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Private experience and observational learning in pharmaceutical demand Tanja Saxell∗† February 13, 2014 I quantify the roles of the physician's own experience and the past choices of other doctorsin pharmaceutical demand. I develop a model of medical decision-making under uncer-tainty about the quality of the match between the patient and drug treatment. Unlikeprevious demand models, I take into account both private and social learning, and allowheterogeneity in product quality across individuals. I test whether information on thepast choices of other doctors improves drug choices. Using rich data from the market forcholesterol drugs, I show that treatment patterns relying heavily on the past choices ofother doctors can lead to over-prescribing in terms of eciency. My results suggest thatcontinuity of care, where a patient is repeatedly consulting the same doctor, is an ecientpolicy to limit such behavior.
Keywords: social and private learning, structural modeling, unobserved quality, asym-metric information, demand, information diusion, physician behavior ∗Government Institute for Economic Research and University of Helsinki, email. tanja.saxell@vatt. †I am deeply grateful to my advisor Otto Toivanen for numerous useful suggestions and continuous encouragement. I also received very helpful comments from Gregory Crawford, Tuomas Takalo, JamesBurgess, Pauli Murto, Juuso Välimäki, Matti Liski and seminar participants at the Rising Star Sessionfor Health Markets at the International Industrial Organization Conference, the 9th World Congress onHealth Economics, the Annual Conference of the Royal Economic Society and the HECER Microeco-nomics and Industrial Organization Workshop. I am very thankful to the Social Insurance Institution ofFinland for providing me data.
Consumers may use their own experiences to learn about product quality. At the sametime, they may follow the past choices of their peers to deduce what others believe aboutquality. Private and social learning are relevant in many markets, including stock trading,demand for restaurant services or houses and rms' investment decisions. Yet, there isvery little previous work quantifying whether private and social learning help to reduceuncertainty around choices. In this paper, I explore these issues in pharmaceutical demandunder uncertainty about the quality of the match between the patient and drug treatment.
I will show that treatment patterns relying heavily on the past choices of other doctorscan lead to over-prescribing in terms of eciency. I analyze whether continuity of care,where a patient is repeatedly consulting the same doctor, is an ecient policy to limitsuch behavior. The policy is commonly used in primary care to promote the process oflearning and to improve medical decision-making: However, there are other aspects to the doctor-patient relationship that have im-portant implications on eciency. The distinctive feature of general practice agencyis that the doctor-patient relationship is usually long-term and more likely to becharacterized by repeated transactions [.] In general practice repeated transactionsare also potentially benecial because the GP becomes more aware of the context ofthe patients' health problems, and has more information about the patients' medicalhistory, social circumstances, values and preferences.
Anthony Scott (2000), Handbook of Health Economics I develop a model of medical decision-making to ask the following questions.1 Is continuityof care preferable to providing information on the past behavior of other doctors throughpatient records? What are the implications of the long-term doctor-patient relationshipon learning and the eciency of drug choices? Does continuity matter for health carecosts? In the model, each patient reacts dierently to the drug treatment, and physiciansmay learn the individual match quality from their own experiences and the treatmentchoices of patient's previous doctors. I assume that the physicians of the patient maychange the drug therapy, and the number of the doctor-patient consultations determinesthe physician's private experience, or the number of signals, about the match quality.
I focus on the Finnish market for cholesterol drugs that are used to decrease the risk 1I consider physicians' decisions to continue the drug therapy of a patient in primary care. The model can be extended to allow multiple inside goods. This is very straightforward if the health eects of onlyone drug group, say patented products, are uncertain.
for cardiovascular diseases. Benets from improvements in the drug treatment of highcholesterol can be substantial, as heart disease and stroke alone are among the mostwidespread and costly diseases. Still, many doctors claim that cholesterol drugs are over-prescribed to many low-risk patients.2 The model helps to understand why continuity of care can improve physician decision-making. Repeated consultations with the same physician are benecial, because thephysician becomes over time more familiar with the patient's disease and her perceptionson the distribution of health eects become more precise. The physician may thus learnwhether the drug is on average good or bad for the patient which improves her treatmentchoices. If the physicians of the patient change, physicians try to learn the match qualityfrom the treatment choices of previous doctors. As a result of social learning, physiciansmay start to follow or imitate the treatment choices of previous doctors. An inexperiencedphysician may belief that the drug treatment must perform well for the patient who hasused the drug for many years. This optimism leads to over-prescribing when the drug isof low quality.
The model predictions are consistent with empirical evidence from health care and phar-maceutical markets. The extensive literature in medicine and economics (see e.g. Weissand Blustein, 1996, Scott, 2000, King et al., 2008) has documented a positive associa-tion between continuity of care and improved health outcomes, such as lower mortalityand hospitalization rates. Moreover, at least two observations indicate that the physi-cian's personal experience and peer eects aect drug choices. First, my data from thecholesterol drug market conrms that prescriptions are highly responsive to changes inthe length of the doctor-patient relationship.3 Second, prescription behavior by inex-perienced physicians is signicantly aected by the choices of prominent physicians, or"opinion leaders" (Nair et al., 2010). In my data, the previous choices of peers aectprescribing behavior especially if a physician does not have much own experience of thepatient.
A vast majority of the literature on demand for experience goods assumes that agents canonly learn the quality of a product from their own experience (e.g. Crawford and Shum,2005, Kim, 2010, Dickstein, 2011, Chan and Hamilton, 2006, Chernew et al. 2008) or thatall information is public (e.g. Ackerberg, 2003, Ching, 2009). A few recent papers alsolook at the social learning of an agent who makes a once-in-a-lifetime decision (Cipriani 2See e.g. Franklin (2011), Adams (2011), Joelving (2011), BBC (2011).
3Specically, I consider the choices of physicians working in the Finnish public primary care. In this market, the physicians of a patient change frequently for exogenous reasons, such as due to the shortageof physician labor. See section 2.1 for details.
and Guarino, 2012, Knight and Schi, 2010, Zhang, 2010). My main contribution is thatI take into account both private and social learning in demand. I modify the standardmodels of social learning (Chamley, 2004, Bikhchandani, Hirshleifer and Welch, 1992),by allowing agents to learn product quality also from their own experiences. With myframework, I can analyze how the own consumption experiences of an agent interact withinformation received from the past choices of peers in her learning process.4 Furthermore,because private and social learning may induce divergent beliefs about quality, a demandmodel should capture them both in order to produce reliable estimates on product qualityand on the eects of policy experiments on choices.5 Finally, unlike the previous work onsocial learning, I allow heterogeneity (among patients) in quality.
I nd that the average health eects of the cholesterol drug treatment are heterogeneousacross patients. Particularly, the quality of the match is on average high for 72% of pa-tients and low for the remainder. The estimates also imply that most of the uncertaintyassociated with quality vanishes when the patient has used the cholesterol drug treat-ment once. Even if quality was known, uncertainty regarding to health eects remainssignicant. These results have implications on eciency.
The counterfactual experiments suggest that information on the patient's prescriptionhistory does not compensate for the lack of the long-term treatment relationship. If thepatient had only one physician, the physician learns fast and better health outcomesrealize. If quality is high (low), the long-term doctor-patient relationship increases (de-creases) demand for cholesterol drugs. Information on the past choices of other doctorsfor a patient promotes learning about high quality, but not as eciently as continuity ofcare. If quality is low, observing the patient's prescription history increases demand overthe level of ecient prescribing.
The rest of the paper is organized as follows. Section 2 describes the dataset and providesdescriptive evidence on the eects of physician's own experience and the past choices ofother doctors on medical decision-making. Section 3 goes through the structural modeland Section 4 discusses estimation and identication. Section 5 presents estimation re-sults, the t of the model and the results from the counterfactual experiments. Section 6concludes.
4Traditional private and social learning models are special cases of my framework.
5If there is private information unobserved by the econometrician, but all information is assumed to be public, quality estimates become biased. Specically, when quality is in reality high, quality estimateis downwards biased because private information slows down learning and decreases the probability ofchoosing the product. Low quality estimate is, on the other hand, upwards biased because social learningmakes agents too optimistic about quality which increases the probability of choosing the product.
2 Market and data description 2.1 Cholesterol drug markets Cardiovascular diseases (CVD), such as heart attacks, stroke and high blood pressure,aect millions of people globally. Heart disease and stroke alone are among the mostcommon and costly health problems in Europe and the United States.6 Patients whohave experienced CVDs have to deal with high medical expenditures, lost wages andlower productivity.
