MANAGEMENT SCIENCE doi /mnsc ec

Transcription

1 MANAGEMENT SCIENCE doi /mnsc ec e-companion ONLY AVAILABLE IN ELECTRONIC FORM informs 009 INFORMS Electronic Companion Business Unit Reorganization and Innovation in New Product Markets by Samina Karim, Management Science, doi /mnsc

2 Appendix 1: Medical Sector Categories and Product Lines A. Healthcare services B. Ophthalmic devices Ambulatory (Holter) Monitoring Services Contact Lenses Ambulatory Care Facility Management Services Biomolecular Research and Development Clinical Laboratory Testing Services Consulting and Planning Services Contract Research Services; Medical R&D Services Dental Facility Management Services Dental Laboratory Services Diagnostic Imaging Services Disinfection Services, Equipment and Supplies Emergency Medical Services Employment Services Environmental Testing Services Food Service and Catering Operations Health Care Cost Management Health Maintenance Organization (HMO) Management Services Home Health Care Services Hospital Department Management Services Hospital Management Services Hospital Supplies Distribution Hospital/Medical Facility Financing, Planning and Construction Housekeeping and Laundry Services Instrument Refurbishing and Reconditioning Services Instrument Repair and Maintenance Services Laboratory Animals Leasing and Rental Services Medical and Health Insurance Medical Clinic Management Services Medical Data Processing Services Medical Educational and Training Services Nephrology Treatment Services Nursing Home Management Services Optometric Services Other Medical Services Outpatient Facility Management Outpatient Medical and Surgical Services Packaging Services Pharmaceutical Services Preferred Provider Organization (PPO) Management Radiological Monitoring Services Radiological Testing Services Rehabilitation Services Respiratory Therapy Services Sterilization Services Transtelephonic Electrocardiogram Analysis Services Waste Disposal Services, Equipment and Supplies Eyeglass Frames and Lenses Intraocular Lenses Ophthalmic Diagnostic Equipment Ophthalmic Supplies and Accessories Optical Products Opticians' Apparatus C. Pharmaceutical products Animal Products Biochemicals, Chemicals and Related Medical Chemicals Biologicals Biomaterials Blood and Blood Products Consumable Products Chemicals Dietary, Nutritional and Vitamin Supplements Drug Delivery Systems Parenteral and Irrigating Solutions Pharmaceutical Apparatus and Supplies Pharmaceuticals, Drugs and Medicines Radioisotopes Radiopaque Contrast Media Radiopharmaceuticals Veterinary Products D. Dental devices Dental Equipment Dental Products Dental Prosthetics Dental Supplies Dental X-Ray Apparatus

3 Appendix 1: Medical Sector Categories and Product Lines A. Healthcare services B. Ophthalmic devices Ambulatory (Holter) Monitoring Services Contact Lenses Ambulatory Care Facility Management Services Biomolecular Research and Development Clinical Laboratory Testing Services Consulting and Planning Services Contract Research Services; Medical R&D Services Dental Facility Management Services Dental Laboratory Services Diagnostic Imaging Services Disinfection Services, Equipment and Supplies Emergency Medical Services Employment Services Environmental Testing Services Food Service and Catering Operations Health Care Cost Management Health Maintenance Organization (HMO) Management Services Home Health Care Services Hospital Department Management Services Hospital Management Services Hospital Supplies Distribution Hospital/Medical Facility Financing, Planning and Construction Housekeeping and Laundry Services Instrument Refurbishing and Reconditioning Services Instrument Repair and Maintenance Services Laboratory Animals Leasing and Rental Services Medical and Health Insurance Medical Clinic Management Services Medical Data Processing Services Medical Educational and Training Services Nephrology Treatment Services Nursing Home Management Services Optometric Services Other Medical Services Outpatient Facility Management Outpatient Medical and Surgical Services Packaging Services Pharmaceutical Services Preferred Provider Organization (PPO) Management Radiological Monitoring Services Radiological Testing Services Rehabilitation Services Respiratory Therapy Services Sterilization Services Transtelephonic Electrocardiogram Analysis Services Waste Disposal Services, Equipment and Supplies Eyeglass Frames and Lenses Intraocular Lenses Ophthalmic Diagnostic Equipment Ophthalmic Supplies and Accessories Optical Products Opticians' Apparatus C. Pharmaceutical products Animal Products Biochemicals, Chemicals and Related Medical Chemicals Biologicals Biomaterials Blood and Blood Products Consumable Products Chemicals Dietary, Nutritional and Vitamin Supplements Drug Delivery Systems Parenteral and Irrigating Solutions Pharmaceutical Apparatus and Supplies Pharmaceuticals, Drugs and Medicines Radioisotopes Radiopaque Contrast Media Radiopharmaceuticals Veterinary Products D. Dental devices Dental Equipment Dental Products Dental Prosthetics Dental Supplies Dental X-Ray Apparatus

