The Long-Term Impact of Price Controls in Medicare Part D

A1 General Structure of the Model

This Appendix describes The Health Economics Medical Innovation Simulation (THEMIS); a microsimulation model used to simulate the effect of pharmaceutical regulation on health for the population age 55 and over in the United States (US). THEMIS models and tracks the evolution of future health and innovation under different policy regimes, based on methods developed for its predecessor, the RAND future elderly model (FEM) (Goldman et al. 2004, 2005; Lakdawalla et al. 2005; Shekelle et al. 2005). THEMIS consists of a population health module and an innovation module; the latter entitled the global pharmaceutical policy model (GPPM). Each module is a set of dynamic interactions that link present health and innovation to their future values. For example, next year’s health states depend on today’s health states, and on a set of random health shocks that vary with individuals’ own risk-factors – e.g. demographics, health behaviors, and current disease conditions. The innovation module links this year’s stock of drugs to next year’s, by allowing sales and profits from pharmaceutical sales to affect future innovation. Figure A1 outlines the mechanics of the model.

Figure A1:

Mechanics of the GPPM.

In a given year, say 2024, sample individuals may have diseases and/or disabilities that put them at risk of contracting new diseases and disabilities, or even dying, in 2025. Moreover, new drugs are introduced in 2024 that reduce some of these risks. We estimate a health transition model to simulate how population health will look in 2025, given the number of new drug introductions and existing health conditions. Finally, mortality will have shrunk the population in 2025, but the sample is “refreshed” by introducing those who were 54 in 2024, and who now “age into” our target population. This forms the set of sample individuals for 2025. The same process is then repeated to obtain the population in 2026, 2027, and all subsequent years, until the final year of the simulation is reached.

Theoretically, the current rate of innovation depends on future sales, which measure the profitability of current research effort. We assume it takes 10 years – from pre-clinical trials to launch – for a pharmaceutical company to introduce a new drug. This is based on the mean duration observed in the data.^[3] Moreover, we assume that drug companies have rational expectations, in the sense that today’s sales are used as a forecast for sales 10 years in the future. Therefore, the number of new drugs today depends on sales (or market size) 10 years ago. The empirical economics literature provides us with an estimate of how innovation changes in response to changes in market size. For example, this elasticity is applied to the change in market size between 2014 and 2015 to estimate the change in the number of new drugs between 2024 and 2025.

Regulation affects market size. Results from Sood et al. (2008) suggest that price controls leads to a 22.5% reduction in market size. Hence, this is the lever we use to simulate the effect of price controls as well as the effect of introducing co-pay subsidy.

To measure cost and benefits across scenarios, we use life-years and medical expenditures. We translate life-years in dollar terms using a value of a statistical life estimate. For expenditures, we use cost regressions estimated using micro data.

The simulations are stochastic: the arrival of new drugs is random, as is the arrival of new diseases. We discuss how these arrival processes are implemented in the model. Furthermore, we also discuss how weights are used to construct nationally representative estimates.

This document presents details on each of these components. First, we explain how the transition model was estimated using the Health and Retirement Study (HRS) data. Second, we explain how we estimated the clinical effects of new drugs. We then discuss the process of innovation and how it relates to market size. Next we discuss how costs and benefits of alternative policy scenarios were calculated. Finally, we discuss how the stochastic components of the model are implemented and how we used sample weights throughout.

A2 The Health Transition Model

We use the HRS, a nationally representative longitudinal study of the U.S. population age 50+ as our main data source. We use the observed (reported) medical history of respondents to infer incidence rates as a function of prevailing health conditions, age and other socio-demographic characteristics (sex, race, risk factors, such as obesity and smoking). The data from the HRS consists of longitudinal histories of disease incidence, recorded roughly every 2 years, from 1992 to 2002, along with information on baseline disease prevalence in 1992. Since incidence can only be recorded every 2 years, we use a discrete time hazard model.

The estimation of such a model is complicated by three factors. First, the report of conditions is observed at irregular intervals (on average 24 months but varying from 18 to 30), and interview delay appears related to health conditions. Second, the presence of persistent unobserved heterogeneity (frailty) could contaminate the estimation of dynamic pathways or “feedback effects” across diseases. Finally, because the HRS samples from a population of respondents aged 51+, inference is complicated by the fact that spells are left-censored: some respondents are older than 50 at baseline and suffer from health conditions whose age of onset cannot be established.

Since we have a stock sample from the age 55+ population (the HRS starts at age 51, but our model starts at age 55), each respondent goes through an individual-specific series of intervals between interviews. Hence, we have an unbalanced panel over the age range starting from 55 years old. Denote by j_i0 the first age at which respondent i is observed and jiTi the last age of observation. Hence we observe incidence at ages ji=ji0, …, jiTi. Record as hi,ji,m=1 if the individual has condition m as of age j_i. We assume the individual-specific component of the hazard can be decomposed into time-invariant and time-varying pieces. The time-invariant piece is composed of the effect of observed characteristics x_i and permanent unobserved characteristics specific to disease m, η_i,m . The time-varying part is the effect of previously diagnosed health conditions hi,ji−1,−m, (other than the condition m) on the hazard.^[4] We assume an index of the form zm,ji=xiβm+hi,ji−1,−mγm+ηi,m. Hence, the latent component of the hazard is modeled as

We approximate am,ji with an age spline. After several specification checks, a node at age 75 appears to provide the best fit. This simplification is made for computational reasons since the joint estimation with unrestricted age fixed effects for each condition would imply a large number of parameters.