I analyze the Finnish market for cholesterol drugs that are used to decrease the risk forcardiovascular events. I focus on statins (HMG-CoA reductase inhibitors) that is the mostpopular group of cholesterol drugs globally.7 Statins decrease high serum LDL-cholesterol("bad" cholesterol) and increase HDL-cholesterol ("good" cholesterol) by inhibiting anenzyme in the liver that has an important role in the production of cholesterol.8 Highmorbidity to CVDs and a large volume of diagnoses of dyslipidemia, i.e. an abnormalamount of lipids, such as cholesterol and fat, in the blood, have made cholesterol drugsone of the world's largest selling drug groups.
Corresponding to the United States, the following active ingredients are on the Finnishstatin market: Atorvastatin (Lipitor and Torvast), Fluvastatin (Lescol), Lovastatin (Meva-cor, Altocor, Altoprev), Pravastatin (Pravachol, Selektine, Lipostat), Rosuvastatin (Crestor)and Simvastatin (Zocor, Lipex).9 I focus on a physician's decision to continue the pa-tient's statin therapy for several reasons. First, uncertainty is probably the highest in thehealth eects of statins in general. Second, clinical dierences between statins in reducingcardiovascular events have been claimed to be small (National Institute for Health andClinical Excellence, 2006) and thus it is quite natural to consider statins as a one group. Ithereby ignore important questions regarding to a physician's or patient's choice between 6Around 12% of adults suered from heart disease in 2009 − 2010 in the United States (National Center for Health Statistics, 2011). Every year, there are around 152 000 strokes in the UK (BritishHeart Foundation, 2013).
7See e.g. Herper, M. (2010) "Why You May Need Cholesterol Drugs", Forbes, and U.S. Food and Drug Administration (FDA), 2010.
8When cholesterol levels are too high, cholesterol can grow on the walls of blood vessels transporting blood from the heart to other body parts. Over time, these blood vessels can be blocked, preventing theheart from getting enough blood.See e.g. "What is cholesterol?" by the National Heart, Lung and BloodInstitute that is a division of the National Institutes of Health in the USA.
9Within the group of an active ingredient, statins dier also in the form of drugs, package sizes, strengths and prices. I do not consider a combination preparations of a statin and an another activeingredient.
branded and generic products (see e.g. Scott-Morton, 1999, Ching, 2010a and 2010b) andbetween dierent active ingredients (see Crawford and Shum, 2005).10 A treatment decision by a physician is based on the benets and adverse eects of statins.
The statin therapy is initiated if the patient has a high risk for CVDs. The evaluationof the risk is based on several factors, including the patient's gender, age, blood pressureand cholesterol levels. In my model, the initial evaluation is captured by the physician'sprior belief on the average health eect of cholesterol drugs for a particular patient. Inthe follow-up of the drug therapy, a physician evaluates the realization of the treatmentgoals and sustains the patient's treatment motivation. The main goal of cholesterol drugtreatment is to decrease the total cholesterol level below 5 mmol/L (LDL-cholesterol below3 mmol/L). If the patient experiences side eects, the physician decreases the dosage,experiments with an another statin or suspends the cholesterol drug therapy (the Finnishcurrent care for dyslipidemia, 2011).11 As patients respond dierently to statins (theFinnish current care for dyslipidemia, 2011, Jousilahti, 2004), a physician may not knowthe ecacy and side eects for a single patient.12 I take the uncertainty into account andlet the physician to learn the average health eects of statins by observing realized healtheects and the patient's past statin prescriptions.
Cholesterol drugs are also particularly interesting as there is no consensus on an appropri-ate level of cholesterol drug prescribing. Some doctors have claimed that there is a littleevidence that statins reduce the CVDs of low-risk individuals. Doctors supporting theuse of statins have said that they have prevented heart attacks and other CVDs.13 In mymodel, physicians disagree on the health eects of statins, depending on their personal 10I also assume that the physician decides to end the patient's medical treatment. In practice, the nal decision to end the therapy can be done either by the physician or the patient or both.
11Lifestyle changes, including exercising and changes in diet, are often adequate for a low-risk patient.
However, patients are often unwilling to change their lifestyles, even after having a signicant shockin their life. Perhaps 45% of smokers stop smoking after a myocardial infarction which is between 2or 4 times of the success rate of antismoking clinics. Results are not as good for other cardiovascularrisk factors related lifestyle, such as physical exercise or diet. Patients can become even less active afterinfarction. There is also some evidence that changes in self-reported fat intake in one year after infarctioncan be small. (Johnston, 1999) 12For example, statins are reported being useful for men, post menopausal women and patients who have arterial disease or diabetes. It has also been shown that statins decrease by 15% the mortality rateof patients who were 60 years and older and initially clinically asymptomatic. Genetic susceptibility andcertain drug interactions can increase the risk of side eects. For example, approximately 5% of patientshave been reported suering muscular symptoms and an increase in the activity of serum muscularenzymes appears for 0.5 − 2.0% of statin users, even though its clinical signicance is often uncertain.
(The Finnish current care for dyslipidemia, 2011) 13See e.g. Adams (2011), Joelving (2011), BBC (2011).
experience of the patient.
Two features of the Finnish market simplify my empirical analysis. The rst is that achoice of a physician by a patient was very restricted in public primary care. Duringthe observation period, the patient was not allowed to choose the health center. Withinthe health center, the patient's family physician was (exogenously) determined based onthe patient's residential area (Finnish Medical Association, FMA, 2007).14 However, dueto the shortage of physician labor, patients were not often treated by their own familyphysicians.15 I assume that a physician is exogenously determined for the patient inprimary care.16 The second feature is that two characteristics of the Finnish statin market decrease vari-ation in drug prices over time. First, drugs are subject to price cap regulation by thePharmaceuticals Pricing Board that is subordinated to the Ministry of Social Aairs andHealth in Finland. Second, the patents of Fluvastatin, Atorvastatin and Rosuvastatinremained eective during the whole observation period 2003 − 2006. As patent protec-tion limits competition, it is likely that the prices ceilings of the patented products werebinding. In the empirical analysis, I follow much of the previous learning literature (e.g.
Crawford and Shum, 2005) and assume that the drug prices are exogenous. The assump-tion simplies the construction of the structural model as prices do not adjust with theobserved behavior of physicians.17 2.2 Information transmission between physicians In the model, I assume that a physician has personal experience about the patient-specicquality of the drug treatment. As MD Epstein (1999) illustrates in the Journal of theAmerican Medical Association: "Clinical judgment is based on both explicit and tacit 14Family physician practices are widely adopted in many countries. For example in the USA, The American Academy of Family Physicians (AAFP) is one of the largest national medical organizations.
See AAFP, http://www.aafp.org.
15For example in 2006, 9% of the appointments in health centers had a shortfall of physicians and almost the same share of working-age physicians were absent from their permanent jobs. In 46% ofthese cases, this was caused by staying abroad (FMA, 2006c). It has been estimated that 90% of familyphysicians treat other than their own patients every week (see FMA, 2005, 2006a, 2006c, 2007).
16To be more specic, I assume that the probability of getting a certain physician does not depend on the statin treatment or the health of the patient. This probability is needed to recover the choiceprobability for the outside good.
17In the nancial market application of Cipriani and Guarino (2012), bid and ask prices (prices at which a trader can buy and sell) are endogenous because they reect public information containing thehistory of trades and prices.
knowledge. Medical decision-making, however, is often presented only as a consciousapplication to the patient's problem of explicitly dened rules and objectively veriabledata. [.] Seasoned practitioners also apply to their practice a large body of knowledge,skills, values, and experiences that are not explicitly stated by or known to them. [.]While explicit elements of practice are taught formally, tacit elements are usually learnedduring observation and practice." In this section, I evaluate the validity of the assumptionon private information further by discussing the information content of patient recordsand communication between physicians.
A patient record documents and transfers information on a single patient's medicationbetween physician. If all relevant information for medical decision-making is availablein the record, a physician does not have any private information of the patient. To seewhether this is the case, I next consider the information content of patient records.
The focus of patient records is on the patient's medical condition and medication.18 Tosee what type of information is stored in patient records, consider an example of a patientrecord for a dispensary admission in Appendix B. The patient record provides a compactdescription of the patient's health status and the plan, the goal and the follow-up of thetreatment. It also includes the name of the physician, the list of current medication anda brief justication for starting a medical treatment. In general, patient records may alsocontain information on whether medication is permanent and reasons for a physician'sdecision to end the patient's drug therapy.19 Patient records do not perfectly transfer all relevant information for medical decision-making between physicians. The case example demonstrates that the continuation of drugtherapy is not justied (Appendix B). According to an interviewed specialist, this is a verycommon practice, at least in routine cases. Records do not include physician-specic fac-tors, such as the physician's own preferences for medication and information on whetherher medical decision-making is based on medical literature, advertising and treatment 18Patient records regarding to medication include entries about the need of pharmacotherapy and medical foundations, a prescription and given medical treatment, including the name, quantity, form,dosage, dosage form, the date and time of issue of a drug and the name of the physician who has givenor prescribed the drug (The Ministry of Social Aairs and Health, 2005).