4 E. Medical devices Emergency Medical Products Ambulatory (Holter) Monitoring Equipment Endoscopes, Arthroscopes and Related Products Analytical Balances Enteral and Parenteral Hyperalimentation Products Analytical Imaging Equipment Environmentally Controlled Enclosures Analytical Instrument Data Systems Evacuation and Filtration Equipment Analytical Instruments Fermenters, Freeze-Dryers/Processing Equipment Anesthesia Equipment and Accessories Fiberoptic Examining Scopes Animal Equipment and Supplies Freezers and Refrigeration Equipment Anti-Embolism Devices Furniture and Casework Appliances and Utility Equipment Gamma Cameras Arterial Grafts Gas Chromatographs Artificial Voice Devices General Disposables Auditory Testing Equipment Hearing Aid Accessories Automated Cell Sorters Hearing Aids Automated Chemistry Analyzers Heart Valves Automated Immunoassay Systems Heart/Lung Machines Automated Liquid Chromatography Analyzers Home Care Equipment and Supplies Automated Microbiology Analyzers Hyperbaric Chambers Automatic Slide Stainers Hypo/Hyperthermia Therapy Equipment Biofeedback Equipment Image Recording Systems Blood Collection Supplies Immunohematological Testing Instrumentation Blood Flowmeters Implantables Blood Gas Analyzers and Monitors Incontinence Products Blood Pressure Measuring Equipment Infection Control Products Blood Processing Equipment Infusion Devices Calibration and Test Equipment Injectors Cardiac Assist Equipment Kits and Trays Cardiac Pacemakers Laboratory Data Processing Equipment Cardiopulmonary Diagnostic Equipment Laboratory Equipment/Supplies Cardiovascular Accessories Laboratory Glass and Plastic Ware Cell Culturing Systems Laboratory Incubators Centrifuges Laboratory Ware Clinical Laboratory Products Laminar Flow Stations Coagulation Testing Equipment Lamps and Lighting Equipment Computed Tomography (CT) Scanners Lasers Contraceptive Devices Life Support Systems Cryosurgical Equipment Lithotripters Culture Media Lung Function Testing Equipment Defibrillators Magnetic Resonance Imaging (MRI) Equipment Diagnostic Imaging Products Manikins Diagnostic Reagents and Test Kits Mass Spectrometers Digital Subtraction Radiography Equipment Materials Handling Systems Dilutors and Dispensers Medical Communications Systems Dressings and Bandages Medical Data Processing Equipment Electrocardiographs Medical Data Processing Software Systems Electrochemical/Biochemical Sensors Medical Educational and Training Products and Supplies Electrodes, Cables, Leads, and Gels Medical Electronic Diagnostic Equipment Electroencephalographs Medical Equipment Power Sources Electrolyte Analysis Equipment Medical Gasses and Equipment Electromedical Apparatus Medical Linens and Apparel Electromyographs Medical Transportation Electron Microscopes Medical/Surgical Gloves Electronic Blood Cell Counters Medical/Surgical/Hospital Supplies Electronic Thermometers Microbiological and Serological Testing Equipment Electrosurgical Instruments and Accessories Microporous Membrane and Other Filters

5 Microscopy Accessories Microtomes Neonatal Incubators Neurostimulators Nuclear Diagnostic Equipment Nuclear Instruments Nuclear Supplies and Accessories Nucleic Acid/Peptide Synthesizers Neonatal Care Products Operating Tables Optical Microscopes Orthopedic Devices and Appliances Orthopedic Instruments Ostomy Appliances and Supplies Other Medical Equipment Oxygen Therapy Equipment Pacemaker Accessories Pathology Tissue Processors Patient Comfort Aids and Appliances Patient Identification Products and Services Patient Monitoring Equipment and Accessories Patient Restraint Products Patient Transport Systems Patient Weighing Equipment Penile Prosthetic Devices Physical Therapy and Rehabilitation Equipment Physicians' Aids Physicians' Office Testing Equipment Physiological Testing Equipment and Recorders Physiological Therapeutic Equipment Prosthetic Devices Pulmonary Function Testing Equipment Pumps Radiation Therapy Equipment Radioimmunoassay Test Kits Radiological and Nuclear Equipment Radiology/Nuclear Laboratory Data Systems Recorder Paper Charts and Records Renal Dialysis Equipment Renal Dialysis Supplies Renal Dialyzer Reprocessing Equipment Respiratory Gas Analyzers Respiratory Therapy Equipment Scintillation Counting Equipment Separation Products; Chromatography & Electrophoresis Equip. Special Medical Vehicles Specialty Beds Specialty Tables and Chairs Spectrophotometers, Colorimeters, Fluorometers, Nephelometers Sterile Packaging Materials Sterilizing Equipment and Supplies Suction Machines Supply and Other Carts and Cabinets Surgical and Obstetric Drapes Sutures and Fasteners Syringes and Needles Staining Machines Telemetry Equipment Thermographic Diagnostic Equipment Thermometers Tubings, Tubes and Catheters Ultrasonic and Other Transducers and Accessories Ultrasonic Diagnostic Equipment Ultrasonic Instrumentation Urological Equipment Water Treatment Equipment Wheelchairs, Manual Wheelchairs, Motorized X-Ray Apparatus X-Ray Developing Solutions Recovery Equipment X-Ray Film X-Ray Film Loading, Processing and Handling Equipment X-Ray Record Storage and Retrieval Equipment X-Ray Supplies and Accessories X-Ray Tables 3

6 Appendix : Testing a U-shape Relationship Below are the statistical tests to appropriately test for a U shape relationship between degree of reorganization and degree of innovation. These methods are based on the suggestions of Lind and Mehlum (007) that suggest not only (A) checking the coefficient estimates for their magnitude and significance, but also checking the appropriateness of (B) slopes at the extreme points and (C) the inflection point of the estimated U curve. Below, I recreate their tests (shown in their Table 1) using estimates from my Model 8 of Table 4. (A) COEFFICIENTS Model 8 supports Hypothesis 1B which predicts a U shape relationship. The main X term is reorganization (reorg) with estimated coeff β (beta), and the X-squared term is reorganization (sq_reorg) with estimated coeff γ (gamma). Reorganization β = (0.107)** Squared_Reorg γ = (0.006)** Standard errors in parentheses. Significant estimates: ~ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001) Thus, the X and X terms have the expected negative and positive, respectively, magnitudes to support a U-shape. The estimates are both significant. (B) SLOPES (1) Test the slopes of the extreme points for appropriate magnitude and significance: Left side extreme point (x low = 0) Magnitude: Slope at x low β+γx low = Test H0: β+γx low = 0 This is the correct expected magnitude (negative slope for left point of U shape).. test (reort1+(*sq_reort1*0))=0 ( 1) [innovt]reort1 = 0 chi( 1) = 6.98 Prob > chi = This is a two-tailed test. The p-value is less than.008, thus we can reject the alternative hypothesis that the left slope is zero.