Diagnosis, conditional on being alive, is defined as

We consider functional limitation [measured as activities of daily living (ADL) limitation disability], mortality, and the following seven diseases: heart disease, hypertension, diabetes, cancer, lung disease, stroke, and mental illness. Each of these conditions is an absorbing state. The occurrence of mortality censors observation of diagnosis for other diseases in a current year. Mortality is recorded from exit interviews and closely reflects the life-table probabilities of survival.

A3 Calculating the Health Effects of New Drugs

Prior to the introduction of a new drug, it is useful to think of the population as divided into three subgroups: Those undiagnosed for a particular health condition, those diagnosed with a condition and treated with an existing drug, and those who are diagnosed but untreated. The new drug does not benefit the undiagnosed, but can benefit either or both of the diagnosed groups.

Figure A2 illustrates how each sub-population benefits from a new drug. The treated group may benefit because new drugs are potentially more effective than existing treatments. We will call this the “clinical effect.” A fraction of the previously untreated group may, however, gain access to this treatment. This group will thus experience the full health effect of a new drug (relative to no treatment). We will refer to this as the “access effect”. Finally, the remaining untreated individuals do not gain from the introduction of the drug.^[6]

Figure A2:

Effect of a New Drug.

In such a population, the average effect of a new drug will be a weighted average of the clinical and access effect. To see this, denote by (α₀, α₁) the fraction of diagnosed individuals who are untreated before and after the introduction of the new drug, respectively, and define ∆α∞=α₀–α₁. Denote P as the probability of being diagnosed with a new condition or death, and RR_EXISTING=P_NEW/P_EXISTING, RR_PLACEBO=P_NEW/P_PLACEBOto be the relative risk (RR) for those replacing existing therapy with the new drug, and those replacing no therapy with the new drug, respectively. Note that the latter corresponds to the risk given by the new drug, divided by the risk given by placebo treatment. As such, the annual RR for the diagnosed population following the introduction of a new drug (relative to the pre-existing situation) is given by

where P_U is the baseline health risk among the untreated, P_T is the baseline health risk among the treated, and P̅=α₀P_U+(1–α₀)P_T is the average baseline risk in the entire diagnosed population.

The first term in square brackets represents the total reduction in risk for the untreated, while the second term represents the total reduction in risk for the treated. Each is weighted by the proportion of the diagnosed population that is untreated and treated, respectively.

For example, suppose a new drug is introduced which potentially reduces mortality for patients diagnosed with cancer. Compared with existing treatment, this drug is 25% more effective. Compared with no treatment, however, it leads to a 50% decrease in mortality risk. Now, suppose 50% of patients diagnosed with cancer take the existing treatment and that both treated and untreated patient face a survival probability of 75%. Finally, assume the introduction of the new drug means that 25% more patients are treated. This leads to a 25% reduction in untreated patients. Hence, 25% of the diagnosed population derives no benefit, 25% enjoy a 50% decrease in mortality risk because they move from no treatment to the new therapy, and the remaining 50% of the population enjoy the 25% improvement over existing treatment. The average RR is then 0.25+0.25*0.5 + 0.5*0.75=0.75 for the diagnosed population.^[7] Note that ignoring the access effect amounts to imposing ∆_α=0. In this case, only the treated will benefit from the new drug. For many diseases, this access effect can be important, particularly when access is relatively low and existing treatments are not easily accessible. The same calculations can be performed for other risks such as the risk of being diagnosed for another health condition.

Below, we provide methodologies for estimating each of the components of Equation 5. The list of new-top selling drugs section is devoted to the construction of a list of drugs for each of the conditions we consider. In subsequent sections, we discuss how the RRS are taken from clinical trials for these drugs, how the access effect (∆_α) are estimated from claims data, and how we calculate the remaining parameters (α₀, P_U, P_T) from the HRS data.

A3.1 Estimation

For each of the health condition in the transition model, one could in principle consider the whole universe of new drugs and calculate an average effect for each of them. This is likely to be a difficult task. However, top-selling drugs are the most likely to have large effects, and have been in general the most studied and reviewed. This makes the estimated clinical benefits more reliable. For each of our diseases, therefore, we survey the clinical effects for the five “top-selling” drugs in that disease group, and assume conservatively that all other drugs outside the top five have no therapeutic benefits. Therefore, we estimate the effects of drugs in two parts: (i) calculate the probability that a new drug will be a “top-seller,” and (ii) apply the expected therapeutic benefit of a top-selling drug.

A3.1.1 List of New Top-Selling Drugs

We construct a list of new drugs from INGENIX, a large, nationwide, longitudinal claims-based database (1997–2004).^[8] This data set has drug expenditure information from insurance plan enrollees. We use expenditures as a proxy to identify top-selling drugs. Health conditions in INGENIX are provided at the patient level, which makes it difficult to match drugs to health conditions because patients can take medication for multiple diseases at the same time. For example, it is unclear whether a drug used by a heart disease patient with hypertension is used to treat the heart condition or hypertension. Mapping drugs to Redbook drug class and then to health conditions appears to be a superior strategy (Truven Health Analytics Micromedex Solutions 2016). Hence, we first group drugs by class and then assign each class to at least one particular health condition, based on expert opinion and an extensive web search.^[9] The result of this class-health condition match is presented in Appendix A1.

