Ernst Berndt

Louis E. Seley Professor in Applied Economics
Professor of Applied Economics

Biography | Selected Publications

“The Hidden Cost of Low Prices: Limited Access to New Drugs in India,”  Berndt, Ernst R. and Iain M. Cockburn. Health Affairs, 33(9):1567-75, September 2014.

"Price Indexes for Clinical Trial Research: A Feasibility Study,” Berndt, Ernst R. and Iain M. Cockburn. Monthly Labor Review, June 2014, 20 pp.

“Concentration and Changes in Physician Prescribing of Antipsychotic Medications”, Donohue, Julie M., A. James O’Malley, Marcela Horvitz-Lennon, Anna Levine Taub, Ernst R. Berndt and Haiden Huskamp. Psychiatric Services, 2014 March 1; 65(3):315-322.  doi: 10.1176/


"Vaccine Economics”, McElligott, Sean, and Ernst R. Berndt in Anthony Culyer, ed., Encyclopedia of Health Economics, First Edition, San Diego, CA: Elsevier Inc., 2014, 425-431.

“Defining and Quantifying the Use of Personalized Medicines”, Hu, Sean X., Murray L. Aitken, Arnold M. Epstein, Mark R. Trusheim and Ernst R. Berndt. Nature Reviews:  Drug Discovery, online version published 29 November 2013, Hard copy version published December 2013.

“Comparison of Stakeholder Metrics for Traditional and Adaptive Development and Licensing Approaches to Drug Development,” Baird, Lynn G., Mark R. Trusheim, Hans-Georg Eichler, Ernst R. Berndt and Gigi M. Hirsch. Therapeutic Innovation & Regulatory Science, 47(4):474-483, July 2013

“The Impact of Emerging Safety and Effectiveness Evidence on the Use of Physician-administered Drugs: The Case of Bevacizumab for Breast Cancer”, Conti, Rena M., Stacie B. Dusetzina, Ann C. Herbert, Ernst R. Berndt, Haiden A. Huskamp and Nancy L. Keating. Medical Care 51(7):622-627, July 2013

“Defining and Quantifying the Use of Personalized Medicines” with Sean X. Hu, Murray L. Aitken, Arnold M. Epstein, and Mark R. Trusheim, Nature Reviews: Drug Discovery, online version published 29 November 2013, Hard copy version to be published December 2013.

“How Quickly Do Physicians Adopt New Drugs? The Case of Antipsychotics” with Haiden A. Huskamp, Alistar J. O'Malley, Marcela Horvitz-Lennon, Anna Levine Taub and Julie M. Donohue, Psychiatric Services, 64(4):324-330, April 2013.

“Promotion of Prescription Drugs to Consumers and Providers, 2001-2010” with Rachel Kornfield, Julie Donohue and G. Caleb Alexander, PLOS ONE, 8(3):e55504. Doi:10.1371/journal.pone.0055504, published March 4, 2013.

“Uncertain prognosis for high-quality diagnostics: clinical challenges, economic barriers and needed reforms” with Mark R. Trusheim, M.J. Finley Austin and Carsten Rausch, Pharmacogenomics, (2013) 14(3):325-334. (2013)

“Winners and Losers From the Zaltrap Price Discount: Unintended Consequences?” with Rena Conti, Health Affairs Blog, available at, posted February 20, 2013

“Economic Challenges and Possible Policy Actions to Advance Stratified Medicine” with Mark R. Trusheim, Personalized Medicine, 9(4):413-27, 2012.

“Economic Challenges and Possible Policy Actions to Advance Stratified Medicine” with Mark R. Trusheim, Personalized Medicine, 9(4):413-27, 2012.

“Pricing and Reimbursement in U.S. Pharmaceutical Markets” with Joseph P. Newhouse, Patricia M. Danzon and Sean N. Nicholson, eds., Chapter 8 in The Oxford Handbook on the Economics of the Biopharmaceutical Industry, New York: Oxford University Press, pp. 201-265, 2012.

“The Segmentation of Therapeutic Populations in Oncology” with Mark R. Trusheim, Health Management, Policy and Innovation, 1(1):19-34, October 2012.

“The Segmentation of Therapeutic Populations in Oncology” with Mark R. Trusheim, Health Management, Policy and Innovation, 1(1):19-34, October 2012.

