431 -0.01927 0.09626 0.05891 -0.07792 0.03563 -0.01487 0.08251 0.09865 0.04230 0.07783 -0.16647 -0.00461 -0.13910 0.11049 0.11714 -0.01356 -0.04600
MIOCHOL SY/PK PLUS 1288 NSV MIOCHOL SYSTEM PAK 1188 NSV MIOCHOL-E 0894 NSV MZM 1293 NSV NEPTAZANE 1187 SZO OCUPRESS 0492 NSV OCUSERT PILO-20 1187 ALZ OCUSERT PILO-40 1187 ALZ OPTIPRANOLOL 0790 BSP P1 E1 0466 ALC P2 E1 0466 ALC P4 E1 0466 ALC P6 E1 1187 ALC PHOSPHOLINE IODIDE 1187 WYE PILAGAN 0688 ALL PILOCAR OPHTH 0466 NSV PILOPTIC 1084 OTP PROPINE 0680 ALL TIMOLOL MALEATE 0000 USA TIMOPTIC 0978 MSD
36
Noncompliance Drug Name
Rate ( F j )
Noncompliance
F j − Ft
F j − Ft
Drug Name
Rate ( F j )
TIMOPTIC-XE 0194 MSD
0.61687 0.66890 0.38330
0.02277 0.07480 -0.21080
0.48446 0.54841 0.50149 0.74882 0.72542 0.55706 0.71338 0.71757 0.55721 0.39685 0.43413 0.43729 0.50131 0.58966 0.63639 0.56393 0.49854 0.64919 0.59542 0.58812 0.66126 0.65281 0.36733
-0.09817 -0.03422 -0.08114 0.16619 0.14279 -0.02557 0.13075 0.13494 -0.02542 -0.18578 -0.14850 -0.14534 -0.08132 0.00703 0.05376 -0.01870 -0.08409 0.06656 0.01279 0.00549 0.07863 0.07018 -0.19530
0.59386 0.48635 0.42502 0.46470 0.56662 0.74865 0.57238 0.66600 0.49637 0.45817 0.47431 0.43394 0.42610 0.54414
0.07875 -0.02876 -0.09009 -0.05041 0.05151 0.23354 0.05727 0.15089 -0.01874 -0.05694 -0.04080 -0.08117 -0.08901 0.02903
Year 1996 ISOPTO CARPINE 0566 ALC LEVOBUNOLOL HCL 0000 USA METHAZOLAMIDE 0000 USA MIOCHOL 1187 NSV
0.58294 0.64388 0.74988 0.54636
-0.01116 0.04978 0.15578 -0.04774
TRUSOPT 0595 MSD XALATAN 0896 PHU
Year 1997 ACETAZOLAMIDE 0000 USA ADSORBOCARPINE 1187 ALC AKARPINE 0576 AKO AKBETA 0894 AKO AKPRO 0296 AKO ALPHAGAN 1096 ALL BETAGAN 0386 ALL BETIMOL 0695 NSV BETOPTIC 0985 ALC BETOPTIC S 0290 ALC CARBACHOL 0000 USA DARANIDE 0875 MSD DIAMOX 0362 SZO EPIFRIN 1269 ALL E-PILO 0566 NSV EPINAL 1187 ALC GLAUCON 1187 ALC GLAUCTABS 0894 AKO HUMORSOL 1187 MSD IOPIDINE 0588 ALC ISOPTO CARBACHOL 1187 ALC ISOPTO CARPINE 0566 ALC LEVOBUNOLOL HCL 0000 USA METHAZOLAMIDE 0000 USA
0.41926 0.66603 0.65547 0.58381 0.62486 0.66562 0.61126 0.57453 0.71163 0.66303 0.38799 0.73333 0.61663 0.53936 0.48569 0.53168 0.52042 0.62181 0.65611 0.68652 0.58050 0.47532 0.60109 0.79233
-0.16337 0.08340 0.07284 0.00118 0.04223 0.08299 0.02863 -0.00810 0.12900 0.08040 -0.21464 0.15070 0.03400 -0.04327 -0.09694 -0.05095 -0.06221 0.03918 0.07348 0.10389 -0.00213 -0.10731 0.01846 0.20970
MIOCHOL 1187 NSV MIOCHOL SY/PK PLUS 1288 NSV MIOCHOL-E 0894 NSV MZM 1293 NSV NEPTAZANE 1187 SZO OCUPRESS 0492 NSV OCUSERT PILO-20 1187 ALZ OCUSERT PILO-40 1187 ALZ OPTIPRANOLOL 0790 BSP P1 E1 0466 ALC P2 E1 0466 ALC P4 E1 0466 ALC P6 E1 1187 ALC PHOSPHOLINE IODIDE 1187 PILAGAN 0688 ALL PILOCAR OPHTH 0466 NSV PILOPTIC 1084 OTP PROPINE 0680 ALL TIMOLOL MALEATE 0000 USA TIMOPTIC 0978 MSD TIMOPTIC-XE 0194 MSD TRUSOPT 0595 MSD XALATAN 0896 PHU