Appendix A1:

Mapping from Drug Class to Health Condition.

Heart disease	Hypertension	Stroke	Lung disease	Diabetes	Cancer	Depression
Antibiot, Penicillins	Cardiac, ACE Inhibitors	Thrombolytic Agents, NEC	Antibiot, Penicillins	Antidiabetic Ag, Sulfonylureas	Antibiot, Antifungals	Psychother, Antidepressants
Antihyperlipidemic Drugs, NEC	Cardiac, Beta Blockers	Antiplatelet Agents, NEC	Vaccines, NEC	Antidiabetic Agents, Insulins	Antiemetics, NEC	Antimanic Agents, NEC
Cardiac Drugs, NEC	Vasodilating Agents, NEC	Coag/Anticoag, Anticoagulants	Antibiot, Cephalosporin and Rel.	Antidiabetic Agents, Misc	Antineoplastic Agents, NEC
Cardiac, ACE Inhibitors	Cardiac, Alpha-Beta Blockers		Antibiot, Tetracyclines		Folic Acid and Derivatives, NEC
Cardiac, Antiarrhythmic Agents	Hypotensive Agents, NEC		Antibiotics, Misc		Gonadotrop Rel Horm Antagonist
Cardiac, Beta Blockers	Cardiac, Calcium Channel		Antituberculosis Agents, NEC		Immunosuppressants, NEC
Cardiac, Cardiac Clycosides	Symnpatholytic Agents, NEC		Sulfonamides and Comb, NEC		Interferons, NEC
Cardiac, Cardiac Glycosides	Sympatholytic Agents, NEC		Sulfones, NEC		Blood Derivatives, NEC
Hemorrheologic Agents, NEC	Diuretics, Loop Diuretics		Tuberculosis, NEC		Antibiot, Aminoglycosides
Vasodilating Agents, NEC	Diuretics, Potassium-Sparing		Antibiot, B-Lactam Antibiotics
Blood Derivatives, NEC	Diuretics, Thiazides and Related		Antibiot, Erythromycn&Macrolid
Cardiac, Calcium Channel	Cardiac Drugs, NEC		Anticholinergic, NEC
Diuretics, Loop Diuretics			Autonomic, Nicotine Preps
Diuretics, Potassium-Sparing
Diuretics, Thiazides & Related
Thrombolytic Agents, NEC
Antiplatelet Agents, NEC
Coag/Anticoag, Anticoagulants

Source: Web search and expert opinion. Printouts of the sources are available upon requests.

We rank drugs for each health condition according to real revenues in the 2nd full year following introduction. (For instance if the drug launches in 1996, we consider revenues in 1998).^[10] We consider new chemical entities (NCEs) as well as reformulation and recombination drugs, but exclude generics. We define the top five drugs for each health condition as “top-selling drugs”. The name of the drug, Redbook drug class, generic name, and the introduction date are presented in Appendix A2.

Appendix A2:

Top 5 Drugs by Health Condition.