19Essential information in electronic patient documents are reported in the following guidebook and its updated versions (in Finnish): "Opas Ydintietojen, otsikoiden ja näkymien toteuttaminen sähköisessäpotilaskertomuksessa", version 1.1, 28.2.2006.
recommendations. The physician's accumulated knowledge of the patient's preferences,values and circumstances is rarely recorded (see Guthrie et al., 2008). The specialist alsoclaimed that a narrative text format complicates the interpretation of records that mayimpede information transmission. The registering of information takes the physician'stime that may decrease her incentives to record all relevant information.
I evaluate next whether all relevant information for medical decision-making is transferedthrough communication. A physician who cares about her patient may want to consult hercolleagues before deciding on the continuation of the treatment. Because communicationis time-consuming, consultation does not probably happen in routine cases. On the otherhand, the patient, who wants to get as good medical treatment as possible, may wantto communicate all relevant information to her physicians. It is, however, unlikely thatmedical decision-making by physicians is exclusively based on information received fromthe patient (see e.g. Epstein, 1999).
The theoretical cheap-talk20 literature (see for example Crawford and Sobel, 1982, Ol-szewski, 2004) has shown that the truthful information revelation of a consultant (asender, here: other physicians or a patient) to a decision maker (a receiver, here: a physi-cian) is only one of many possible outcomes, even if there is no disagreement betweenparticipants. If the preferences of the consultant are even slightly misalligned with thepreferences of the decision maker, there is some information loss in all equilibria (Craw-ford and Sobel, 1982). If the consultation eort of the physician is unobserved to thepatient, incentives for consultation may not be high.
Finally, if all physicians of a patient share the same information, they should have thesame probability of choosing the medical treatment. As it turns out in the next section,this is not the case.
20In a typical cheap-talk game, the sender may, often costlessly, convey her private information through messages to the receiver. The receiver then takes an action that together with sender's signal aects thepayos of both players.
2.3.1 Sample selection I use a rich dataset of all purchased cholesterol drug prescriptions in Finland from January1 in 2003 to December 31 in 2006. The data is provided by the Social Insurance Institutionof Finland which is responsible for the provision of public social security benets to Finnishresidents. The data identies patients, their physicians and cholesterol drugs.21 I prepare my data for the empirical analysis in the following steps. First, to followpatients from the beginning of cholesterol drug therapy and to avoid left-censoring, Ifocus on "new" patients who did not have any prescriptions during the rst 6 months ofthe observation period i.e., before July 2003.22 Second, I ignore patients with multipleprescriptions or physicians within a day to simplify the analysis further. Third, I considerpatients whose physicians are primarily working in public health centers. Ideally, I wouldlike to concentrate on patients who have only used the services of public health centers butunfortunately the data does not include this information. As a proportion of physicianswork for both the public and the private sectors23, some patients in the sample may haveused private health care services. Fourth, I concentrate on patients who belong to theworking-age (15-64 years) population because the data does not allow me to distinguishthe death of a patient from the ending of the statin treatment. Finally, for computationalreasons, I draw a random sample of 10000 patients from the sample of new working-agepatients whose physicians are working in primary care.
2.3.2 Descriptive evidence In this section, I provide the descriptive analysis of the sample. The results in Table1 demonstrate that the sample consists of very heterogeneous patients. Most of thepatients in my sample were relatively old at the time of the last prescription (an average51 years) and almost half of the patients were men. The number of diagnosis varies24 21Other characteristics than the primary job of a physician (public health center/public hospital/other) received from the survey conducted by the Finnish Medical Association (FMA) are from the registers ofthe Social Insurance Institution of Finland. The response rate of the yearly survey has been very high.
For example, in 2006, the response rate of physicians who received the survey was 80% (FMA, 2006c).
22This six months' time window has been also used by Crawford and Shum (2005).
23In 2006, 19.6% of physicians, who were primarily working in health centers, had a sideline job (FMA, 24The number of diagnosis is observed if the patient was on sick-leave.
in substantially around its mean (0.7).25 A signicant portion of patients (55%) werecensored in the sample i.e., they had their last prescription within the last six months ofthe observation period.
Table 1: Descriptive statistics for the sample of patients1 Std.Dev. Only non-censored At the time Gender (1: male, 0: female) Censoring indicator (1: yes, 0: no) Patient's medical treatmentTreatment ending (1: yes, 0: no) Nbr of prescriptions Nbr of physicians Prescriptions of a current physician Visit a physician specialized ininternal diseases Visit a non-specialized physician Total number ofphysician's prescriptions Physician change (1: yes, 0: no)2 Active ingredient change(1: yes, 0: no)2 Number of observations 1 The relevant population consists of new working-age patients who have used statins and the services of public health centers. The size of the random sample is 10 000 patients.
2 Note that here the number of prescriptions is at least 2 because the change in the value of the variable from the previous prescription is computed by using the dierence between itscurrent and lagged value.
Following Crawford and Shum (2005), I assume that the drug therapy of a non-censoredpatient ends after the last prescription in the data. If the patient is censored, the end of 25Information on the number of diagnosis is observed if a patient received sickness benets from the Social Insurance Institution of Finland.
the therapy is not observed. If the censoring interval is too short, the estimation resultsmay be biased. This is particularly true if the patient's drug treatment is prescribed atthe end of the observation period and he has more than two prescriptions.26 Dickstein(2011) used an alternative approach where the treatment episode of a patient ends at thelast prescription if there was a gap of 90 days within the treatment history. A patientappearing in the data again after the gap is then treated as a new patient.
The cholesterol drug therapies of non-censored patients in the sample were on averagerelatively short, approximately 2 prescriptions (Table 1). The probability that the pa-tient's therapy ends at any stage of therapy is 0.34. The average number of physicians perpatient was 1.3 and the total number of prescriptions received from a particular physicianwas 1.65. Most of the patients (70%) were treated by a non-specialized physician. Theaverage price of a prescription was 41 eur.
Table 2 presents the distribution of the total number of prescriptions and physicians at thetime of the (non-censored) patient's last prescription. Most of the non-censored patients(52%) had only one prescription and 80% of the patients were in a permanent physician-patient relationship. Even though the distributions of the total number of prescriptionsand physicians are skewed to the right, 48% of non-censored patients had more than oneprescription and 20% were treated by more than one physician.
Table 2: The percentage share of non-censored patients in the sample conditional on thetotal number of prescriptions and physicians at the last prescription 80.36 16.12 3.52 100.00 I consider next the incidence of a physician change in the sample of patients. Table 1illustrated that the breakdown of the physician-patient relationship was very common.
The probability that the patient's physician changes from the previous prescription was 26As a robustness check, I used a one-year censoring interval and dened a patient to be "new" if he did not have prescriptions during the rst year. Then, the probability that the patient is censoredwas somewhat higher (0.73) than with the original censoring interval. The probability that the patient'streatment ends was 0.40 which is fairly close to the corresponding probability with other denition (0.34).
33%. A high standard deviation also indicates signicant diversity among patients in theincidence of a physician change.
Then, I analyze how the number of interactions between a physician and a patient aectsprescriptions. I consider rst how the probability of continuing the (non-censored) pa-tient's statin therapy depends on the lagged number of physicians (Figure 1). I nd thatthe continuation probability is 50% for patients who have only one physician, i.e. whodo not have any physician switches. The choice probability decreases to 42% for patientshaving two physicians and further to 33% for patient with three physicians.
Probability of therapy continuation 0.2 Number of physicians Figure 1: The probability of treatment continuation and its 95% condence intervals bythe number of physicians for non-censored patients, sample averages I investigate next whether the decreasing pattern between the choice probability and thenumber of physicians is driven by the phase of the patient's therapy. To see if this isthe case, I estimate the following linear probability model for the continuation of the(non-censored) patient's statin therapy, ait = α + Xi(t−1)β + eit, t > 1, where ait is an indicator variable that gets value 1 if the statin therapy of patient i is continued at time, or prescription, t and 0 otherwise27, Xi(t−1) is a vector of laggedexplanatory variables and eit is the error term.
The results presented in Table 3 suggest that the continuation probability increases by13% when the number of previous physicians increases by one. The lagged length of thedoctor-patient relationship has an opposite eect on the continuation probability. Thesendings may suggest that physicians do not share the same information about the healtheects of the cholesterol drug treatment for a patient.
27To be more precise, ait = 0 only once when the patient's statin therapy ends.
Table 3: Descriptive regressions for the probability of therapy continuation in the sampleof non-censored patients Model (1) Model (2) Own experience:prescriptions/current physician Nbr of physicians Fixed eects:physician, ATC-code, hospital district 1 Explanatory variables are lagged by a one prescription.