“The Unbundling of Advertising Agency Services: An Economic Analysis” with Mohammad Arzaghi, James C. Davis and Alvin J. Silk, Review E.R. Berndt, C.V - page 30 of Marketing Science, 10 (2012), Article 4. DOI:10.1515/1546-5616.1164. (2012)

“A Primer on the Economics of Prescription Pharmaceutical Pricing in Health Insurance Markets” with Thomas G. McGuire and Joseph P. Newhouse, Forum for Health Economics & Policy, 14(2), Article 10, November 2011.

“Advance Market Commitment for Pneumococcal Vaccines: Moving from Theory to Practice” with Tania Cernuschi, Eliane Furrer, Nina Schwalbe, Andrew Jones and Susan McAdams, Bulletin of the World Health Organization, posted online 14 October 2011, ID: BLT.11.08770

An Overview of Henry Grabowski's Scholarly Contributions (2011)

“Brand Loyalty, Generic Entry and Price Competition in Pharmaceuticals in the Quarter Century after the 1984 Waxman-Hatch Legislation” with Murray L. Aitken, International Journal of the Economics of Business, 18(2):177-201, July 2011.

”Diffusion of New Drugs in the Post-TRIPS Era”with Nathan Blalock and Iain M. Cockburn, International Journal of the Economics of Business, 18(2):203-24, July 2011.

“Economic Perspectives On The Advance Market Commitment For Pneumococcal Vaccines” with Christopher M. Snyder, Mark William Begor, Health Affairs, 30(8):1508-17, August 2011.

“Medicare Part D at Age Five: What Has Happened to Seniors' Prescription Drug Prices?” with Murray L. Aitken, Report by the IMS Institute for Healthcare Informatics, July 2011, 12 pp.

“Quality Adjustment for Healthcare Spending on Chronic Disease: Evidence from Diabetes Treatment, 1999-2009" American Economic Review, 101(3):206-211, May 2011. with Nilay D. Shah, Karen N. Eggleston, Steven A. Smith and Joseph P. Newhouse

“Quantifying Factors for the Success of Stratified Medicine” with Mark R Trusheim, Breon Burgess, Sean Xinghua Hu, Theresa Long, Steven D. Averbuch, Aiden A. Flynn, Alfons Lieftucht, Abhijit Mazumder, Judy Milloy, Peter Shaw, David Swank, Jian Wang, Federico Goodsaid and Michael C. Palmer, Nature Reviews: Drug Discovery, 10:817-33, November 2011.

“Bridging the Gap: Improving Clinical Development and the Regulatory Pathways for Health Products for Neglected Diseases” with Thomas J. Bollyky and Iain M. Cockburn, Clinical Trials, published online 25 November 2010, DOI: 10.1177/1740774510386390

“Characterizing Markets for Biopharmaceutical Innovations: Do Biologics Differ from Small Molecules?” with Mark R. Trusheim and Murray L. Aitken, Forum for Health Economics & Policy, Manuscript 1200, June 2010, 48 pp.

“Hedonic Price Indexes for Personal Computer Operating Systems and Productivity Suites” with Alan G. White, Jaison R. Abel and Cory W. Monroe, Annales d'Economie et de Statistique, Special Issue in Memory of Zvi Griliches, 79/80:787-807, 2005 (actually published June 2010).

The Net Value of Health Care for Patients with Type 2 Diabetes, 1997 to 2005 (2009)

“The Net Value of Health Care for Patients with Type 2 Diabetes, 1997 to 2005” with Karen N. Eggleston, Nilay D. Shah, Steven A. Smith, Amy E. Wagie, Arthur R. Williams, Jerome H. Grossman, Kirsten Hall Long, Ritesh Banerjee and Joseph P. Newhouse. Annals of Internal Medicine. 151(6):386-393, September 2009.