Drug name	Class	Active ingredient	Innovation type	Introduction date
Heart disease
LIPITOR	Antihyperlipidemic Drugs, NEC	Atorvastatin Calcium	New Ingredient	1996.12
ZETIA	Antihyperlipidemic Drugs, NEC	Ezetimibe	New Ingredient	2002.10
PLAVIX	Antiplatelet Agents, NEC	Clopidogrel Bisulfate	New Ingredient	1997.11
CARTIA XT	Calcium Channel Blocker	Diltiazem Hydrochloride	New Formulation	1998.7
WELCHOL	Anti-hyperlipidemic, NEC	Colesevelam Hydrochloride	New Ingredient	2000.5
Hypertension
CARTIA XT	Cardiac, Calcium Channel	Diltiazem Hydrochloride	New Formulation	1998.7
TRACLEER	Vasodilating Agents, NEC	Bosentan	New Ingredient	2001.11
BENICAR	Cardiac Drugs, NEC	Olmesartan Medoxomil	New Ingredient	2002.4
AVAPRO	Cardiac Drugs, NEC	Irbesartan	New Ingredient	1997.9
DIOVAN	Cardiac Drugs, NEC	Valsartan	New Ingredient	1996.12
Stroke
PLAVIX	Antiplatelet Agents, NEC	Clopidogrel Hydrochloride	New Ingredient	1997.11
AGGRENOX	Antiplatelet Agents, NEC	Dipyridamole + Aspirin	New Combination	1999.11
AGRYLIN	Antiplatelet Agents, NEC	Anagrelide Hydrochloride	New Ingredient	1997.3
ARIXTRA	Coag/Anticoag, Anticoagulants	Fondaparinux Sodium	New Ingredient	2001.12
INNOHEP	Coag/Anticoag, Anticoagulants	Tinzaparin Sodium	New Ingredient	2000.7
Lung disease
ADVAIR DISKUS	Adrenals & Comb, NEC	Fluticasone Propionate+ Salmeterol Salmeterol Xinafoate	New Combination	2000.8
FLOVENT	Adrenals & Comb, NEC	Fluticasone Propionate	New Formulation	1996.3
BIAXIN XL	Antibiot, Erythromycn&Macrolid	Clarithromycin	New Formulation	2000.3
AUGMENTIN XR	Antibiot, Penicillins	Amoxicillin + Clavulanate	New Formulation	2002.9
ZYVOX	Antibiotics, Misc	Linezolid	New Ingredient	2000.4
Diabetes
ACTOS	Antidiabetic Agents, Misc	Pioglitazone Hydrochloride	New Ingredient	1999.7
AVANDIA	Antidiabetic Agents, Misc	Rosiglitazone Maleate	New Ingredient	1999.5
REZULIN	Antidiabetic Agents, Misc	Withdrawn	New Ingredient	1997.1
GLUCOPHAGE XR	Antidiabetic Agents, Misc	Metformin Hydrochloride	New Formulation	2000.10
GLUCOVANCE	Antidiabetic Ag, Sulfonylureas	Glyburide + Metformin Hydrochloride	New Combination	2000.7
Cancer
GLEEVEC	Antineoplastic Agents, NEC	Imatinib Mesylate	New Ingredient	2001.5
CASODEX	Antineoplastic Agents, NEC	Bicalutamide	New Ingredient	1995.10
TEMODAR	Antineoplastic Agents, NEC	Temozolomide	New Ingredient	1999.8
XELODA	Antineoplastic Agents, NEC	Capecitabine	New Ingredient	1998.4
AROMASIN	Antineoplastic Agents, NEC	Exemestane	New Ingredient	1999.10
Depression
LEXAPRO	Psychother, Antidepressants	Escitalopram Oxalate	New Indication	2002.8
PAXIL CR	Psychother, Antidepressants	Paroxetine Hydrochloride	New Formulation	1999.2
CELEXA	Psychother, Antidepressants	Citalopram Hydrovromide	New Ingredient	1998.7
EFFEXOR XR	Psychother, Antidepressants	Venlafaxine Hydrochloride	New Formulation	1997.1
WELLBUTRIN SR	Psychother, Antidepressants	Buproprion Hydrochloride	New Formulation	1996.10

The choice of the second full year after introduction is somewhat arbitrary. Ultimately, we are interested in the lifetime revenues of the drug, but this is unobserved. Our analysis suggests that the choice of year does not substantially affect the results. Table A6 displays the pairwise correlations between sales ranks calculated using the first full year after launch, second full year after launch, third full year after launch, and fourth full year after launch. It demonstrates that the correlations between these various rank statistics is extremely high – typically well above 0.90, and in many cases above 0.95.

Table A6:

Pairwise Correlations between Sales Ranks Calculated from Different Years in the Life-cycle of Drugs.

	Years after launch year
	First	Second	Third	Fourth
Heart disease
First year	1.00
Second year	0.98	1.00
Third year	0.94	0.97	1.00
Fourth year	0.93	0.96	0.99	1.00
Hypertension
First year	1.00
Second year	0.97	1.00
Third year	0.93	0.97	1.00
Fourth year	0.90	0.94	0.98	1.00
Stroke
First year	1.00
Second year	0.70	1.00
Third year	1.00	0.99	1.00
Fourth year	1.00	0.98	0.99	1.00
Lung disease
First year	1.00
Second year	0.96	1.00
Third year	0.89	0.94	1.00
Fourth year	0.87	0.91	0.94	1.00
Diabetes
First year	1.00
Second year	0.97	1.00
Third year	0.90	0.96	1.00
Fourth year	0.86	0.93	0.98	1.00
Cancer
First year	1.00
Second year	0.96	1.00
Third year	0.93	0.95	1.00
Fourth year	0.90	0.92	0.96	1.00
Depression
First year	1.00
Second year	0.85	1.00
Third year	0.81	0.98	1.00
Fourth year	0.85	0.97	0.99	1.00

For each disease, we calculate sales ranks in the first full year after launch, second full year after launch, third full year after launch, and fourth full year after launch. These calculations are based on the INGENIX data. To ensure that the set of drugs is uniform across these calculations, we restrict our attention to drugs that launched before 2001, but after 1994. The table reports the pairwise correlations between ranks computed using each of these years in the drug’s life-cycle.

A3.1.2 Calculating Effects on Health

For each of the top-selling drugs, we survey the medical literature for clinical trials. When the trials do not provide an estimate for the health condition we are interested in, we assume the drug has no effect. Hence, these estimates can be seen as conservative. We do the same when the estimate is not statistically significant. When more than one estimate is available, we use the mean of the effects found.

We searched for the impacts of top-selling drugs on mortality, and on the incidence of all 6 other health conditions under consideration. However, we follow Goldman et al. (2005) in ruling out some causal links, based on expert opinion. For example, we assume that there is a causal link between hypertension and diabetes, but not from hypertension to cancer. We do not investigate the effect of new drugs on recovery or cure rates. Table A7 summarizes results from the survey of the literature for those effects. Appendix A3 gives detail on the calculation of each estimate. These calculations provide the estimates of RR_EXISTING and RR_PLACEBO in eq. (1).