2 Variables are for cholesterol drug prescriptions.
2 Standard errors in parentheses.
3 * p < 0.05, ** p < 0.01, *** p < 0.001.
To get further evidence on peer eects and the role of private experience in demand, Table4 illustrates how medical spending in the sample depends on the length of the physician-patient relationship, after controlling for observed characteristics. When the number ofphysicians increases by one, the total costs of the therapy at any stage decreases by 7euros which is 15% of the average costs of statins in the sample. Table 4 also shows thatthe more the physician has experience of the patient, the less the previous choices of peers - measured by the number of cholesterol drug prescriptions provided by other doctors toa single patient - aect an average medical spending at any phase of the therapy.28 Whenthe physicians of a patient change frequently relative to the stage of the drug therapy,the eect of physician's own experience on the total costs becomes small. These resultsare consistent with "asymmetric peer eects" where inexperienced physicians rely onexperienced doctors to decrease uncertainty around their prescription decisions (see e.g.
Nair et al., 2010). Still, the ndings remain very indicative without putting any structurein the model that helps to isolate the eects of personal experience and social learning onmedical decision-making.
28I measure the physician's own experience with the number of interactions with the patient.
Table 4: Descriptive regressions for treatment costs in the sample of patients Explained variable Total cost, Total cost, Nbr of physicians Own experience:prescriptions/current physician Other physicians' experience:prescriptions/previous physicians Own experience*others' experience Nbr of prescriptions Prescription date Min prescription date Fixed eects:physician, ATC-code, hospital district 1 Total (cumulative) costs at a given stage of the therapy.
2 Variables are for cholesterol drug prescriptions.
2 Standard errors in parentheses.
3 * p < 0.05, ** p < 0.01, *** p < 0.001.
3 A theoretical model of pharmaceutical demand In this section, I present a structural model of medical decision-making with privateexperience and observational learning. In each period during the drug therapy, the patient(he) is randomly matched to a physician (she). After an initial treatment choice, thephysician investigates the patient and gets private information about the quality of thematch between the patient and the drug treatment. During the course of the patient'stherapy, the physician may learn quality from from her own experience and the previouschoices of other doctors for this particular patient.29Consider patient i who comes for the rst time to a public health center to seek drugtreatment for her medical condition. After entrance, a physician is randomly assignedto the patient. As the sensitivity of patients to cholesterol drugs dier, the physiciandoes not know ex-ante the average health eects, or quality, of the drug treatment forthis particular patient. To form the prior belief on quality, the physician evaluates thepatient's risk for CVDs based on the patient's observed characteristics. The physiciantakes the prior belief and her privately observed idiosyncratic preferences into accountwhen she decides whether to initiate the cholesterol drug therapy.
In the follow-up of the drug therapy at time (or prescription number) t, patient i comesagain to the health center where he is randomly matched physician l. First, the physi-cian performs a diagnostic procedure, physical examination and tests for the patient toprivately evaluate the ecacy and side eects of the drug treatment. This evaluationis modeled by an experience signal xilt. Simultaneously, she looks at patient records tosee how long the patient has been using the drug. Conditional on the prior, the pastchoices of other doctors indexed by l1, ., lt−1, hit = {ail11, ., ailt−1(t−1)}, and all privateexperience signals that the physician has received during the course of the patient's drugtherapy up to and including time t, she updates her belief about its quality.
Recall that in previous social learning models (Cipriani and Guarino, 2012, Knight andSchi, 2010, Zhang, 2010) agents can receive only one experience signal. Based on thisposterior belief and her private preference shocks for the drug treatment and the outsidegood, vil1t and vil0t respectively, the physician makes a decision on the continuation of the 29A relatively easy extension of the model is to enrich the choice set of physicians that could include other medical treatment alternatives, such as non-patented products, with the known (to physicians) butpossibly random quality. An extension that allows several inside goods with uncertain qualities comes atthe cost of computation.
patient's therapy. Further decisions follow until any physician decides to end the drugtherapy. The timing of events is summarized by Figure 2.
Match to a physician l A treatment choice Figure 2: The timing of events in period t during the follow-up of the therapy: 1.) apatient is rst matched to a physician, 2.) the physician observes a new signal xilt andthe past choices of other doctors hit and private idiosyncratic preference shocks, vil1t andvil0t, 3.) the physician makes a treatment choice on all her private signals received up toand including time t, public information hit and private preference shocks.
In the long-term treatment relationship, the physician learns about the average healtheects of the drug treatment from her own experience. If the relationship breaks down,a physician attempts to infer quality from the past choices of other doctors. The less thephysician has own experience of the patient, the more the past choices of peers aect herprescription behavior. If the patient has used the drug treatment long, an inexperiencedphysician may perceive that the drug must be eective. When the drug is of high quality,observing the past choices of other doctors improves learning. On contrary, the optimismon quality leads to over-prescribing when the drug is of low quality.
To keep the model tractable and to avoid the salient computational burden, I assumethat a physician maximizes her expected per-period utility. The assumption of myopicbehavior is often made in the structural learning literature (e.g. Coscelli and Shum, 2004,Ching, 2009, Chernew et al., 2008) and it abstracts away incentives to experiment withthe drug treatment to get new information about quality in the next period (see e.g.
Crawford and Shum, 2005).30 Following e.g. Crawford and Shum (2005) and Dickstein (2011), the model does not takeinto account learning across patients.31 This type of learning could be incorporated to the 30My future plan is to estimate a dynamic version of the model.
31For learning across patients, see Kim (2010) and Coscelli and Shum (2004). Note also that Crawford model by using the entry of a new active ingredient, Rosuvastatin. This extension comesagain with the cost of computation and tractability because physicians and the econome-trician have to keep track on the posteriors of all doctors. Because many cholesterol drugshave been on the market since the end of the 1980s or the early 1990s, learning about thedistribution of health eects across patients does not probably have a signicant role inmy application.
In the following sections, I present the model in detail. I rst formulate a deterministicprocess governing the assignment of a physician for a patient.32 Because the physician isnot forward-looking in her treatment continuation choices, the assignment, or matching,probability does not aect her behavior. Then, I describe a therapy continuation choiceunder uncertainty and the information structure, including the distribution of signals(health eects) and the patient-specic quality. Finally, I derive the posterior beliefof the physician about quality, conditional on her private experience and the patient'sprescription history.
3.2 The theoretical model 3.2.1 Physician and patient matching In each period until the therapy ends, patient i is assigned to a physician. The physician iseither "new" i.e., she does not have the previous treatment relationship with the patient,or is any of the previously drawn "old" physicians 1, ., Nit. The number of old physiciansat time t + 1 increases by one, Ni(t+1) = Nit + 1, if the new physician treats the patientat time t, and otherwise it remains unchanged, Ni(t+1) = Nit.
I assume that the patient is assigned to the new physician with probability κi and tothe old physician with probability (1 − κit) × 1 . This specication implies that each old physician is randomly selected for the patient from the pool of the previously drawnphysicians with the same probability 1 .33 I assume the following functional form for the matching probability of patient i: and Shum (2005) allow the possibility of non-rational expectations, because in their model physicians'prior beliefs for one particular drug, Omeprazole, can evolve over time, which captures common changesin priors, for example, due to advertising. However, posteriors may also vary through a dierent type ofmechanism, namely based on the previous medication decisions of a particular physician or other doctors.
32The assignment probability is used to recover the probability of the outside good (see Section 4.1).
33Note that only 3.5% of patients had more than 2 physicians in my data (see Table 2).
κi = Pi(dit = 1) = In the above expression, yi is N(θy, σ2)- distributed patient level random coecient. The variance of the random coecient, σ2, measures the magnitude of heterogeneity in match- ing probabilities across patients. The heterogeneity is potentially important because theprobability of a physician change can dier between patients, for example, by residentialarea.
3.2.2 A therapy continuation choice under uncertainty Assume that physician l is drawn for patient i at time t. The physician decides whetherto continue the drug therapy of patient i, ailt = 1, or end the therapy for good, ailt = 0,conditional on her information at that time, Iilt. In the perfect Bayesian equilibrium, thephysician chooses to continue the medical therapy if the expected utility from the medicaltreatment exceeds the utility from the outside option (the non-purchase option), ailt = 1 ⇔ E(uil1t Iilt) ≥ uil0t.