Cost-Benefit Analysis of the FDA: The Case of the Prescription Drug User Fee Acts (2008)

"Direct-to-Consumer Advertising in Health Care: An Overview of Economic Issues" Incentives and Choice in Health Care (2008)

"Early Retirement and DI/SSI Applications: Exploring the Impact of Depression" Health In Older Ages: The Causes and Consequences of Declining Disability Among the Elderly (2008)

Economic Incentives and Contracts: The Use of Psychotropic Medications (2008)

Generic Entry, Reformulations, and Promotion of SSRIs (2008)

Prescription Drug Spending Trends in the U.S.: Looking Beyond the Turning Point (2008)

A Primer on the Economics of the Re-Importation of Prescription Drugs (2007)

Advance Market Commitments for Vaccines Against Neglected Diseases: Estimating Costs and Effectiveness (2007)

Antihypertensive Drugs: A Perspective on the Value of Improved Blood Pressure Control in the USA (2007)

Authorized Generic Drugs, Price Competition and Consumers' Welfare (2007)

Dynamic Competition in Pharmaceuticals: Cross-National Evidence from New Drug Diffusion (2007)

Faster, Smaller, Cheaper: An Hedonic Price Analysis of PDAs (2007)

Medicare Part D and Prescription Drug Prices (2007)

"Price Indexes for Microsoft's Personal Computer Software Products" Hard-to-Measure Goods and Services: Essays in Honor of Zvi Griliches (2007)

Real Output in Mental Health Care During the 1990s (2007)

Stratified Medicine: Strategic and Economic Implications of Combining Drugs and Clinical Biomarkers (2007)

The December Effect in FDA Drug Approvals: Assessing the Submissions Echo Hypothesis (2007)

"The United States' Experience with Direct-to-Consumer Advertising of Prescription Drugs: What Have We Learned?" Pharmaceutical Innovation: Incentives, Competition, and Cost-Benefit Analysis in International Perspective (2007)

The Value of Antihypertensive Drugs: A Perspective on Medical Innovation (2007)

Trends in the Globalization of Clinical Trials (2007)

How Safe Is Too Safe? Public Safety Versus Innovation at the FDA (2006)

Objective and Self-Report Work Performance Measures: A Comparative Analysis (2006)

“Opportunities for Improving the Drug Development Process: Results from a Survey of Industry and the FDA” Innovation Policy and the Economy (2006)

The Boskin Commission After A Decade: After-life or Requiem? (2006)

The Impact of Incremental Innovation on Biopharmaceuticals: Drug Utilization in Original and Supplemental Indications (2006)

Industry Funding of the FDA: Effects of PDUFA on Approval Times and Withdrawal Rates (2005)

Panel Data Analysis of U.S. Coal Productivity (2005)

Performance Decrements Resulting from Illness in the Workplace: The Effect of Headaches (2005)

Reductions in Anaemia and Fatigue are Associated with Improvements in Productivity in Cancer Patients Receiving Chemotherapy (2005)

The Economic Burden of Anemia in Cancer Patients Receiving Chemotherapy (2005)

The Impact of Anaemia and its Treatment on Employee Disability and Medical Costs (2005)

Vaccine Advance-Purchase Agreements for Low-Income Countries: Practical Issues (2005)

“Benefit Plan Design, and Prescription Drug Utilization Among Asthmatics: Do Patient Copayments Matter?” Frontiers in Health Policy (2004)

Changes In The Costs of Treating Mental Health Disorders: An Overview Of Recent Research Findings (2004)

“Cost Economies in the Global Advertising and Marketing Services Business” The Global Market: Developing a Strategy to Manage Across Borders (2004)

Economic Impacts of Anxiety Disorders: A Review (2004)

Effects of Pharmaceutical Promotion on Adherence to Guideline Treatment of Depression (2004)

Holding Company Cost Economies in the Global Advertising and Marketing Services Business (2004)

Prescriber Intent, Off-Label Usage, and Early Discontinuation of Antidepressant (2004)

Quality-Constant Prices for the Ongoing Treatment of Schizophrenia: An Exploratory Study (2004)

The Clinical and Occupational Correlates of Work Productivity Loss Among Employed Patients with Depression (2004)

Unemployment, Job Retention and Productivity Loss Among Employees with Depression (2004)

Unique Issues Raised by Drug Benefit Design (2004)

Consumption Externalities and Diffusion in Pharmaceutical Markets: Antiulcer Drugs (2003)

"Demand Effects of Recent Changes in Prescription Drug Promotion" Frontiers in Health Policy Research (2003)

“The Long Shadow of Patent Expiration: Generic Entry and Rx to OTC Switches” Scanner Data and Price Indexes (2003)

The Relationship of Employee- Reported Work Limitations to Work Productivity (2003)

An Analysis of the Diffusion of New Antidepressants: Variety, Quality, and Marketing Efforts (2002)