Table A7:

Summary of Clinical Effects Found in Medical Literature: Reduction in Risk of Acquiring New Health Conditions.

Risk factor	Reduction in risk of acquiring comorbidity (relative to P=placebo, E=existing treatment)
	Heart disease		Hypertension		Stroke		Lung disease		Diabetes		Cancer		Depression		Mortality
	P	E	P	E	P	E	P	E	P	E	P	E	P	E	P	E
Heart disease					53%	0%							0%	0%	0%	0%
Hypertension	36%	0%			27%	0%							0%	0%	0%	0%
Stroke													0%	0%	0%	0%
Lung disease													0%	0%	0%	20%
Diabetes	31%	0%	0%	0%	47%	0%							0%	0%	48%	0%
Cancer					0%	0%							0%	0%	16%	27%
Depression															0%	0%

See Appendix A3 for details on the calculations. This matrix assumes a set of causal clinical mechanisms described in Goldman et al. (2004). An empty cell implies that a clinical restriction is imposed that rules out a causal relationship from one disease to another.

Appendix A3:

Details and Reference for Calculation of Clinical Effects in Tabel A7.

Causal	Link	Drug	Control group	Reference	Calculation
From	To
Heart	Stroke	LIPITOR	Placebo	Schwartz, G. G., A. G. Olsson, M. D. Ezekowitz, P. Ganz, M. F. Oliver, D. Waters, A. Zeiher, B. R. Chaitman, S. Leslie, and T. Stern. 2001. “Effects of atorvastatin on early recurrent ischemic events in acute coronary syndromes: the MIRACL study: a randomized controlled trial.” JAMA 285 (13):1711–8.	Translate RRR into annual RRR by assuming RRR to be constant over years
Hypertension	Heart	LIPITOR	Placebo	Sever, P. S., B. Dahlof, N. R. Poulter, H. Wedel, G. Beevers, M. Caulfield, R. Collins, S. E. Kjeldsen, A. Kristinsson, G. T. McInnes, J. Mehlsen, M. Nieminen, E. O'Brien, and J. Ostergren. 2003. “Prevention of coronary and stroke events with atorvastatin in hypertensive patients who have average or lower-than-average cholesterol concentrations, in the Anglo-Scandinavian Cardiac Outcomes Trial--Lipid Lowering Arm (ASCOT-LLA): a multicentre randomised controlled trial.” Lancet 361 (9364):1149–58	Translate RRR into annual RRR by assuming RRR to be constant over years
Hypertension	Stroke	LIPITOR	Placebo	Sever, P. S., B. Dahlof, N. R. Poulter, H. Wedel, G. Beevers, M. Caulfield, R. Collins, S. E. Kjeldsen, A. Kristinsson, G. T. McInnes, J. Mehlsen, M. Nieminen, E. O'Brien, and J. Ostergren. 2003. “Prevention of coronary and stroke events with atorvastatin in hypertensive patients who have average or lower-than-average cholesterol concentrations, in the Anglo-Scandinavian Cardiac Outcomes Trial--Lipid Lowering Arm (ASCOT-LLA): a multicentre randomised controlled trial.” Lancet 361 (9364):1149–58	Translate RRR into annual RRR by assuming RRR to be constant over years
Diabetes	Heart	LIPITOR	Placebo	Colhoun, H. M., D. J. Betteridge, P. N. Durrington, G. A. Hitman, H. A. Neil, S. J. Livingstone, M. J. Thomason, M. I. Mackness, V. Charlton-Menys, and J. H. Fuller. 2004. “Primary prevention of cardiovascular disease with atorvastatin in type 2 diabetes in the Collaborative Atorvastatin Diabetes Study (CARDS): multicentre randomised placebo-controlled trial.” Lancet 364 (9435):685–96.	Translate RRR into annual RRR by assuming RRR to be constant over years
Diabetes	Stroke	LIPITOR	Placebo	Colhoun, H. M., D. J. Betteridge, P. N. Durrington, G. A. Hitman, H. A. Neil, S. J. Livingstone, M. J. Thomason, M. I. Mackness, V. Charlton-Menys, and J. H. Fuller. 2004. “Primary prevention of cardiovascular disease with atorvastatin in type 2 diabetes in the Collaborative Atorvastatin Diabetes Study (CARDS): multicentre randomised placebo-controlled trial.” Lancet 364 (9435):685–96.	Translate RRR into annual RRR by assuming RRR to be constant over years
Lung disease	Mortality	ZYVOX	Vancomycin	FDA drug label of ZYVOX: http://www.accessdata.fda.gov/drugsatfda_docs/label/2005/021130s008,009,021131s009,010,021132s008,009lbl.pdf	RRR=cure rate in treatment group/cure rate in control group
Diabetes	Mortality	ACTOS or AVANDIA	Placebo	Sheehan, M. T. 2003. “Current therapeutic options in type 2 diabetes mellitus: a practical approach.” Clin Med Res 1 (3):189–200 Khaw, K. T., N. Wareham, R. Luben, S. Bingham, S. Oakes, A. Welch, and N. Day. 2001. “Glycated haemoglobin, diabetes, and mortality in men in Norfolk cohort of european prospective investigation of cancer and nutrition (EPIC-Norfolk).” BMJ 322 (7277):15–8.	Both lower Hemoglobin A1C levels by 1.5 percentage points, a 1% increase in HbA1c lead to a relative risk increase of 1.28 relative to placebo, so RRR=1/(1.28×1.5))=0.52
Cancer	Mortality	TEMODAR+ radiotherapy	Radiotherapy	Stupp, R., M. E. Hegi, W. P. Mason, M. J. van den Bent, M. J. Taphoorn, R. C. Janzer, S. K. Ludwin, A. Allgeier, B. Fisher, K. Belanger, P. Hau, A. A. Brandes, J. Gijtenbeek, C. Marosi, C. J. Vecht, K. Mokhtari, P. Wesseling, S. Villa, E. Eisenhauer, T. Gorlia, M. Weller, D. Lacombe, J. G. Cairncross, and R. O. Mirimanoff. 2009. “Effects of radiotherapy with concomitant and adjuvant temozolomide versus radiotherapy alone on survival in glioblastoma in a randomised phase III study: 5-year analysis of the EORTC-NCIC trial.” Lancet Oncol 10 (5):459–66.	RRR=average if RRR in each clinical trial, which is translated into annual RRR by assuming RRR to be constant over years
		TAXOTERE+ XERLODA	TAXOTERE	FDA drug label of XELODA: http://www.accessdata.fda.gov/drugsatfda_docs/label/2005/020896s016lbl.pdf
Cancer	Mortality	GLEEVEC	Interferon-α+ Cytarabine	Roy, L., J. Guilhot, T. Krahnke, A. Guerci-Bresler, B. J. Druker, R. A. Larson, S. O'Brien, C. So, G. Massimini, and F. Guilhot. 2006. “Survival advantage from imatinib compared with the combination interferon-alpha plus cytarabine in chronic-phase chronic myelogenous leukemia: historical comparison between two phase 3 trials.” Blood 108 (5):1478–84.	Translate RRR into annual RRR by assuming RRR to be constant over years