I assume that the per-period utility received from the medical treatment, uil1t, dependson the quality signal, or health eects, xilt, and a vector of control variables, Zil1t. Thecontrols include, for example, the (average) price of statins, observed patient level char-acteristics and the time trend capturing general market level changes over time due toadvertising. These controls are observed by both physicians and the econometrician. Be-cause patient records do not contain information on preference shocks, I assume that thephysician's idiosyncratic, Type 1 extreme value distributed tastes for the drug treatmentand the outside option, vil1t and vil0t, are her private information. Following the previousliterature (e.g. Crawford and Shum, 2005), I assume a Constant Absolute Risk Aversion(CARA) sub-utility specication for the health eects. To be more specic, I considerthe following utility function, u(xilt, Zil1t, vil1t) = −e−r·xilt + Zil1tα + vil1t, where r > 0 is the risk aversion coecient.
I assume that the utility of the outside good for the physician l of patient i at time t,uil0t, is a function of a vector of observed characteristics, Zil0t, and the physician's privatepreference shock, vil0t, u(Zil0t, vil0t) = Zil0tβ + vil0t.
To ensure identication in the discrete choice model, I make a typical restriction that theconstant of the outside option is zero. Recall that the utility of the outside good varieswith the patient's observed characteristics (see Chan and Hamilton, 2006, for a similarapproach). For example, cholesterol drugs prevent coronary events in the long-run afterthe patient's drug therapy has ended.34 I control this with the number of prescriptions.
3.2.3 Health eects The quality of the match between the patient and the drug treatment (referred as "qual-ity"), θi, is without loss of generality either high θ1 or low θ0 with prior probabili-ties pi(θ1) and 1 − pi(θ1), respectively. 35 The variance of random quality, Var(θi) =E(θ2) − (E(θ i))2 = pi(1 − pi)(θ2 1θ0), measures prior uncertainty regarding to quality. The prior is uninformative when it equals 1/2.
The prior probability is common knowledge for physicians but it may vary across patients,depending on the patient's observed characteristics. I assume that each physician has thefollowing prior belief that the treatment has high quality for patient i: where Zp is a vector of patient level characteristics at the time of the rst prescription.
In the follow-up of the patient's drug therapy at time t > 1, the physician observesan experience signal, or health eects associated with the use of cholesterol drugs. Iassume that health eects are independent and normally distributed conditional on thetrue quality, xilt θi ∼ N (θi, σ2), 34The literature has explained this with the stabilization of existing plaque and the slowing of the progression of coronary artery disease (Ford et al., 2007).
35The model could be generalized to allow a continuous quality level but the computation of the posterior probability for quality θ conditional on information at time t It, f(θ It), becomes more dicultthan in the binary case as it would involve integration over quality levels θ.
where σ2 measures uncertainty regarding to health eects. The distributions of signals andpriors are common knowledge and θ1, θ0, σ2, γ0 and γ are parameters to be estimated.36 Because prior beliefs are heterogeneous across patients, the unconditional (mixture) den-sity of health eects, f(xilt), depends on the observed characteristics of the patient. Thismeans that the sensitivity of patients on the ecacy and side eects of statins may dierfor example by their gender and age, as the medical literature suggests (see Section 1).
3.2.4 A physician's information set Because signals are private information to physicians, a physician's information set for thepatient at time t, Iθ , includes her own private experience of the patient and the previous therapy continuation choices of other physicians. Formally, Iθ = x ilt ∪ hit {ailt0 , t0 < t} where xilt is the set of signals that physician l has received up to (and including) time t andhit {ailt0, t0 < t} is the patient's prescription history, hit = {ail11, ., ailt−1(t−1)}, withoutthe physician l's actions, {ailt0, t0 < t}. Because the preference shocks of physician l areher private information, the nal information set of physician l at time t for patient i isgiven by Iilt = Iθ ∪ v ilt where vilt is the set of preference shocks that physician l has received up to (and including) time t.
3.2.5 The expected utility The expected utility of physician l associated with the continuation of the drug therapyfor patient i conditional on her information at time t, Iilt, can be written as: E(uil1t Iilt) = Eθi IEx θi,I(−e−rxilt) + Zil1tα + vil1t i I (−e−rθi+ 1 − (1 − λilt)e−rθ0+12 + Zil1tα + vil1t.
λilt = P r(θ1 Iilt) is the posterior probability that quality is high. The rst equality followsfrom the law of iterated expectations and the second one from the moment generatingfunction of the normal distribution.
The expected utility of the risk averse physician decreases with uncertainty about the eectof the drug therapy on the patient's health, σ2. The risk aversion parameter increases the 36The model could be extended to allow unobserved heterogeneity. In this case, the mean and variance of a signal can dier depending on the type of the patient that is observed by his physicians.
expected utility through quality parameters θ1 and θ0 and decreases it through the riskpremium 1r2σ2. Clearly, the latter eect starts to dominate when either σ2 or the risk aversion parameter r is large enough, namely r > 2θk , k ∈ {0, 1}.
3.2.6 Public and private beliefs In this section, I describe how the physician updates her beliefs about the quality of thedrug treatment. I nd that the posterior belief about quality, λilt, is a function of theprior and the physician's private and public beliefs. The private belief is the probabilityof quality, conditional on physician's accumulated private experience of the patient, xilt.
The public belief is the probability of quality, conditional on the past choices of otherdoctors. I show that the private experience aects the private belief through a sum ofsignals. It turns out that this property decreases the computational burden of the modelsubstantially. Even though the physician does not observe the private information ofother doctors, she tries to infer quality from their past therapy continuation choices.
The posterior belief Let Pi(θ1 xilt) denote the private belief of physician l that quality is high for patienti at time t conditional on her private experience xilt. I denote by qilt = P (θ1 l, hit)the corresponding public belief that is conditional on the previous therapy continuationdecisions of other physicians l0 6= l.
Conditional on health eects xilt and the past choices of other doctors for patient i,physician l updates her beliefs about the quality of the treatment for patient i usingBayes' rule and the iid nature of the health eects, λilt = Pi(θ1 l, hit, xilt) it l, θ1)f (xilt θ1)pi(θ1) P (hit l, θ1)f (xilt θ1)pi(θ1) + P (hit l, θ0)f (xilt θ0)pi(θ0) In the above expression, P (hit l, θ) is the probability of other doctors' treatment continu-ation choices for the patient and f(xilt θ) is the probability of health eects, conditionalon the true quality of the drug, θ ∈ {θ0, θ1}.
The posterior can be linked to the prior, private and public beliefs as follows: qiltf (xilt θ1) + (1 − qilt)f (xilt θ0) iltPi(θ1 xilt)/pi(θ1) qiltPi(θ1 xilt)/pi(θ1) + (1 − qilt)Pi(θ0 xilt)/pi(θ0) where the rst equality follows from (8). To see this, multiply and divide (8) by 1/P (l, hit)and note that qilt = Pi(hit l,θ1)pi(θ1) where P (l, h it) is the probability of the public medication history of the patient without the physician l's actions. The second equality in (9) followsfrom the rst one by dividing and multiplying the rst equality by 1/f(xilt) and byobserving that f(xilt θ) = P(θ xilt) for θ ∈ {θ The posterior belief is determined by the prior, pi(θ1), and private and public beliefs,Pi(θ1 xilt) and qilt. When the public (private) belief is uninformative (equals 1/2), theposterior belief depends only on the private (public) and prior beliefs. When the physicianputs weight only on her prior and private experience, the model corresponds to a tradi-tional structural learning model where agents learn only from their private experience(see e.g. Coscelli and Shum, 2004, Crawford and Shum, 2005, Ackerberg, 2003). Recallalso that the posterior is an increasing function of private and public beliefs. Hence thehigher these beliefs are, the more condent the physician becomes that the quality of themedical treatment is high.
The last step is to derive the evolution of private and public beliefs.
The private belief First, I describe how the physician learns from her private experience. Assume thatthe physician has seen the patient S times in the follow-up of the therapy and has ob-served health xil1, ., xilS. Denote by f(xil1, ., xilS θ) the joint probability of health eectsxil1, ., xilS conditional on θ for θ ∈ {θ0, θ1}. By using the normality and independence ofhealth eects, the physician updates her private belief about θ1 for patient i according toBayes' rule: il1, ., xilS θ1)pi(θ1) i(θ1 xil1, ., xilS ) f (xil1, ., xilS θ1)pi(θ1) + f (xil1, ., xilS θ0)pi(θ0) (−2(θ1−θ0)XilS +S(θ2−θ2)) pi(θ0) The posterior37 depends on signals xil1, ., xilS only through their sum XilS = PS x which is also normally distributed given the true quality, XilS θi ∼ N (Sθi, Sσ2).
The result generalizes to continuous, normally distributed quality, θi ∼ N(θ, σ2).
A physician learns the true quality through her own experience when the number of signalsis large enough. Assume that quality is high.38 In this case, the joint probability for signalsconverges to zero more slowly than the corresponding probability for low quality. To seethis, examine the denominator in (10) that can be rewritten as when xils = θ1 + σeils for eils ∼ N(0, 1). Because the expected value of eils is zero, thedenominator approaches one when the number of signals S increases.