Depression Treatment: A Life-Long Commitment? (2002)

Deregulating Directto- Consumer Marketing of Prescription Drugs: Effects on Prescription and Over-the-Counter Product Sales (2002)

Healthcare Expenditures in Patients Treated with Venlaxafine or Selective Serotonin Reuptake Inhibitors for Depression and Anxiety (2002)

Intermedia Substitutability in the U.S. National Advertising Market (2002)

Labor Force Activity in Cancer Patients with Anemia (2002)

Measuring the Costs and Benefits of Pharmaceutical Expenditures (2002)

Pharmaceuticals in U.S. Health Care: Determinants of Quantity and Price (2002)

Promotion of Prescription Drugs to Consumers (2002)

The Impact of Treatment-Resistant Depression on Healthcare Utilization and Costs (2002)

The Medical Treatment of Depression, 1991-1996: Productive Inefficiency, Expected Outcome Variations, and Price Indexes (2002)

“Creating Price Indexes for Measuring Productivity in Mental Health Care” Frontiers in Health Policy Research (2001)

“Introduction” Medical Care Output and Productivity, Studies in Income and Wealth (2001)

Price and Quality of Desktop and Mobile Personal Computers: A Quarter Century Historical Overview (2001)

"Price Indexes for Acute Phase Treatment of Depression" Medical Output and Productivity (2001)

"Price Indexes for Medical Care Goods and Services: An Overview of Measurement Issues" Medical Output and Productivity (2001)

“Reducing the Societal Costs of Depression: Opportunities in the Millennium” Depression: Social and Economic Timebomb (2001)

"Sources of Productivity Growth in the American Coal Industry" New Developments in Productivity Analysis, Studies in Income and Wealth, (2001)

The Emerging Position of the Internet as an Advertising Medium (2001)

Comparing SSRI Treatment Costs for Depression Using Retrospective Claims Data: The Role of Non-Random Selection and Skewed Data (2000)

Health Care Use and At-Work Productivity Among Employees With Mental Disorders (2000)

Lost Human Capital from Early-Onset Chronic Depression (2000)

"Medical Care Prices and Output" Handbook of Health Economics (2000)

On the Economic Impacts of Medical Treatments: Work Productivity and Functioning (2000)

Research on Price Index Measurement: Agendas for the Next Twenty Years (2000)

Cost-Effectiveness, Quality-Adjusted Life Years, and Supportive Care: Recombinant Human Erythropoietin as Treatment of Cancer- Associated Anemia (1999)

Costing Out Care: Antihistamines and the Workplace (1999)

Course and Cost of Treatment for Depression with Fluoxetine, Paroxetine and Sertraline (1999)

“Introduction: New Developments in Measuring Medical Care” Measuring the Prices of Medical Treatments (1999)

Loss of Work Productivity Due to Illness and Medical Treatment (1999)

“Price Indexes for the Treatment of Depression” Measuring the Prices of Medical Treatments (1999)

The Economic Burden of Anxiety Disorders in the 1990's (1999)

"Is Price Inflation Different for the Elderly? An Empirical Analysis of Prescription Drugs" Frontiers in Health Policy Research (1998)

Measuring Prices and Quantities of Treatments for Depression (1998)

Prescription Drug Prices for the Elderly (1998)

Workplace Illness: Calculating Return on Investment from Reducing Workplace Illness (1998)

Workplace Performance Effects from Chronic Depression and Its Treatment (1998)

Alternative Insurance Arrangements and the Treatment of Depression: What Are Facts? (1997)

The Next Phase of Managed Care: Targeting Investments in Employee Health (1997)

"The Roles of Marketing, Product Quality and Price Competition in the Growth and Composition of the U.S. Anti-Ulcer Drug Industry" The Economics of New Products, Studies in Income and Wealth (1997)

"Depression in the Workplace: An Economic Perspective" Selective Seratonin Reuptake Inhibitors (1996)

Pharmaceutical Innovations and Market Dynamics: Tracking Effects on Price Indexes for Antidepressant Drugs (1996)

System Average Rates of U.S. Investor-Owned Electric Utilities: A Statistical Benchmark Study (1996)

"An Updated and Extended Study of the Price Growth of Prescription Pharmaceutical Preparations" Competitive Strategies in the Pharmaceutical Industry (1995)