7 Right side extreme point (x high = 6) Magnitude: Slope at x high β+γx high = Test H0: β+γx high = 0 This is the correct expected magnitude (positive slope for right point of U shape).. test (reort1+(*sq_reort1*6))=0 ( 1) [innovt]reort1 + 5 [innovt]sq_reort1=0 chi( 1) = 6.45 Prob > chi = This is a two-tailed test. The p-value is less than.011, thus we can reject the alternative hypothesis that the right slope is zero. () Sasabuchi test for true U shape: The true alternative of a U-shape is that the slope at the left extreme is not negative (slope >=0) and/or the slope at the right extreme is not positive (slope <=0). To test this, we need to perform one-tailed tests of the alternative hypothesis for each extreme point separately. Note that the square-root of the chi distribution is equivalent to the standard normal distribution. The z statistic is then equivalent to the square_root of chi, multiplied by the sign of the expression being tested (β+γx low has a negative sign, β+γx high has a positive sign). Left side extreme point (x low = 0) Test H0: β+γx low >= 0. test (reort1+(*sq_reort1*0))=0 ( 1) [innovt]reort1 = 0 chi( 1) = 6.98 Prob > chi = display normal(-1*sqrt(r(chi))) This is a one-tailed test; -1 represents the sign of the expression β+γx low. The p- value is less than.004, thus we can reject the alternative hypothesis that the left slope is positive. Right side extreme point (x high = 6) Test H0: β+γx high <= 0

8 . test (reort1+(*sq_reort1*6))=0 ( 1) [innovt]reort1 + 5 [innovt]sq_reort1=0 chi( 1) = 6.45 Prob > chi = display 1-(normal(1*sqrt(r(chi)))) This is a one-tailed test; 1 represents the sign of the expression β+γx high. The p- value is less than.006, thus we can reject the alternative hypothesis that the right slope is negative. (C) INFLECTION POINT (1) Calculate the ( extremum ) inflection point and compare to estimates for appropriate magnitude Estimated inflection point = 8 reorganizations (from Figure 5 based on Model 8 estimates). Calculated inflection point is at x = -β/γ =.83/(*.017) = 8.3. Since reorganizations are discreet integers this calculated inflection point matches the estimated inflection point of 8. () Calculate 95% confidence interval for the inflection point using Fieller or delta method: To calculate confidence intervals for ratio estimates, the Fieller method is more appropriate than the delta method when dealing with finite samples (Beyene and Moineddin, 005; Lind and Mehlum, 007). Below, I calculate the Fieller method confidence interval at 95% from the formula provided by Beyene and Moineddin (005). Recall that the confidence interval of interest is around the x-value of the inflection point, where x = -β/γ = ½(-β/γ) Let θ = -β/γ = (later we ll cut the interval in half) Let α =.05 Equation 1: (1-α)% Fieller confidence interval for θ: θ + 1/ k V1 Z / (1 ) α V θ + ± V + θv + θ V k V k V γ k V

9 Where the matrix below represents variance-covariance of estimates for β (reorganization) and γ (squared_reorg) from Model 8: V 1 = V 1 =V 1 V 1 = V = And Z α / = V And k = Zα / = γ Plugging in all of the appropriate values noted above into Equation 1 yields: For θ = -β/γ: 95% confidence interval of [9.50, 7.10] and For x = ½ θ = -β/γ : 95% confidence interval of [4.75, 13.55] Thus, the estimated inflection point of 8 is within the confidence interval for the calculated inflection point. References Beyene, J. and R. Moineddin (005). "Methods for confidence interval estimation of a ratio parameter with application to location quotients." BMC Medical Research Methodology 5: Lind, J. T. and H. Mehlum (007). With or without U? The appropriate test for a U shaped relationship. Working paper, Univerity of Oslo, Norway.

10 E. Medical devices Emergency Medical Products Ambulatory (Holter) Monitoring Equipment Endoscopes, Arthroscopes and Related Products Analytical Balances Enteral and Parenteral Hyperalimentation Products Analytical Imaging Equipment Environmentally Controlled Enclosures Analytical Instrument Data Systems Evacuation and Filtration Equipment Analytical Instruments Fermenters, Freeze-Dryers/Processing Equipment Anesthesia Equipment and Accessories Fiberoptic Examining Scopes Animal Equipment and Supplies Freezers and Refrigeration Equipment Anti-Embolism Devices Furniture and Casework Appliances and Utility Equipment Gamma Cameras Arterial Grafts Gas Chromatographs Artificial Voice Devices General Disposables Auditory Testing Equipment Hearing Aid Accessories Automated Cell Sorters Hearing Aids Automated Chemistry Analyzers Heart Valves Automated Immunoassay Systems Heart/Lung Machines Automated Liquid Chromatography Analyzers Home Care Equipment and Supplies Automated Microbiology Analyzers Hyperbaric Chambers Automatic Slide Stainers Hypo/Hyperthermia Therapy Equipment Biofeedback Equipment Image Recording Systems Blood Collection Supplies Immunohematological Testing Instrumentation Blood Flowmeters Implantables Blood Gas Analyzers and Monitors Incontinence Products Blood Pressure Measuring Equipment Infection Control Products Blood Processing Equipment Infusion Devices Calibration and Test Equipment Injectors Cardiac Assist Equipment Kits and Trays Cardiac Pacemakers Laboratory Data Processing Equipment Cardiopulmonary Diagnostic Equipment Laboratory Equipment/Supplies Cardiovascular Accessories Laboratory Glass and Plastic Ware Cell Culturing Systems Laboratory Incubators Centrifuges Laboratory Ware Clinical Laboratory Products Laminar Flow Stations Coagulation Testing Equipment Lamps and Lighting Equipment Computed Tomography (CT) Scanners Lasers Contraceptive Devices Life Support Systems Cryosurgical Equipment Lithotripters Culture Media Lung Function Testing Equipment Defibrillators Magnetic Resonance Imaging (MRI) Equipment Diagnostic Imaging Products Manikins Diagnostic Reagents and Test Kits Mass Spectrometers Digital Subtraction Radiography Equipment Materials Handling Systems Dilutors and Dispensers Medical Communications Systems Dressings and Bandages Medical Data Processing Equipment Electrocardiographs Medical Data Processing Software Systems Electrochemical/Biochemical Sensors Medical Educational and Training Products and Supplies Electrodes, Cables, Leads, and Gels Medical Electronic Diagnostic Equipment Electroencephalographs Medical Equipment Power Sources Electrolyte Analysis Equipment Medical Gasses and Equipment Electromedical Apparatus Medical Linens and Apparel Electromyographs Medical Transportation Electron Microscopes Medical/Surgical Gloves Electronic Blood Cell Counters Medical/Surgical/Hospital Supplies Electronic Thermometers Microbiological and Serological Testing Equipment Electrosurgical Instruments and Accessories Microporous Membrane and Other Filters