All values not available from the clinical literature are imputed as 1, i.e. assuming no clinical effect.

RRR, relative risk reduction.

To interpret the table, note that a value of 1.0 means that the new drug has the same impact on health as the relevant alternative, or correspondingly, a value of 0.8 means that the new drug lowers risk by 20%.

A3.1.3 Access Effect

To calculate the access effect, we need to construct an estimate of ∆_α which is the decrease in the fraction of untreated individuals following the introduction of a new drug. We estimate this effect using prescription claims data from the INGENIX data. By merging the drug consumption data with data on the introduction date of new drugs (from Appendix A2), we get a panel data set of the number of prescriptions consumed monthly for each class before and after the introduction of the top five drugs (from 1997.1 to 2004.12).^[11] Our strategy is to compute the effect of a launch on prescriptions relative to the trend in prescriptions for a specific class. The statistical model that implements this strategy explains the logarithm of monthly prescriptions in a class c as

(6)log(Cc,t)=αc+gc(t)+δ0Lc,t0−3+δ3Lc,t3−6+δ6Lc,t6−12+δ12Lc,t12++εc,t

α_c are class fixed effects, g_c(t) is some class-specific function of calendar time. The variables Lc,tk are indicator functions that take value 1 when a new blockbuster drug has been on the market for k months. Finally ε is some unobserved disturbance with zero mean. We specify linear class-specific time trends: g_c(t)=η_ct, which was not rejected against a more flexible specification. Hence the total effect of a new drug on prescriptions after 12 months is given by δ₁₂. Table A8 presents estimation results.

Table A8:

Access Effect Regression Results.

	Coefficient	p-Value
Launched 0~3	0.067	0.417	Number of observations: 2711
months
Launched 3~6	0.183	0.095
months
			R2: 0.973
Launched 6~12	0.245	0.032
months
			Time period: Jan 1997~Dec 2004
Launched ≥12	0.213	0.042
months

OLS regression of log(number of prescriptions).

Standard errors allow for clustering at the USC-5 class level.

New top sellers tend to have a relatively strong effect on the number of prescriptions after 3 months. After 1 year, there is a 24.5% increase in the number of prescriptions. This estimate is statistically significant at the 5% level. Figure A3 presents the estimates of the effect. We use 21% as our estimate of the access effect.

Figure A3:

Access Effects.

Notes: Based on estimation results from Table A8. Regression of monthly log(number of prescriptions) on launch of new chemical entities and reformulations.

A3.1.4 Access and Incidence Rates by Conditions

Three more estimates are needed to compute average RRs from eq. (1). First, we need to know, for each condition, the fraction of diagnosed individuals not taking existing drugs (α₀). Second, we need estimates of the incidence rates for those treated (P_T) and untreated (P_U). We use the HRS for that purpose. The HRS is a nationally representative longitudinal study of the age 50+ population. It asks about lifetime prevalence of the seven conditions we use as well as the consumption of drugs for those diagnosed with these conditions. It also tracks mortality. Mortality rates from the HRS follow closely figures from life-tables (Adams et al. 2004).^[12] Most of the differences are attributable to the fact that HRS samples the non-institutionalized population.