Calculating the Workplace Cost of Chronic Disease (1995)

Econometric Estimates of Price Indexes for Personal Computers in the 1990's (1995)

Economic Consequences of Illness in the Workplace (1995)

Electric Utility Rates and the Evaluation of Management Performance (1995)

High-Tech Capital Formation and Economic Performance in U.S. Manufacturing Industries: An Exploratory Analysis (1995)

Information Technology and the Productivity Paradox (1995)

Information, Marketing and Pricing in the U.S. Anti-Ulcer Drug Market (1995)

Costs, Institutional Mobility Barriers, and Market Structure: Advertising Agencies as Multiproduct Firms (1994)

Uniform Pharmaceutical Pricing: An Economic Analysis. Washington, D.C.: AEI Press, 1994.

A Theoretical and Empirical Investigation of the Box-Cox Model and a Nonlinear Least Squares Alternative (1993)

Auditing the Producer Price Index: Micro Evidence from Prescription Pharmaceutical Preparations (1993)

Cost Effects of Mergers and Deregulation in the U.S. Rail Industry (1993)

Depression: A Neglected Major Illness (1993)

Measuring the Energy Efficiency and Productivity Impacts of Embodied Technical Progress (1993)

"Price Indexes for Microcomputers: An Exploratory Study" Price Measurements and their Uses, Studies in Income and Wealth (1993)

Rail Costs and Capital Adjustments in a Quasi-Regulated Environment (1993)

Scale and Scope Effects on Advertising Agency Costs (1993)

The Economic Burden of Depression in 1990 (1993)

Deregulation, Mergers, and Cost Savings in Class I U.S. Railroads, 1974-1986 (1992)

Fifty Years of Economic Measurement: The Jubilee of the Conference on Research in Income and Wealth. Chicago: University of Chicago Press, 1992.

Governance Structure, Managerial Characteristics, and Firm Performance in the Deregulated Rail Industry (1992)

Output Measurement in the Service Sectors (Nber Studies in Income and Wealth, Vol 56). Edited by Zvi Griliches. Chicago: University of Chicago Press, 1992.

"Dynamic Models of Input Demands: A Comparison Under Different Formulations of Adjustment Costs" Advances in the Economics of Energy and Resources (1991)

Energy Use, Technical Change and Productivity Growth: A Survey of Economic Issues (1991)

"Editors' Introduction" Fifty Years of Economic Measurement: The Jubilee of the Conference on Research in Income and Wealth (1990)

"Energy Price Shocks and Productivity Growth in the Japanese and U.S. Manufacturing Sectors" Productivity Growth in Japan and the United States (1990)

"Canadian Energy Demand After the Oil Shocks" Petro Markets: Probing the Economics of Continental Energy (1989)

"Rates of Return and Capital Aggregation Using Alternative Rental Prices" Technology and Capital Formation (1989)

Dynamic Econometric Modeling: Proceedings of Third International Symposium in Economic Theory and Economics. Edited by Halbert White. Cambridge, Mass.: Cambridge University Press, 1988.

"Envelope Consistent Functional Separability" Dynamic Econometric Modeling (1988)

"Energy Price Shocks and Productivity Growth: A Survey" The Analysis of Energy Markets (1987)

"Interindustry Differences in the Effects of Energy Price-Induced Capital Utilization Changes on Multifactor Productivity Measurement" Advances in the Economics of Energy and Resources (1987)

Editors' Introduction (1986)

"Electrification, Embodied Technical Progress, and Labor Productivity Growth in U.S. Manufacturing, 1889-1939" Electricity Use, Productive Efficiency and Economic Growth (1986)

Energy Price Shocks and Productivity Growth in U.S. and U.K. Manufacturing (1986)

Measuring and Assessing Capacity Utilization in the Manufacturing Sectors of Nine OECD Countries (1986)

Modeling Energy Demand: The Choice Between Input and Output Energy Measures (1986)

Productivity Measurement with Adjustments for Variations in Capacity Utilization and Other Forms of Temporary Equilibrium (1986)

Energy Demand in the Transportation Sector of Mexico (1985)

"From Technocracy to Net Energy Analysis: Engineers, Economists and Recurring Energy Theories of Value" Progress in Natural Resource Economics (1985)