11 Microscopy Accessories Microtomes Neonatal Incubators Neurostimulators Nuclear Diagnostic Equipment Nuclear Instruments Nuclear Supplies and Accessories Nucleic Acid/Peptide Synthesizers Neonatal Care Products Operating Tables Optical Microscopes Orthopedic Devices and Appliances Orthopedic Instruments Ostomy Appliances and Supplies Other Medical Equipment Oxygen Therapy Equipment Pacemaker Accessories Pathology Tissue Processors Patient Comfort Aids and Appliances Patient Identification Products and Services Patient Monitoring Equipment and Accessories Patient Restraint Products Patient Transport Systems Patient Weighing Equipment Penile Prosthetic Devices Physical Therapy and Rehabilitation Equipment Physicians' Aids Physicians' Office Testing Equipment Physiological Testing Equipment and Recorders Physiological Therapeutic Equipment Prosthetic Devices Pulmonary Function Testing Equipment Pumps Radiation Therapy Equipment Radioimmunoassay Test Kits Radiological and Nuclear Equipment Radiology/Nuclear Laboratory Data Systems Recorder Paper Charts and Records Renal Dialysis Equipment Renal Dialysis Supplies Renal Dialyzer Reprocessing Equipment Respiratory Gas Analyzers Respiratory Therapy Equipment Scintillation Counting Equipment Separation Products; Chromatography & Electrophoresis Equip. Special Medical Vehicles Specialty Beds Specialty Tables and Chairs Spectrophotometers, Colorimeters, Fluorometers, Nephelometers Sterile Packaging Materials Sterilizing Equipment and Supplies Suction Machines Supply and Other Carts and Cabinets Surgical and Obstetric Drapes Sutures and Fasteners Syringes and Needles Staining Machines Telemetry Equipment Thermographic Diagnostic Equipment Thermometers Tubings, Tubes and Catheters Ultrasonic and Other Transducers and Accessories Ultrasonic Diagnostic Equipment Ultrasonic Instrumentation Urological Equipment Water Treatment Equipment Wheelchairs, Manual Wheelchairs, Motorized X-Ray Apparatus X-Ray Developing Solutions Recovery Equipment X-Ray Film X-Ray Film Loading, Processing and Handling Equipment X-Ray Record Storage and Retrieval Equipment X-Ray Supplies and Accessories X-Ray Tables 3

12 Appendix : Testing a U-shape Relationship Below are the statistical tests to appropriately test for a U shape relationship between degree of reorganization and degree of innovation. These methods are based on the suggestions of Lind and Mehlum (007) that suggest not only (A) checking the coefficient estimates for their magnitude and significance, but also checking the appropriateness of (B) slopes at the extreme points and (C) the inflection point of the estimated U curve. Below, I recreate their tests (shown in their Table 1) using estimates from my Model 8 of Table 4. (A) COEFFICIENTS Model 8 supports Hypothesis 1B which predicts a U shape relationship. The main X term is reorganization (reorg) with estimated coeff β (beta), and the X-squared term is reorganization (sq_reorg) with estimated coeff γ (gamma). Reorganization β = (0.107)** Squared_Reorg γ = (0.006)** Standard errors in parentheses. Significant estimates: ~ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001) Thus, the X and X terms have the expected negative and positive, respectively, magnitudes to support a U-shape. The estimates are both significant. (B) SLOPES (1) Test the slopes of the extreme points for appropriate magnitude and significance: Left side extreme point (x low = 0) Magnitude: Slope at x low β+γx low = Test H0: β+γx low = 0 This is the correct expected magnitude (negative slope for left point of U shape).. test (reort1+(*sq_reort1*0))=0 ( 1) [innovt]reort1 = 0 chi( 1) = 6.98 Prob > chi = This is a two-tailed test. The p-value is less than.008, thus we can reject the alternative hypothesis that the left slope is zero.

13 Right side extreme point (x high = 6) Magnitude: Slope at x high β+γx high = Test H0: β+γx high = 0 This is the correct expected magnitude (positive slope for right point of U shape).. test (reort1+(*sq_reort1*6))=0 ( 1) [innovt]reort1 + 5 [innovt]sq_reort1=0 chi( 1) = 6.45 Prob > chi = This is a two-tailed test. The p-value is less than.011, thus we can reject the alternative hypothesis that the right slope is zero. () Sasabuchi test for true U shape: The true alternative of a U-shape is that the slope at the left extreme is not negative (slope >=0) and/or the slope at the right extreme is not positive (slope <=0). To test this, we need to perform one-tailed tests of the alternative hypothesis for each extreme point separately. Note that the square-root of the chi distribution is equivalent to the standard normal distribution. The z statistic is then equivalent to the square_root of chi, multiplied by the sign of the expression being tested (β+γx low has a negative sign, β+γx high has a positive sign). Left side extreme point (x low = 0) Test H0: β+γx low >= 0. test (reort1+(*sq_reort1*0))=0 ( 1) [innovt]reort1 = 0 chi( 1) = 6.98 Prob > chi = display normal(-1*sqrt(r(chi))) This is a one-tailed test; -1 represents the sign of the expression β+γx low. The p- value is less than.004, thus we can reject the alternative hypothesis that the left slope is positive. Right side extreme point (x high = 6) Test H0: β+γx high <= 0