To construct estimates of the transition rates (P), we use hazard models estimated on the 1992–2002 waves of the HRS. The hazard models include baseline demographics, prevalence indicators at the previous wave, risk behaviors, and age. Table A9 gives the lifetime prevalence in 2004 of various conditions, the fraction untreated among the diagnosed population and predicted transition rates based on hazard models.

Table A9:

HRS Disease Prevalence, Drug Usage, and Predicted Incidence Rate.

Diagnosis	Prevalence	Fraction of untreated among the diagnosed	Effect of new drug launch on fraction untreated	Predicted incidence rate of comorbidities (by treatment status)
				Heart disease		Hypertension		Stroke		Depression		Mortality
	Untreated	Treated	Untreated	Treated	Untreated	Treated	Untreated	Treated	Untreated	Treated
Heart disease	25%	34%	−14%					3%	3%	3%	3%	4%	5%
Hypertension	55%	11%	−11%	5%	5%			2%	2%	2%	2%	3%	3%
Stroke	8%	63%	−8%							4%	4%	6%	7%
Lung disease	10%	47%	−11%							4%	5%	5%	5%
Diabetes	18%	18%	−17%	7%	7%	7%	8%	3%	3%	3%	3%	4%	4%
Cancer	14%	77%	−5%					2%	2%	3%	2%	4%	4%
Mental	17%	43%	−12%									3%	3%

Calculations from the HRS 2004 data. Empty cells indicate that clinical restrictions rule out the diagnosis as a risk factor for the relevant comorbidity.

Of the 54.6% of individuals aged 50+ in 2004 with hypertension, only 11% do not take medication for that condition according to the HRS. A somewhat larger fraction with diabetes and heart disease does not take medication (18.3% and 33.8%). Cancer and stroke are the two conditions with the fewest respondents treated with drugs (77.2% and 63.3% are untreated). The next column presents the estimate of ∆_α: the reduction in the fraction untreated following introduction of a new drug. Applying the effect calculated of 21% found in the previous section leads to a substantial reduction in the fraction untreated for most diseases. Finally, predicted average incidence rates prior to introduction are similar across groups of treated and untreated patients, if not higher in the treated group. Hence, we explicitly take into account of the fact that benefits for the untreated may be lower than for the treated because their condition is less severe.

A3.1.5 Average Effect of Top-Selling Drugs

We use estimates along with previously estimated parameters to construct the average RRs from eq. (1). Table A10 gives the results for each of the causal link we identified in Table A1.

Table A10:

Average Health Effect of a New Top-selling Drug.

Diagnosis	Reduction in risk of comorbities following introduction of new top-seller
	Comorbidity
	Heart	Hypertension	Stroke	Lung disease	Diabetes	Cancer	Depression	Mortality
Heart			6.7%				0.0%	0.0%
Hypertension	3.8%		2.9%				0.0%	0.0%
Stroke							0.0%	0.0%
Lung disease							0.0%	11.5%
Diabetes	5.2%	0.0%	8.1%				0.0%	8.5%
Cancer			0.0%				0.0%	6.6%
Depression								0.0%

These estimates are conservative, since they do not include effects on the undiagnosed population. We also assume drugs other than those in the top five list have no effect on health. Moreover, whenever we could not find a clinical effect from a peer-reviewed study we assume that a new drug has no effect.

A3.1.6 Fraction of Top-Selling Drugs (1995–2002)

We use data from the Food and Drug Administration (FDA) to compute how many NCEs – including reformulations and recombinations, in addition to “true” new chemical entities – were introduced over the 1995–2002 period. We compute the fraction of top-seller NCEs as a fraction of all NCEs over the period using the year in which they were approved by the FDA. We map each approved drug to health condition(s) by using the indications listed by the FDA in its annual report. Table A11 presents the results for the fraction of blockbuster NCEs from 1995–2002. The fraction of new top-selling drugs is quite different across diseases ranging from 9% for cancer to 33% for stroke.

Table A11:

Probability of a New Top-seller Drug for each Health Condition, 1995–2002.

New drugs	Heart		Hypertension		Stroke		Lung disease		Diabetes		Cancer		Depression
	Total	Top	Total	Top	Total	Top	Total	Top	Total	Top	Total	Top	Total	Top
1995	8	0	8	0	4	0	4	0	2	0	8	1	0	0
1996	5	1	6	1	1	0	8	1	2	0	10	0	2	1
1997	4	1	6	1	3	2	7	0	3	1	6	0	3	1
1998	6	1	4	1	1	0	5	0	0	0	7	1	2	1
1999	1	0	1	0	2	1	5	0	4	2	7	2	4	1
2000	4	1	2	0	2	1	4	3	6	2	5	0	1	0
2001	5	0	2	1	1	1	7	1	1	0	4	1	2	0
2002	5	1	3	1	1	0	5	1	2	0	6	0	3	1
Total	38	5	32	5	15	5	45	6	20	5	53	5	17	5
Average annual drugs	4.8	0.6	4	0.6	1.9	0.6	5.6	0.8	2.5	0.6	6.6	0.6	2.1	0.6
Fraction top-seller		13%		16%		33%		13%		25%		9%		29%

Information on new chemical entities, new formulation, and new combination drugs taken from the FDA websites. The FDA lists indications for each drug which were then mapped to our set of conditions. “Top-seller” drugs identified using INGENIX prescription claims data, as described in the text.