"Modeling the Aggregate Demand for Electricity: Simplicity vs. Virtuosity" Advances in the Economics of Energy and Resources (1984)

Residential Electricity Demand in Mexico: A Model Distinguishing Access from Consumption (1984)

"Concavity and the Specification of Technical Progress in U.S. Manufacturing" Econometrie et crise de l'energie (1983)

"Econometric Models of Energy Demand in the Transportation and Residential Sectors of Mexico" Current Economic and Financial Issues of the North American and Caribbean Countries (1983)

Energy-Output Coefficients: Complex Realities Behind Simple Ratios (1983)

"The Demand for Heavy Oil Derived from Asphalt" Heavy Versus Light Oil: Technical Issues and Economic Considerations (1983)

"The Specification and Measurement of Technical Change in U.S. Manufacturing" Advances in the Economics of Energy and Resources (1982)

"An Introductory Review of the Economics of Natural Resource Substitution" Modeling and Measuring Natural Resource Substitution (1981)

Energy Prices and Productivity Trends in the Canadian Manufacturing Sector, 1957-76 : Some Exploratory Results. Ottawa: Minister of Supply and Service Canada, 1981.

Engineering and Econometric Interpretations of Energy-Capital Complementarity: Reply (1981)

Modeling and Measuring Natural Resource Substitution. Cambridge, Mass.: MIT Press, 1981.

"Modeling the Simultaneous Demand for Factors of Production" The Economics of the Labour Market (1981)

Short Run Labor Productivity in a Dynamic Model (1981)

"An Econometric Model of Alberta Electricity Demand" Energy Policy Modelling: U.S. and Canadian Experiences (1980)

On Testing Theories of Financial Intermediary Portfolio Selection (1980)

Tax Normalization, Regulation and Economic Efficiency (1980)

Engineering and Econometric Interpretations of Energy-Capital Complementarity (1979)

Estimation of Logging Costs and Timber Supply Curves from Forestry Inventory Data (1979)

Income Redistribution and Employment Effects of Rising Energy Prices (1979)

Parametric Productivity Measurement and Choice Among Flexible Functional Forms (1979)

Utility Bond Rates and Tax Normalization (1979)

Aggregate Energy, Efficiency, and Productivity Measurement (1978)

"Canadian Energy Demand and Economic Growth" Oil in the Seventies: Essays on Energy Policy (1977)

Conflict Among Criteria for Testing Hypotheses in the Multivariate Linear Regression Model (1977)

Demand for Natural Gas: Residential and Commercial Markets in Ontario and British Columbia (1977)

Flexible Functional Forms and Expenditure Distributions: An Application to Canadian Consumer Demand Functions (1977)

Tax Credits for Employment Rather than Investment (1977)

Reconciling Alternative Estimates of the Elasticity of Substitution (1976)

Estimation and Hypothesis Testing in Singular Equation Systems with Autoregressive Disturbances (1975)

Technology, Prices and the Derived Demand for Energy (1975)

"An Economic Interpretation of the Energy-GNP Ratio" Energy: Demand Conservation and Institutional Problems (1974)

"Forecasting North American Energy Demand: Issues and Problems" The Mackenzie Pipeline: Arctic Gas and Canadian Energy Policy (1974)

Testing for the Existence of a Consistent Aggregate Index of Labor Inputs (1974)

"Production Structure" U.S. Energy Resources and Economic Growth (1973)

"The Internal Structure of Functional Relationships: Separability, Substitution, and Aggregation," Review of Economic Studies, Berndt, Ernst R. and Laurits R. Christensen, 3, 403-410 (1973)

The Translog Function and the Substitution of Equipment, Structures, and Labor in U.S. Manufacturing, 1929- 68 (1973)

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Affordable Care Act (ACA); Applied economics; Applied microeconomics; Applied probability; Biopharmaceutical; Biotechnology; Cancer; Clinical trials; Data analytics; Drug models; Econometrics; Economics; Education; Game theory; Health management; Healthcare; Healthcare industry; HIV; Industrial organization; Industrial organization; Industrial partnerships; Institutional partnerships; Intellectual property; Intellectual property; Intellectual property law; Market research; Medicaid; Medical decision making; Medical devices; Medicare; Medicine; Microeconomics; Outsourcing; Pharmaceuticals; Pricing; Regulation and policy; Sampling; Statistics; Stochastic modeling