At the patient population level, the weights of the exponential terms increase when thepriors of patients, pi(θ1), ∀i, decrease. This delays private learning about high quality andincreases variation in private posteriors across patients. Note also that for high enoughsignal realizations i.e., XilS > S((θ1)2−(θ0)2 , the private posterior decreases with the uncer- tainty parameter σ2, making physicians less likely to continue the drug therapy.
37Note that this is a valid probability distribution as the posterior of signals given the true state is restricted between zero and one.
38Private learning on low quality is analogous.
The public belief Next, I consider the social learning of the physician from the past choices of other doctors.
After observing the action of physician −l, ai−lt, the physician l (and all other physiciansexcept physician −l) updates her posterior belief about high quality by using the followingBayes formula: i−lt hit, θ1)qilt P (ai−lt hit, θ1)qilt + P (ai−lt hit, θ0)(1 − qilt) The public posterior belief at time t + 1 is determined by the (conditional) choice prob-abilities for high and low qualities and the public belief of physician l at time t. Giventhat the public beliefs correspond to priors at the beginning of the therapy, qil1 = pi(θ1),the nal step is to compute the probability of a physician −l's choice, conditional on thepatient's prescription history and true quality, P r(ai−lt hit, θ) for θ ∈ {θ0, θ1}. This isdone in two steps.
First assume that physician l observes the physician −l's signals, but not her preferenceshocks. Let's dene a threshold for the dierence of private valuations vi−l0t − vi−l1t forwhich physician −l is indierent between the continuation and ending of the drug therapy, Wi−l1t − Wi−l0t = vi−l0t − vi−l1t, where Wi−l1t = E(ui−l1t Ii−lt) − vi−l1t is the expected mean utility of the treatment andWi−l0t = ui−l0t − vi−l0t is the corresponding mean utility from the outside good.
Conditional on her signals, the public belief and control variables, a physician's optimalaction is to continue the drug therapy if and only if the dierence in private valuationsis less or equal to the threshold, vil0t − vil1t ≤ vil0t − vil1t. If physician l observes thatphysician −l continued the therapy, she infers that the realization of the dierence inprivate valuations must have been less or equal to this threshold. The larger the threshold,the larger the probability that the drug therapy is chosen.39 With the assumption on the distribution of vi−l0t−vi−l1t, the conditional choice probabilityP (ai−lt Xi−lt, hit) can be recovered from the thresholds vil0t − vil1t for all Xi−lt. Equiv-alently, when private valuations are Type 1 extreme value distributed, the conditionalprobability that physician −l chooses the drug therapy is 39See Goeree et al., 2005 for theoretical work with one private signal.
P (ai−lt = 1 Xi−lt, hit) = P (E(ui−l1t Iilt) ≥ ui−l0t Xi−lt, hit) eWi−l0t + eWi−l1t As physician l does not observe the physician −l's private experience, the second step isto compute the choice probability, conditional on the patient's prescription history andquality. The conditional choice probabilities for θ0 and θ1 are calculated by using the lawof iterated expectations, P (ai−lt = 1 hit, θ) = dF (Xi−lt θ) for θ ∈ {θ0, θ1}.
eWi−l0t + eWi−l1t where I average out the eect of the sum of signals on the physician's behavior. Withoutthe property that the private belief depends on signals through their sum, the computationof the conditional choice probability would involve S integrals, instead of one. I computethe choice probability numerically by using Simpson's method with 100 uniform gridpoints.
When physician −l decides to continue the drug therapy of patient i, the public belief ofphysician l at time t + 1, qil(t+1), increases from qilt and hence she becomes more opti-mistic about quality. To see this, note rst that the sum of signals Xi−lt is higher underθ1 than θ0. The expected utility associated with the continuation of the drug therapy forphysician −l, E(ui−l1t Ii−lt), is increasing with the posterior belief λi−lt. The higher thesum of signals Xi−lt is, the more condent the physician becomes that quality is high i.e., ∂λi−lt ≥ 0. Therefore, P (a i−lt = 1 Xi−lt, hit) in (14) is at least as high when quality is θ1 than θ0. Because F (Xi−lt θ1) has rst-order stochastic dominance over F (Xi−lt θ0) forθ1 > θ0, P (ai−lt = 1 hit, θ1) ≥ P (ai−lt = 1 hit, θ0). As a result, the public posterior ofphysician l increases from the previous period i.e., qil(t+1) ≥ qilt.
4 The econometric model and identication In this section, I present the simulated likelihood function of the structural learning modeland discuss identication. I use the following data to compute the simulated likelihoodfunction: 1.) the total number of physician visits for patient i, Ti, where the statin therapyof patient i was continued in periods 1, ., Ti − 1 and the outside option was chosen in period Ti if the patient is non-censored, 2.) the number of patient i's "old" physicians attime t, Nit, 3.) an indicator variable if a previously chosen physician l is drawn for patienti again among Nit old physicians, dold, 4.) a vector of control variables aecting utilities received from the statin therapy and the outside good, Zilt, 5.) the censoring indicator,ci, and 6.) the characteristics of patient i at the beginning of the therapy, Zp, that aect the prior probability.
4.1 The likelihood function The likelihood contribution of censored patient i contains the following probabilities foreach period t ∈ {1, ., Ti−1} and physician l ∈ {1, ., Nit+1} who is drawn for the patientat the beginning of period t: 1.) the probability that physician l is matched to patient iand 2.) the probability that physician l chooses the statin therapy for patient i conditionalon the sum of signals and the patient's prescription history, pilt = P r(ailt = 1 Xilt, hit).
Because health eects xilt, preference shocks vilkt, k ∈ {0, 1}, and random coecientsyi are unobserved by the econometrician, their eects to the likelihood contribution ofpatient i must be integrated out.
The likelihood contribution of censored patient i is a previously drawn doctor which consists of the likelihood contributions of the patient's previously drawn and newdoctors. For example, 1−κi is the probability that old physician l is drawn for the patient at the beginning of period t and pil1t is the probability that the treatment of patient i iscontinued at time t by this physician l.
The data does not contain any information on the identity of the physician who decidedto end the therapy. To tackle this problem, I rst form the joint probability that acertain physician is drawn for the patient and the same physician chooses to end the drugtherapy. Then I sum these joint probabilities over the physicians of the patient to recoverthe probability that any physician ends the therapy at time Ti.
Formally, the likelihood contribution for the observed data of non-censored patient i is is the joint probability that an old physician l is drawn and she decides to end the treatment and κipi(N is the corresponding joint probability for new physician NiT + 1.
Because expectations over signals in the likelihood function contributions are dicult tocompute numerically, I use their simulated counterparts Lc,s and Lnc,s. For example, for non-censored patients, where S is the number of simulations. To compute the simulated likelihood functioncontribution for each patient, I draw S realization of random coecients ys governing physicians switching probabilities and Ti × S realizations of signals and preference shocksto get choice probabilities for each period and patient.40Finally, the simulated log-likelihood function is [cilogLc,s(θ) + (1 − c In general, simulation error increases the variance of the he maximum simulated likeli-hood (MSL) ˆθMSL estimator compared to the maximum likelihood (ML) estimator. Thissimulation error disappears asymptotically when the number of simulations increases at a rate higher than N. As the estimation of the model is computationally intensive, Iset the number of simulations per patients to ten.41 Obviously, simulation error may bean issue when the number of simulations is small and therefore estimation results mustbe interpreted with this caveat. To get appropriate standard errors, I use the standardformula for the simulated estimate of the asymptotic variance which relies on the BHHHestimate for the information matrix. I estimate the model by using the derivative freesimplex method (see e.g. Cameron and Trivedi, 2005).
40Note that only one physician makes a treatment choice each period and therefore in total Ti × S simulations of signals and preference shocks are needed for each patient.
41For example, Crawford and Shum, 2006, had 30 simulations per patient. I plan to experiment with the number of simulations to see how the results would change.
4.2 Identication In this section, I briey consider the structural assumptions of the demand model and thevariation in the data that help identify the parameter vector Θ = (θ0, θ1, σ2, γ0, γ , α, θ To a large extent, identication relies on similar arguments that have been presented inthe previous literature on demand for experience goods (see e.g. Crawford and Shum,2005).
Market shares at the beginning of the therapy identify the parameters of the prior dis-tribution, γ0 and γ , because the treatment choice of the physician is then governed by her prior belief. Because the private learning of the physician decreases uncertainty as-sociated with the quality of the medical treatment, choice probabilities at the end of thelong-term drug therapy identify parameters for unobserved quality, θ0 and θ1. This isparticularly true if the patient is in a long-term treatment relationship with his physician.