14 . test (reort1+(*sq_reort1*6))=0 ( 1) [innovt]reort1 + 5 [innovt]sq_reort1=0 chi( 1) = 6.45 Prob > chi = display 1-(normal(1*sqrt(r(chi)))) This is a one-tailed test; 1 represents the sign of the expression β+γx high. The p- value is less than.006, thus we can reject the alternative hypothesis that the right slope is negative. (C) INFLECTION POINT (1) Calculate the ( extremum ) inflection point and compare to estimates for appropriate magnitude Estimated inflection point = 8 reorganizations (from Figure 5 based on Model 8 estimates). Calculated inflection point is at x = -β/γ =.83/(*.017) = 8.3. Since reorganizations are discreet integers this calculated inflection point matches the estimated inflection point of 8. () Calculate 95% confidence interval for the inflection point using Fieller or delta method: To calculate confidence intervals for ratio estimates, the Fieller method is more appropriate than the delta method when dealing with finite samples (Beyene and Moineddin, 005; Lind and Mehlum, 007). Below, I calculate the Fieller method confidence interval at 95% from the formula provided by Beyene and Moineddin (005). Recall that the confidence interval of interest is around the x-value of the inflection point, where x = -β/γ = ½(-β/γ) Let θ = -β/γ = (later we ll cut the interval in half) Let α =.05 Equation 1: (1-α)% Fieller confidence interval for θ: θ + 1/ k V1 Z / (1 ) α V θ + ± V + θv + θ V k V k V γ k V

15 Where the matrix below represents variance-covariance of estimates for β (reorganization) and γ (squared_reorg) from Model 8: V 1 = V 1 =V 1 V 1 = V = And Z α / = V And k = Zα / = γ Plugging in all of the appropriate values noted above into Equation 1 yields: For θ = -β/γ: 95% confidence interval of [9.50, 7.10] and For x = ½ θ = -β/γ : 95% confidence interval of [4.75, 13.55] Thus, the estimated inflection point of 8 is within the confidence interval for the calculated inflection point. References Beyene, J. and R. Moineddin (005). "Methods for confidence interval estimation of a ratio parameter with application to location quotients." BMC Medical Research Methodology 5: Lind, J. T. and H. Mehlum (007). With or without U? The appropriate test for a U shaped relationship. Working paper, Univerity of Oslo, Norway.

16 Appendix 1: Medical Sector Categories and Product Lines A. Healthcare services B. Ophthalmic devices Ambulatory (Holter) Monitoring Services Contact Lenses Ambulatory Care Facility Management Services Biomolecular Research and Development Clinical Laboratory Testing Services Consulting and Planning Services Contract Research Services; Medical R&D Services Dental Facility Management Services Dental Laboratory Services Diagnostic Imaging Services Disinfection Services, Equipment and Supplies Emergency Medical Services Employment Services Environmental Testing Services Food Service and Catering Operations Health Care Cost Management Health Maintenance Organization (HMO) Management Services Home Health Care Services Hospital Department Management Services Hospital Management Services Hospital Supplies Distribution Hospital/Medical Facility Financing, Planning and Construction Housekeeping and Laundry Services Instrument Refurbishing and Reconditioning Services Instrument Repair and Maintenance Services Laboratory Animals Leasing and Rental Services Medical and Health Insurance Medical Clinic Management Services Medical Data Processing Services Medical Educational and Training Services Nephrology Treatment Services Nursing Home Management Services Optometric Services Other Medical Services Outpatient Facility Management Outpatient Medical and Surgical Services Packaging Services Pharmaceutical Services Preferred Provider Organization (PPO) Management Radiological Monitoring Services Radiological Testing Services Rehabilitation Services Respiratory Therapy Services Sterilization Services Transtelephonic Electrocardiogram Analysis Services Waste Disposal Services, Equipment and Supplies Eyeglass Frames and Lenses Intraocular Lenses Ophthalmic Diagnostic Equipment Ophthalmic Supplies and Accessories Optical Products Opticians' Apparatus C. Pharmaceutical products Animal Products Biochemicals, Chemicals and Related Medical Chemicals Biologicals Biomaterials Blood and Blood Products Consumable Products Chemicals Dietary, Nutritional and Vitamin Supplements Drug Delivery Systems Parenteral and Irrigating Solutions Pharmaceutical Apparatus and Supplies Pharmaceuticals, Drugs and Medicines Radioisotopes Radiopaque Contrast Media Radiopharmaceuticals Veterinary Products D. Dental devices Dental Equipment Dental Products Dental Prosthetics Dental Supplies Dental X-Ray Apparatus

17 E. Medical devices Emergency Medical Products Ambulatory (Holter) Monitoring Equipment Endoscopes, Arthroscopes and Related Products Analytical Balances Enteral and Parenteral Hyperalimentation Products Analytical Imaging Equipment Environmentally Controlled Enclosures Analytical Instrument Data Systems Evacuation and Filtration Equipment Analytical Instruments Fermenters, Freeze-Dryers/Processing Equipment Anesthesia Equipment and Accessories Fiberoptic Examining Scopes Animal Equipment and Supplies Freezers and Refrigeration Equipment Anti-Embolism Devices Furniture and Casework Appliances and Utility Equipment Gamma Cameras Arterial Grafts Gas Chromatographs Artificial Voice Devices General Disposables Auditory Testing Equipment Hearing Aid Accessories Automated Cell Sorters Hearing Aids Automated Chemistry Analyzers Heart Valves Automated Immunoassay Systems Heart/Lung Machines Automated Liquid Chromatography Analyzers Home Care Equipment and Supplies Automated Microbiology Analyzers Hyperbaric Chambers Automatic Slide Stainers Hypo/Hyperthermia Therapy Equipment Biofeedback Equipment Image Recording Systems Blood Collection Supplies Immunohematological Testing Instrumentation Blood Flowmeters Implantables Blood Gas Analyzers and Monitors Incontinence Products Blood Pressure Measuring Equipment Infection Control Products Blood Processing Equipment Infusion Devices Calibration and Test Equipment Injectors Cardiac Assist Equipment Kits and Trays Cardiac Pacemakers Laboratory Data Processing Equipment Cardiopulmonary Diagnostic Equipment Laboratory Equipment/Supplies Cardiovascular Accessories Laboratory Glass and Plastic Ware Cell Culturing Systems Laboratory Incubators Centrifuges Laboratory Ware Clinical Laboratory Products Laminar Flow Stations Coagulation Testing Equipment Lamps and Lighting Equipment Computed Tomography (CT) Scanners Lasers Contraceptive Devices Life Support Systems Cryosurgical Equipment Lithotripters Culture Media Lung Function Testing Equipment Defibrillators Magnetic Resonance Imaging (MRI) Equipment Diagnostic Imaging Products Manikins Diagnostic Reagents and Test Kits Mass Spectrometers Digital Subtraction Radiography Equipment Materials Handling Systems Dilutors and Dispensers Medical Communications Systems Dressings and Bandages Medical Data Processing Equipment Electrocardiographs Medical Data Processing Software Systems Electrochemical/Biochemical Sensors Medical Educational and Training Products and Supplies Electrodes, Cables, Leads, and Gels Medical Electronic Diagnostic Equipment Electroencephalographs Medical Equipment Power Sources Electrolyte Analysis Equipment Medical Gasses and Equipment Electromedical Apparatus Medical Linens and Apparel Electromyographs Medical Transportation Electron Microscopes Medical/Surgical Gloves Electronic Blood Cell Counters Medical/Surgical/Hospital Supplies Electronic Thermometers Microbiological and Serological Testing Equipment Electrosurgical Instruments and Accessories Microporous Membrane and Other Filters