A4 GPPM Innovation Module

The innovation module translates changes in market size into new innovation. Acemoglu and Lin (2004) found that, on the margin, a one percent increase in pharmaceutical market share leads to approximately a four percent increase in the annual number of drugs. More recently, David et al. (2009) have estimated that the internal rate of return is 13% for biologics and 7.5% for small molecules. This translates into manufacturers producing one additional biologic drug for every additional $161.3 million of annual potential revenue and one new small molecule drug for every additional $109.4 million of annual potential revenue. From here we can estimate the elasticity of innovation (ε) using the following formulas.

• (7)Small molecule (SM): ε=(1/109.4)∗(SM revenues/# SM drugs)
• (8)Biologics (B): ε=(1/161.3)∗(B revenues/#B drugs)

According to the Pharmaceutical Research and Manufacturers of America (PhRMA), total U.S. pharmaceutical sales in 2010 were $184.7 billion (all values reported in 2015$). Similarly, the Congressional Research Service reports that U.S. biologic sales in 2011 were $58.8 billion (Schacht and Thomas 2012). The FDA reported in 2014 that they approved an average of 26 new drugs per year (including both biologics and small molecules) between 2004 and 2013 ( U.S. Food and Drug Administration Center for Drug Evaluation and Research 2014). BioWorld reports that the average number of biologics approved between 2008 and 2013 is 5–6 per year (Serebrov 2013). This approach suggests an elasticity estimate of 4.1% (2.0–4.1%) for small molecules and 5% (3.0–5.0%) for biologics. We implemented an elasticity of 3.0% for small molecules and 4.7% for biologics in the model. DiMasi and Grabowski (2007) report that there is an 8-year lag between the decision to start research on a new drug and the time it arrives on the market. Hence, new drugs at time t depend on changes in market size at t–8. We therefore assume an innovation delay of 8 years in the model.

A5 Costs and Benefits

A6 Stochastic Simulation and Weighting

The horizon for each simulation is 2005–2150 by which time all 2060 new entrants have died. We start the simulation with the HRS 2004 sample. We adjust weights so that they match 2004 population counts provided by the United Nations’ (UN) Population Program. We do this by age in order to smooth out bumps in the age distribution. Each year, the population of age 55 respondents in 2004 is added back adjusting their weights for projected demographic trends. Table A13 presents forecasted growth rates. By using the age 55, 2004 cohort repeatedly and only adjusting for growth, we do not take into account composition effects due to different growth rates across different segment of the population (say obese population).

Since the sample size for each age group is small, weighting introduces a significant amount of variability. To reduce this variability, we use two replicate datasets of the new cohorts and adjust appropriately the weights.

We use an average of 30 replications of the simulation in order to reduce simulation noise. Each replication takes roughly five minutes on a HP DL145 Linux box running on 2 dual core Intel 2.2 GHZ processors with 8 GB of RAM (programmed with OxMetrics). Since we run many scenarios for different parameter values we make use of parallel computing on 2 DL145 machines (total of eight processors) using a message passing interface (MPI). Each processor is assigned a scenario, performs the calculations, and writes the result to file.

A7 Model Validity

The model is structured and calibrated using the best available data, but the most relevant test of validity compares its predictions to actual data. In this spirit, we compared the model’s performance at predicting the population, against widely accepted UN estimates of the elderly population. And, to the greatest extent permitted by the data, we compared the model’s projections for disease growth against actual data on disease prevalence in the U.S. Due to the relative novelty of biologics as compared to small molecule drugs, these validations were done only using the effects of innovation on small molecules.

A7.1 Population Projections

We compared to UN population forecasts to the model’s baseline forecasts for the 60+ population in the U.S. The results are presented in Figure A4. The UN forecasts for the U.S. population project a trend with a slight kink at 2030. The model is able to replicate this kink, and matches the UN forecasts almost exactly after this point. Prior to the kink point, the model’s forecasts are about two to three percent lower than the UN forecasts.

Figure A4:

U.S. Population as Forecasted by the UN, and as Predicted by the GPPM.

A7.2 Disease and Mortality Projections

In addition to predicting population, the model also predicts disease prevalence. For the U.S. population, we start with the U.S. HRS database, and split this into two. Using one half of the sample, we estimate the GPPM model, and simulate health transitions over a 10-year period, using this subsample. We then compare those estimated health transitions to actual 10-year health transitions in the other half of the HRS sample. Figure A5 compares the model’s predicted prevalence of disease and disability (and the rate of mortality) after 10 years, to the actual HRS prevalence of disease and disability after 10 years. Overall, the model tracks the actual prevalence of disease, disability, and mortality fairly closely, always remaining within one to two percentage points of the actual data. In percent (as opposed to percentage point) terms, the deviations are largest for cancer and stroke, where one and two percentage point differences translate into roughly twelve to thirteen percent deviations. Considering both the sampling variability in the “actual” prevalence rates, and the estimation error in the model parameters, the model performs reasonably well at fitting the data. Formal tests reveal that the confidence intervals around the model estimates always contain the actual prevalence rate, although this conclusion is meaningful only up to the statistical precision of the comparison sample.

Figure A5:

Actual and Predicted Disease Prevalence and Mortality Incidence in U.S. HRS Population, after 10 Years.