Year 1998 ACETAZOLAMIDE 0000 USA ADSORBOCARPINE 1187 ALC AKARPINE 0576 AKO AKBETA 0894 AKO ALPHAGAN 1096 ALL AZOPT 0498 ALC BETAGAN 0386 ALL BETIMOL 0695 NSV BETOPTIC 0985 ALC BETOPTIC S 0290 ALC CARBACHOL 0000 USA COSOPT 0498 MSD DARANIDE 0875 MSD DIAMOX 0362 SZO
0.44933 0.48038 0.50454 0.59213 0.61183 0.64622 0.52799 0.49056 0.61186 0.64068 0.32167 0.37598 0.58904 0.61525
-0.06578 -0.03473 -0.01057 0.07702 0.09672 0.13111 0.01288 -0.02455 0.09675 0.12557 -0.19344 -0.13913 0.07393 0.10014
METHAZOLAMIDE 0000 USA MIOCHOL 1187 NSV MIOCHOL SY/PK PLUS 1288 NSV MIOCHOL-E 0894 NSV MZM 1293 NSV NEPTAZANE 1187 SZO OCUPRESS 0492 NSV OCUSERT PILO-20 1187 ALZ OCUSERT PILO-40 1187 ALZ OPTIPRANOLOL 0790 BSP P1 E1 0466 ALC P2 E1 0466 ALC P4 E1 0466 ALC P6 E1 1187 ALC
37
Noncompliance Drug Name
Rate ( F j ))
Noncompliance
F j − Ft
F j − Ft
Drug Name
Rate ( F j )
PHOSPHOLINE IODIDE 1187 WYE
0.54078 0.57277 0.59664 0.52816 0.59354 0.54224 0.60864 0.62098 0.58863 0.30434
0.02567 0.05766 0.08153 0.01305 0.07843 0.02713 0.09353 0.10587 0.07352 -0.21077
0.54951 0.41869 0.41715 0.43263 0.58471 0.55407 0.64129 0.57070 0.49296 0.45733 0.40913 0.41880 0.51960 0.45191 0.49273 0.43315 0.50660 0.49986 0.35409 0.57024 0.52658 0.62960 0.22853
0.06930 -0.06152 -0.06306 -0.04758 0.10450 0.07386 0.16108 0.09049 0.01275 -0.02288 -0.07108 -0.06141 0.03939 -0.02830 0.01252 -0.04706 0.02639 0.01965 -0.12612 0.09003 0.04637 0.14939 -0.25168
Year 1998 EPIFRIN 1269 ALL E-PILO 0566 NSV EPINAL 1187 ALC GLAUCON 1187 ALC GLAUCTABS 0894 AKO HUMORSOL 1187 MSD IOPIDINE 0588 ALC ISOPTO CARBACHOL 1187 ALC ISOPTO CARPINE 0566 ALC LEVOBUNOLOL HCL 0000 USA
0.53476 0.45331 0.45229 0.36727 0.49366 0.43844 0.54043 0.58395 0.47176 0.54844
0.01965 -0.06180 -0.06282 -0.14784 -0.02145 -0.07667 0.02532 0.06884 -0.04335 0.03333
PILAGAN 0688 ALL PILOCAR OPHTH 0466 NSV PILOPTIC 1084 OTP PROPINE 0680 ALL TIMOLOL MALEATE 0000 USA TIMOPTIC 0978 MSD TIMOPTIC-XE 0194 MSD TRUSOPT 0595 MSD XALATAN 0896 PHU
Year 1999 ACETAZOLAMIDE 0000 USA ADSORBOCARPINE 1187 ALC AKARPINE 0576 AKO AKBETA 0894 AKO ALPHAGAN 1096 ALL AZOPT 0498 ALC BETAGAN 0386 ALL BETIMOL 0695 NSV BETOPTIC 0985 ALC BETOPTIC S 0290 ALC CARBACHOL 0000 USA COSOPT 0498 MSD DARANIDE 0875 MSD DIAMOX 0362 SZO EPIFRIN 1269 ALL E-PILO 0566 NSV GLAUCON 1187 ALC GLAUCTABS 0894 AKO HUMORSOL 1187 MSD IOPIDINE 0588 ALC ISOPTO CARBACHOL 1187 ALC ISOPTO CARPINE 0566 ALC LEVOBUNOLOL HCL 0000 USA