18 Microscopy Accessories Microtomes Neonatal Incubators Neurostimulators Nuclear Diagnostic Equipment Nuclear Instruments Nuclear Supplies and Accessories Nucleic Acid/Peptide Synthesizers Neonatal Care Products Operating Tables Optical Microscopes Orthopedic Devices and Appliances Orthopedic Instruments Ostomy Appliances and Supplies Other Medical Equipment Oxygen Therapy Equipment Pacemaker Accessories Pathology Tissue Processors Patient Comfort Aids and Appliances Patient Identification Products and Services Patient Monitoring Equipment and Accessories Patient Restraint Products Patient Transport Systems Patient Weighing Equipment Penile Prosthetic Devices Physical Therapy and Rehabilitation Equipment Physicians' Aids Physicians' Office Testing Equipment Physiological Testing Equipment and Recorders Physiological Therapeutic Equipment Prosthetic Devices Pulmonary Function Testing Equipment Pumps Radiation Therapy Equipment Radioimmunoassay Test Kits Radiological and Nuclear Equipment Radiology/Nuclear Laboratory Data Systems Recorder Paper Charts and Records Renal Dialysis Equipment Renal Dialysis Supplies Renal Dialyzer Reprocessing Equipment Respiratory Gas Analyzers Respiratory Therapy Equipment Scintillation Counting Equipment Separation Products; Chromatography & Electrophoresis Equip. Special Medical Vehicles Specialty Beds Specialty Tables and Chairs Spectrophotometers, Colorimeters, Fluorometers, Nephelometers Sterile Packaging Materials Sterilizing Equipment and Supplies Suction Machines Supply and Other Carts and Cabinets Surgical and Obstetric Drapes Sutures and Fasteners Syringes and Needles Staining Machines Telemetry Equipment Thermographic Diagnostic Equipment Thermometers Tubings, Tubes and Catheters Ultrasonic and Other Transducers and Accessories Ultrasonic Diagnostic Equipment Ultrasonic Instrumentation Urological Equipment Water Treatment Equipment Wheelchairs, Manual Wheelchairs, Motorized X-Ray Apparatus X-Ray Developing Solutions Recovery Equipment X-Ray Film X-Ray Film Loading, Processing and Handling Equipment X-Ray Record Storage and Retrieval Equipment X-Ray Supplies and Accessories X-Ray Tables 3

19 Appendix : Testing a U-shape Relationship Below are the statistical tests to appropriately test for a U shape relationship between degree of reorganization and degree of innovation. These methods are based on the suggestions of Lind and Mehlum (007) that suggest not only (A) checking the coefficient estimates for their magnitude and significance, but also checking the appropriateness of (B) slopes at the extreme points and (C) the inflection point of the estimated U curve. Below, I recreate their tests (shown in their Table 1) using estimates from my Model 8 of Table 4. (A) COEFFICIENTS Model 8 supports Hypothesis 1B which predicts a U shape relationship. The main X term is reorganization (reorg) with estimated coeff β (beta), and the X-squared term is reorganization (sq_reorg) with estimated coeff γ (gamma). Reorganization β = (0.107)** Squared_Reorg γ = (0.006)** Standard errors in parentheses. Significant estimates: ~ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001) Thus, the X and X terms have the expected negative and positive, respectively, magnitudes to support a U-shape. The estimates are both significant. (B) SLOPES (1) Test the slopes of the extreme points for appropriate magnitude and significance: Left side extreme point (x low = 0) Magnitude: Slope at x low β+γx low = Test H0: β+γx low = 0 This is the correct expected magnitude (negative slope for left point of U shape).. test (reort1+(*sq_reort1*0))=0 ( 1) [innovt]reort1 = 0 chi( 1) = 6.98 Prob > chi = This is a two-tailed test. The p-value is less than.008, thus we can reject the alternative hypothesis that the left slope is zero.

20 Right side extreme point (x high = 6) Magnitude: Slope at x high β+γx high = Test H0: β+γx high = 0 This is the correct expected magnitude (positive slope for right point of U shape).. test (reort1+(*sq_reort1*6))=0 ( 1) [innovt]reort1 + 5 [innovt]sq_reort1=0 chi( 1) = 6.45 Prob > chi = This is a two-tailed test. The p-value is less than.011, thus we can reject the alternative hypothesis that the right slope is zero. () Sasabuchi test for true U shape: The true alternative of a U-shape is that the slope at the left extreme is not negative (slope >=0) and/or the slope at the right extreme is not positive (slope <=0). To test this, we need to perform one-tailed tests of the alternative hypothesis for each extreme point separately. Note that the square-root of the chi distribution is equivalent to the standard normal distribution. The z statistic is then equivalent to the square_root of chi, multiplied by the sign of the expression being tested (β+γx low has a negative sign, β+γx high has a positive sign). Left side extreme point (x low = 0) Test H0: β+γx low >= 0. test (reort1+(*sq_reort1*0))=0 ( 1) [innovt]reort1 = 0 chi( 1) = 6.98 Prob > chi = display normal(-1*sqrt(r(chi))) This is a one-tailed test; -1 represents the sign of the expression β+γx low. The p- value is less than.004, thus we can reject the alternative hypothesis that the left slope is positive. Right side extreme point (x high = 6) Test H0: β+γx high <= 0