The identication of quality parameters can be also seen from the expected utility ofthe drug treatment (equation (7)). After xing the parameters of the prior distribution,γ0 and γ , and the variance of signals, σ2, changes in the posterior belief λ number of prescriptions identify the quality parameters. Heterogeneity in the choices ofphysicians both across patients and over time identify the standard deviation of signals.
Because quality has two possible values θ0 and θ1, it is not possible to separately identifythe quality parameters and the risk aversion coecient, r. I normalize the risk aversionparameter to one which is close to the parameter estimate of Crawford and Shum (2005).42 In this section, I present results from the estimation of the structural learning model anddescribe the t of the model. Because the risk of cardiovascular diseases increases withage and is higher for men than for pre-menopausal women, I allow the prior probability todepend the log of age at t = 1 and gender. The prior depends also on an indicator variablefor whether the patient was treated by an internal disease specialist at the time of therst physician visit. It is likely that the patient, who used the services of the specialist,is more severely ill and gains more from cholesterol drugs.
I allow the utilities associated with the statin treatment and the outside good to dependon several observed variables. First, I let the utility from therapy continuation to depend 42An alternative is to interpret parameters θ and σ2 relative to risk aversion coecient r, e.g. ˆθ1 = rθ1, where ˆθ1 is the estimated parameter.
on for the average price of statins at time t. I also control for a time trend in monthssince January 2003 because market level changes, such as advertising, might as well aectthe utility from statins. Because the patient's health might deteriorate when he becomesolder, I let the utility without cholesterol drugs to depend on age at time t. As cholesteroldrugs prevent coronary events in the long-run after the patient's drug therapy has ended,I allow the outside good utility to vary with the number of prescriptions.43 Discussion of the results and the t of the model Table 5 presents the parameter estimates and their standard errors. The rst set containsthe key parameters of the model: quality levels θ0 and θ1 and the standard deviation ofhealth eects, σ (see 6). Figure 3 presents the conditional and unconditional distributionsof signals, f(xilt θ0), f(xilt θ1) and f(xilt), for the estimated parameters and the averageof priors pi(θ1).
43Alternatively, the controls of the outside good could be included in a vector of inside good controls.
Table 5: Parameter estimates for the learning model in the sample of patients Estimate Std.Err.
Signal (xilt) parametersLow quality (θ0) High quality (θ1) Prior parametersConstant (γ0) log(Age in years at t=1) Visit an internal diseasespecialist at t=1 (1: yes, 0: no) Prior mean and std Physician matching probabilityRandom coecientConstant (θy) Physician switching probability,mean and average std Control variablesPatient's deductible, eur Time trend in months/10 Outside good controlsPatient's age/10 years Number of prescriptions/10 Number of observations Number of patients Number of simulations1 Simulated log-likelihood function 1 The number of simulations per patient and physician High match valueUnconditional Probability density Figure 3: The conditional and mixture probability densities of signals, f(xilt θ0), f(xilt θ1)and f(xilt), for estimated parameters and the average prior in the sample of patients The results demonstrate substantial uncertainty and heterogeneity among patients inthe quality and health eects of the statin treatment. The parameter estimate for highquality θ1 (1.34) is in absolute terms over 6 times higher than the estimate of low quality,θ0 (−0.22). The variance estimate of signals, σ2, implies that physicians face signicantuncertainty about the health eects of statins even if quality was known. To be moreprecise, the variance of signals is 5 times higher than the low quality estimate ˆθ0 and 82%of the value of the high quality estimate ˆθ1.
Heterogeneity in health eects implies that information and learning may signicantlyimprove medical decision-making by a physician. Without uncertainty about quality, theincentives of the physician to continue the patient's therapy may be much higher whenquality is high rather than low. A high uncertainty in health eects decreases the expectedutility of a risk-averse physician, slows down her learning44 and diminishes her incentivesto continue the patient's statin therapy.
The second set of parameters in Table 5 includes estimates for the physician's prior beliefthat the quality of the statin treatment is high, pi(θ1). As expected, the physician has 44This can be seen from the denominator of equation (15) in which iid physician l's shocks eils, s ∈ {1, ., S}, for patient i get more weight when standard deviation σ increases.
a higher prior probability if her patient is older and male and thus has a higher risk ofCVDs compared with other patients. Quite intuitively, the prior belief is higher if thepatient has visited an internal disease specialist at the time of the rst prescription.
Depending on the characteristics of patients, the prior probability varies across patientsfrom 65% to 75% and has a mean of 72% with a small standard deviation. At thebeginning of the therapy, the physician beliefs that quality is more likely to be high thanlow. Because the average prior belief is fairly uninformative, the posterior belief of thephysician λilt is mostly determined by her private and public beliefs. This, coupled witha relatively large variance of signals, σ2, implies that the learning of the physician fromher private experience may take some time.
Third, I report the parameters of the random coecient yi that aects the probabilitythat the patient is assigned for a new physician, κi. The set of parameters for the randomcoecient includes the constant, θy, and the standard deviation, σy. The results suggestthat the estimated standard deviation ˆσy (1.06) is much higher than the estimated mean θy (−0.05). These ndings imply that the probability of getting a new physician variessubstantially (0-99%) around its mean (49%). The (average) standard deviation of κi is0.19 that is 32% of the estimated mean of κi. Heterogeneity in assignment probabilitiesacross patients can arise for several reasons, including dierences between municipalitiesin their ability to recruit permanent physician labour.
The nal set of variables includes control variables aecting utilities associated with thestatin therapy and the outside option. The price of statins has a very small, negativeeect on the expected utility from the statin treatment. A physician can be insensitiveto changes in average prices because a signicant part of expenses is covered by thenational health insurance. Over time, the expected utility of the physician from the statintreatment decreases. This may reect changes in advertising by pharmaceutical rms overa product's life cycle and other market level changes. Physicians whose patients are older,and hence have a higher risk of having more severe diseases, are less likely to end the statintherapy as their patients gain less from the outside alternative. The utility associated theoutside good increases with the number of prescriptions. This may happen because thestatin therapy is likely to have long-term eects on the patient's health even after thestatin therapy has ended.
Finally, I consider the model t by comparing average predicted and observed choice prob-abilities. For each physician-patient pair, I compute the predicted probability of choosingthe statin treatment, conditional on the sum of signals and the patient's prescription his-tory, P (ailt = 1 Xilt, hit). I then compare the corresponding observed choice probabilities to these predicted probabilities, as presented in Figure 4. The model ts the data rela-tively well even though it slightly over-predicts the observed average choice probabilityat the beginning of the treatment and under-predicts after that. At the aggregate level,the model ts the data reasonably well: the average observed probability of choosingthe statin therapy is 79% which is close to the predicted probability, 81%. The averagepredicted probability of getting a new physician is lower (49%) than the correspondingobserved probability (60%).
Prescription number Figure 4: Dierence between observed and predicted choice probabilities by the numberof prescriptions in the sample, an average over patients, physician visits and simulations 6 Counterfactual experiments After estimating the parameters, I quantify the roles of private and observational learningin medical decision-making. The main objective is to evaluate to the length of the doctor-patient relationship aects the process of learning and the eciency of medical decision-making. To be more specic, I evaluate whether the policy promoting continuity of careis preferable to providing information on the past choices of other doctors.
I rst investigate what happens if the patient had only one physician. In this case, thephysician learns only from her private experience. Next, I investigate whether information on the past choices of other doctors compensates for the lack of continuity of care. Todo this, I compare treatment outcomes and costs in the long-term treatment relationshipwith the policy where the patient has a dierent physician every period. A physician hasthen a one-shot opportunity to investigate the patient to get information on the healtheects of cholesterol drugs but she observes the patient's treatment history. To understandthe role of peer eects in demand, I study how the behavior of the physician changes ifinformation on the past choices of other doctors was not available. In this experiment,the physician has to rely only on her private experience and the prior belief. Finally, Ievaluate the consequences of the policy where the physician does not learn. In this case,the physician decides about the continuation of the patient's therapy without investigatinghim. I compare the results with the baseline scenario predicted by the estimated model.