0.49206 0.52278 0.53875 0.50446 0.59232 0.60294 0.54157 0.51973 0.52152 0.55133 0.37549 0.39049 0.61312 0.60432 0.51259 0.43379 0.43356 0.55142 0.50120 0.57205 0.50432 0.51469 0.47945
0.01185 0.04257 0.05854 0.02425 0.11211 0.12273 0.06136 0.03952 0.04131 0.07112 -0.10472 -0.08972 0.13291 0.12411 0.03238 -0.04642 -0.04665 0.07121 0.02099 0.09184 0.02411 0.03448 -0.00076
METHAZOLAMIDE 0000 USA MIOCHOL 1187 NSV MIOCHOL SY/PK PLUS 1288 NSV MIOCHOL-E 0894 NSV MZM 1293 NSV NEPTAZANE 1187 SZO OCUPRESS 0492 NSV OCUSERT PILO-20 1187 ALZ OCUSERT PILO-40 1187 ALZ OPTIPRANOLOL 0790 BSP P1 E1 0466 ALC P2 E1 0466 ALC P4 E1 0466 ALC P6 E1 1187 ALC PHOSPHOLINE IODIDE 1187 WYE PILOCAR OPHTH 0466 NSV PILOPTIC 1084 OTP PROPINE 0680 ALL TIMOLOL MALEATE 0000 USA TIMOPTIC 0978 MSD TIMOPTIC-XE 0194 MSD TRUSOPT 0595 MSD XALATAN 0896 PHU
Table 4 : Average Noncompliance Rate with Glaucoma Prescription per Year Year Noncompliance Rate Ft
1995
1996
1997
1998
1999
0.62561 (0.01342)
0.59410 (0.01580)
0.58063 (0.01206)
0.51511 (0.01052)
0.48021 (0.00966)
Numbers in parenthesis refer to standard deviations. Standard deviations have been estimated by a standard Bootstrap technique.
38
Graph 1 : Evolution of Sales and Advertisement Products with Sustained Promotion Effort 4
Sales (in $ Millions)
250
3
200 2
150 100
1
Total Ads (in $ Millions)
300
50 0
0 1996
1997
1998
1999
Year
Sales Alphagan
Sales Xalatan
Total Ads Alphagan
Total Ads Xalatan
Sales Market Average
50
1.0
40
0.8
30
0.6
20
0.4
10
0.2
0
0.0 1995
1996
1997
1998
1999
Year Sales Betagan
Sales Iopidine
=
Total Ads Betagan
Total Ads Iopidine
Total Ads Market Average
39
Total Ads (in $ Millions)
Sales (in $ Millions)
Graph 2 : Evolution of Sales and Advertisement Products with Decreasing Promotion Effort
4
0.68
3
0.66
2
0.64
1
0.62
0
0.6 1995
1996
1997
1998
1999
Year Ads to Sales Ratio
Price per Day of Treatment
Graph 4 : Comparison of Estimated Residuals
Residuals from General Nonparametric Model (Equation 4.5)
0.12
0.08
0.04
0 -0.12
-0.08
-0.04
0
0.04
-0.04
-0.08
-0.12
Residuals from our Structural Model (Equation 4.4)
40
0.08
0.12
Average Price per Day of Treatment (in $)
Ads to Sales Ratio (in %)
Graph 3 : Evolution of Prices and Ads to Sales Ratio
Graph 5 : Probability Density Function of Noncompliance
Probability Density Function
0.4
0.3
0.2
0.1
0 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Noncompliance Rate
Average Between 1995 and 1999
Year 1995
Year 1999
Graph 6 : Relative Rate of Noncompliance and Advertisement toward Doctors (Products with at least 10,000$ of Advertisement toward Doctors)
Advertisement (in Log of $ Thousand)
9 8 7 6 5 4 3 2 1 0 -0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
Individual Minus Average Annual Rates of Noncompliance
41
0.1
0.15