21 . test (reort1+(*sq_reort1*6))=0 ( 1) [innovt]reort1 + 5 [innovt]sq_reort1=0 chi( 1) = 6.45 Prob > chi = display 1-(normal(1*sqrt(r(chi)))) This is a one-tailed test; 1 represents the sign of the expression β+γx high. The p- value is less than.006, thus we can reject the alternative hypothesis that the right slope is negative. (C) INFLECTION POINT (1) Calculate the ( extremum ) inflection point and compare to estimates for appropriate magnitude Estimated inflection point = 8 reorganizations (from Figure 5 based on Model 8 estimates). Calculated inflection point is at x = -β/γ =.83/(*.017) = 8.3. Since reorganizations are discreet integers this calculated inflection point matches the estimated inflection point of 8. () Calculate 95% confidence interval for the inflection point using Fieller or delta method: To calculate confidence intervals for ratio estimates, the Fieller method is more appropriate than the delta method when dealing with finite samples (Beyene and Moineddin, 005; Lind and Mehlum, 007). Below, I calculate the Fieller method confidence interval at 95% from the formula provided by Beyene and Moineddin (005). Recall that the confidence interval of interest is around the x-value of the inflection point, where x = -β/γ = ½(-β/γ) Let θ = -β/γ = (later we ll cut the interval in half) Let α =.05 Equation 1: (1-α)% Fieller confidence interval for θ: θ + 1/ k V1 Z / (1 ) α V θ + ± V + θv + θ V k V k V γ k V

22 Where the matrix below represents variance-covariance of estimates for β (reorganization) and γ (squared_reorg) from Model 8: V 1 = V 1 =V 1 V 1 = V = And Z α / = V And k = Zα / = γ Plugging in all of the appropriate values noted above into Equation 1 yields: For θ = -β/γ: 95% confidence interval of [9.50, 7.10] and For x = ½ θ = -β/γ : 95% confidence interval of [4.75, 13.55] Thus, the estimated inflection point of 8 is within the confidence interval for the calculated inflection point. References Beyene, J. and R. Moineddin (005). "Methods for confidence interval estimation of a ratio parameter with application to location quotients." BMC Medical Research Methodology 5: Lind, J. T. and H. Mehlum (007). With or without U? The appropriate test for a U shaped relationship. Working paper, Univerity of Oslo, Norway.

23 Appendix 1: Medical Sector Categories and Product Lines A. Healthcare services B. Ophthalmic devices Ambulatory (Holter) Monitoring Services Contact Lenses Ambulatory Care Facility Management Services Biomolecular Research and Development Clinical Laboratory Testing Services Consulting and Planning Services Contract Research Services; Medical R&D Services Dental Facility Management Services Dental Laboratory Services Diagnostic Imaging Services Disinfection Services, Equipment and Supplies Emergency Medical Services Employment Services Environmental Testing Services Food Service and Catering Operations Health Care Cost Management Health Maintenance Organization (HMO) Management Services Home Health Care Services Hospital Department Management Services Hospital Management Services Hospital Supplies Distribution Hospital/Medical Facility Financing, Planning and Construction Housekeeping and Laundry Services Instrument Refurbishing and Reconditioning Services Instrument Repair and Maintenance Services Laboratory Animals Leasing and Rental Services Medical and Health Insurance Medical Clinic Management Services Medical Data Processing Services Medical Educational and Training Services Nephrology Treatment Services Nursing Home Management Services Optometric Services Other Medical Services Outpatient Facility Management Outpatient Medical and Surgical Services Packaging Services Pharmaceutical Services Preferred Provider Organization (PPO) Management Radiological Monitoring Services Radiological Testing Services Rehabilitation Services Respiratory Therapy Services Sterilization Services Transtelephonic Electrocardiogram Analysis Services Waste Disposal Services, Equipment and Supplies Eyeglass Frames and Lenses Intraocular Lenses Ophthalmic Diagnostic Equipment Ophthalmic Supplies and Accessories Optical Products Opticians' Apparatus C. Pharmaceutical products Animal Products Biochemicals, Chemicals and Related Medical Chemicals Biologicals Biomaterials Blood and Blood Products Consumable Products Chemicals Dietary, Nutritional and Vitamin Supplements Drug Delivery Systems Parenteral and Irrigating Solutions Pharmaceutical Apparatus and Supplies Pharmaceuticals, Drugs and Medicines Radioisotopes Radiopaque Contrast Media Radiopharmaceuticals Veterinary Products D. Dental devices Dental Equipment Dental Products Dental Prosthetics Dental Supplies Dental X-Ray Apparatus