To perform the policy experiments, I simulate 10 prescription paths for each patient inthe observed sample of 10 000 patients used in the estimation of the model.45 I begin by describing the development of posterior beliefs over time and dispersion amongpatients under dierent policy experiments. I then investigate how treatment adherence,expected utilities and costs change when the length of the treatment relationship andthe amount of available information were changed. I measure adherence by the predictedlength of the drug therapy and the probability of choosing the statin therapy conditionalon the information of the physician, P (ailt = 1 Iθ ) (see Dickstein, 2011, for the similar The speed of learning Figure 5 describes the development of the average posterior belief over patients, physiciansand simulations, conditional on high quality. At the beginning of the therapy, a physicianis fairly pessimistic about the eect of the drug treatment on patient health since theaverage prior for low quality is 28%. Most of the uncertainty regarding to quality vanishesafter the rst physician visit. At this stage of the therapy, the physician has observedhow well the rst prescription decreased the patient's cholesterol levels and whether anyside eects realized. In the long-term treatment relationship, the physician learns qualityfast, by the eighth physician visit. In short-term relationships, physicians become more 45When the number of predicted prescriptions is less than the observed one, I use the observed char- acteristics of patients. Otherwise, I assume that patients come to seek treatment for high cholesterolonce a year. The time trend increases by 12 months, the patient's age by a one year and the numberof prescriptions by one in period t + 1 from the previous period t. An exception is the average price ofstatins at time t which I replace with the average over time, products and patients.
optimistic on quality during the course of the patient's therapy, but learning is slower thanin the long-term relationship. The bottom half of Figure 5 presents the standard deviationof posterior beliefs. At the rst prescription, variation in posteriors arises because priorbeliefs are heterogeneous across patients. Reecting high variation in health eects, thestandard deviation increases to 0.2 at the second prescription. As expected, learningdiminishes the variances of the posteriors gradually.
BaselineOne physician Physician switch every periodNo public info, baselinePhysician switch every period, no public info Prescription number BaselineOne physician Physician switch every periodNo public info, baselinePhysician switch every period, no public info Posterior, standard deviation Prescription number Figure 5: The mean (higher gure) and variance (lower gure) of the posterior beliefλilt = P r(θ1 Iilt) given that true quality is high (θi = θ1) in the sample of patients The top of Figure 6 illustrates the development of the average posterior when the patient-specic quality is low. In this case, large dierences in average posteriors between dierent scenarios arise. In the long-term treatment relationship, the physician learns again fast. Ifphysicians change frequently, the average posterior starts to increase after a few prescrip-tions. Again, the physician becomes more optimistic about quality when other doctorshave chosen the drug treatment for the patient previously. The bottom part of Figure6 shows that heterogeneity in posteriors at the aggregate level is higher among patientswhen quality is low rather than high. The standard deviation of posteriors are fairlysimilar in the counterfactual experiments. In particular, a high variation in the posteriorsremains also in the permanent treatment relationship, even though the posterior belief isdecreasing over time.46 46Note that the exponential term in equation (10) is eS(θ0−θ1)2−2(θ1−θ0)σ PS e if θi = θ0. When 2(θ1 − θ0)σ PS ils is high relative to constant term S(θ0 − θ1)2, there can be much variation in the posterior beliefs of physicians among patients.
One physicianPhysician switch every period No public info, baselinePhysician switch every period, no public info Prescription number BaselineOne physician Physician switch every periodNo public info, baselinePhysician switch every period, no public info Posterior, standard deviation 0.2 Prescription number Figure 6: The mean (higher gure) and variance (lower gure) of the posterior beliefλilt = P r(θ1 Iilt) given that true quality is low (θi = θ0) in the sample of patients Overall, the results suggest that the long-term doctor-patient relationship promotes theprocess of learning about quality. The physician becomes optimistic about quality when she observes the past choices of other doctors. When quality is high, information on theprescription history improves learning, but not as eciently as the long-term relationship.
When quality is low, such information slows down learning. These results have implica-tions on prescriptions, costs and eciency.
The length of the doctor-patient relationship I rst examine how the long-term doctor-patient relationship aects outcomes and costs.
Table 6 presents averages for the expected utility, the adherence of the treatment andthe total costs, conditional on quality. The results suggest that continuity of care pro-motes learning and improves medical decision-making by a physician. Consider rst thepatient with high quality of the match with cholesterol drugs. In this case, the long-termphysician-patient relationship leads to the highest expected utility and the treatment ad-herence among evaluated experiments. Still, the treatment adherence and the total costsincrease only slightly from the estimated benchmark. When quality is low, I nd thatcontinuity of care decreases treatment length by 5% and the total costs of the drug ther-apy by 5% compared with the estimated benchmark. This is so, since the physician learnsfast that the treatment does not suit well for the patient.
Table 6: Counterfactual simulations in the sample of patients No public info4 No public info, physician3 change every High quality θ1:Expected utility Expected utility,≥ 5 prescriptions Probability ofstatin therapy Total cost/100 eur Low quality θ0:Expected utility Expected utility,≥ 5 prescriptions Probability ofof statin therapy Total cost/100 eur 1 These values are calculated by using the observed sample of 10 000 patients and 10 simulated prescription sequences per patient.
2 The baseline scenario is predicted by the model estimates.
3 In this experiment, the physician-patient relationship is permanent.
4 Public information on the previous treatment continuation choices of other physicians is not available.
5 The physician does not learn and hence the posterior belief equals to the prior belief, i.e. λilt = pi(θ1).
I next investigate the consequences of the policy where a new physician treats the patientin every period (Table 6). When the physician does not have much own experience of thepatient, she relies more on the past choices of other doctors. Consider rst the patientwith high quality of the match with statins. In this case, continuity of care does notmuch improve drug choices or change treatment outcomes compared to the policy wheretreatment relationships are short-term but the prescription history is observed.
Consider then the patient with the low quality of the match in Table 6. In this case, thelength of the treatment relationship has more pronounced eect on treatment outcomesand costs. This happens because social learning increases the optimism of the physicianabout the quality and can lead to over-prescribing. The results show that the policy withthe short-term relationship increases the adherence by 3% and the total costs by 8% fromthe experiment with continuity of care. Table 6 demonstrates that the physician would be slightly better-o, in terms of eciency, without information on the prescription historywhen physicians change frequently. Specically, when treatment relationships are short-term, providing information on the past choices of other doctors increases the adherenceby 1% and the total costs by 2% from the policy without such information. Again interms of eciency, even worse outcomes arise if learning is not possible.
The results have several policy implications. Continuity of care helps the physician to ndout sooner the health eects of the drug treatment. This reduces the costs of uncertaintyand improves her medical decision-making, as suggested by the existing reduced-form lit-erature (Weiss and Blustein, 1996, Scott, 2000, King et al., 2008). The second conclusionis that information on the patient's prescription history does not compensate for the lackof the long-term treatment relationship. When the treatment suits well for the patient,prescription records promote learning, but not as eciently as continuity of care. If aphysician does not have much own experience, treatment patterns based on the observedmedication history of the patient may hinder learning and lead to over-prescribing for afraction of patients.
I quantied the roles of private experience and the past choices of other doctors in pharma-ceutical demand. I constructed a structural model of demand for pharmaceuticals underuncertainty about the quality of the match between the patient and the drug treatment.
I analyzed whether continuity of care is preferable to providing information on the pastbehavior of other doctors through patient records.
Using rich data from the market for cholesterol drugs, I found that prescriptions are highlyresponsive to the length of the doctor-patient relationship. I illustrated that the numberof interactions between the physician and the patient have important implications on theeciency of drug choices. My analysis suggested that treatment patterns relying heavilyon the past choices of other doctors may lead to over-prescribing for a fraction of patients.
I also showed that the long-term treatment relationship can limit over-prescribing andimprove medical decision-making.
The structural model can be extended to allow the other important features of the phar-maceutical market. The rst extension is to make physicians forward-looking in theirdecision-making, creating incentives for experimentation to get more information. Sec-ond, the model can be broadened to incorporate several inside goods. The framework can be also applied in other experience good markets, such as nancial markets, wheretraders are investing in assets with uncertain returns.
A typical example of a patient story for one dispensary visit: The reason of entryA patient comes with the referral of physician X due to atrial brillation At issue a 65 years old retired gymnastics teacher. In an anamnesis 2003 acute coronarythrombosis, angioplasty RCA. Discovered then also a decreasing diverticulum of an aortaad 50mm, controls in fall. In the Doppler-ultrasound-research of neck veins in 2005 wasdiscovered in left arteria carotis interna stenosis less 50%. Discovered year 2007 COPD.
The patient smoked over 30 years, quit 6 years ago. In a tolerance test 8/07, no coronaryischaemia.
The patient has visited in the health center of X due to dizziness. Discovered elevatedblood pressure, irregular beat. Hear enzymes and other laboratory values normal, pro-BNP over 500. Patient's medication at this moment Pravachol 20mg x 1, Linatil 20mgx 1, Carvedilol 12.5mg x 2. Started Marevan due to atrial brillation, aiming to docardioversion.
Today taken INR, only 1.3. Hence cardioversion cannot be done now. Pulse also fairly fast80-90/min, RR-level 180-170/110-100. Carvedilol ad raised 25mg + 12.5mg. INR-controlswill continue in the side of outpatient treatment. Phone contact after a month.
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