24 E. Medical devices Emergency Medical Products Ambulatory (Holter) Monitoring Equipment Endoscopes, Arthroscopes and Related Products Analytical Balances Enteral and Parenteral Hyperalimentation Products Analytical Imaging Equipment Environmentally Controlled Enclosures Analytical Instrument Data Systems Evacuation and Filtration Equipment Analytical Instruments Fermenters, Freeze-Dryers/Processing Equipment Anesthesia Equipment and Accessories Fiberoptic Examining Scopes Animal Equipment and Supplies Freezers and Refrigeration Equipment Anti-Embolism Devices Furniture and Casework Appliances and Utility Equipment Gamma Cameras Arterial Grafts Gas Chromatographs Artificial Voice Devices General Disposables Auditory Testing Equipment Hearing Aid Accessories Automated Cell Sorters Hearing Aids Automated Chemistry Analyzers Heart Valves Automated Immunoassay Systems Heart/Lung Machines Automated Liquid Chromatography Analyzers Home Care Equipment and Supplies Automated Microbiology Analyzers Hyperbaric Chambers Automatic Slide Stainers Hypo/Hyperthermia Therapy Equipment Biofeedback Equipment Image Recording Systems Blood Collection Supplies Immunohematological Testing Instrumentation Blood Flowmeters Implantables Blood Gas Analyzers and Monitors Incontinence Products Blood Pressure Measuring Equipment Infection Control Products Blood Processing Equipment Infusion Devices Calibration and Test Equipment Injectors Cardiac Assist Equipment Kits and Trays Cardiac Pacemakers Laboratory Data Processing Equipment Cardiopulmonary Diagnostic Equipment Laboratory Equipment/Supplies Cardiovascular Accessories Laboratory Glass and Plastic Ware Cell Culturing Systems Laboratory Incubators Centrifuges Laboratory Ware Clinical Laboratory Products Laminar Flow Stations Coagulation Testing Equipment Lamps and Lighting Equipment Computed Tomography (CT) Scanners Lasers Contraceptive Devices Life Support Systems Cryosurgical Equipment Lithotripters Culture Media Lung Function Testing Equipment Defibrillators Magnetic Resonance Imaging (MRI) Equipment Diagnostic Imaging Products Manikins Diagnostic Reagents and Test Kits Mass Spectrometers Digital Subtraction Radiography Equipment Materials Handling Systems Dilutors and Dispensers Medical Communications Systems Dressings and Bandages Medical Data Processing Equipment Electrocardiographs Medical Data Processing Software Systems Electrochemical/Biochemical Sensors Medical Educational and Training Products and Supplies Electrodes, Cables, Leads, and Gels Medical Electronic Diagnostic Equipment Electroencephalographs Medical Equipment Power Sources Electrolyte Analysis Equipment Medical Gasses and Equipment Electromedical Apparatus Medical Linens and Apparel Electromyographs Medical Transportation Electron Microscopes Medical/Surgical Gloves Electronic Blood Cell Counters Medical/Surgical/Hospital Supplies Electronic Thermometers Microbiological and Serological Testing Equipment Electrosurgical Instruments and Accessories Microporous Membrane and Other Filters

25 Microscopy Accessories Microtomes Neonatal Incubators Neurostimulators Nuclear Diagnostic Equipment Nuclear Instruments Nuclear Supplies and Accessories Nucleic Acid/Peptide Synthesizers Neonatal Care Products Operating Tables Optical Microscopes Orthopedic Devices and Appliances Orthopedic Instruments Ostomy Appliances and Supplies Other Medical Equipment Oxygen Therapy Equipment Pacemaker Accessories Pathology Tissue Processors Patient Comfort Aids and Appliances Patient Identification Products and Services Patient Monitoring Equipment and Accessories Patient Restraint Products Patient Transport Systems Patient Weighing Equipment Penile Prosthetic Devices Physical Therapy and Rehabilitation Equipment Physicians' Aids Physicians' Office Testing Equipment Physiological Testing Equipment and Recorders Physiological Therapeutic Equipment Prosthetic Devices Pulmonary Function Testing Equipment Pumps Radiation Therapy Equipment Radioimmunoassay Test Kits Radiological and Nuclear Equipment Radiology/Nuclear Laboratory Data Systems Recorder Paper Charts and Records Renal Dialysis Equipment Renal Dialysis Supplies Renal Dialyzer Reprocessing Equipment Respiratory Gas Analyzers Respiratory Therapy Equipment Scintillation Counting Equipment Separation Products; Chromatography & Electrophoresis Equip. Special Medical Vehicles Specialty Beds Specialty Tables and Chairs Spectrophotometers, Colorimeters, Fluorometers, Nephelometers Sterile Packaging Materials Sterilizing Equipment and Supplies Suction Machines Supply and Other Carts and Cabinets Surgical and Obstetric Drapes Sutures and Fasteners Syringes and Needles Staining Machines Telemetry Equipment Thermographic Diagnostic Equipment Thermometers Tubings, Tubes and Catheters Ultrasonic and Other Transducers and Accessories Ultrasonic Diagnostic Equipment Ultrasonic Instrumentation Urological Equipment Water Treatment Equipment Wheelchairs, Manual Wheelchairs, Motorized X-Ray Apparatus X-Ray Developing Solutions Recovery Equipment X-Ray Film X-Ray Film Loading, Processing and Handling Equipment X-Ray Record Storage and Retrieval Equipment X-Ray Supplies and Accessories X-Ray Tables 3

26 Appendix : Testing a U-shape Relationship Below are the statistical tests to appropriately test for a U shape relationship between degree of reorganization and degree of innovation. These methods are based on the suggestions of Lind and Mehlum (007) that suggest not only (A) checking the coefficient estimates for their magnitude and significance, but also checking the appropriateness of (B) slopes at the extreme points and (C) the inflection point of the estimated U curve. Below, I recreate their tests (shown in their Table 1) using estimates from my Model 8 of Table 4. (A) COEFFICIENTS Model 8 supports Hypothesis 1B which predicts a U shape relationship. The main X term is reorganization (reorg) with estimated coeff β (beta), and the X-squared term is reorganization (sq_reorg) with estimated coeff γ (gamma). Reorganization β = (0.107)** Squared_Reorg γ = (0.006)** Standard errors in parentheses. Significant estimates: ~ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001) Thus, the X and X terms have the expected negative and positive, respectively, magnitudes to support a U-shape. The estimates are both significant. (B) SLOPES (1) Test the slopes of the extreme points for appropriate magnitude and significance: Left side extreme point (x low = 0) Magnitude: Slope at x low β+γx low = Test H0: β+γx low = 0 This is the correct expected magnitude (negative slope for left point of U shape).. test (reort1+(*sq_reort1*0))=0 ( 1) [innovt]reort1 = 0 chi( 1) = 6.98 Prob > chi = This is a two-tailed test. The p-value is less than.008, thus we can reject the alternative hypothesis that the left slope is zero.

27 Right side extreme point (x high = 6) Magnitude: Slope at x high β+γx high = Test H0: β+γx high = 0 This is the correct expected magnitude (positive slope for right point of U shape).. test (reort1+(*sq_reort1*6))=0 ( 1) [innovt]reort1 + 5 [innovt]sq_reort1=0 chi( 1) = 6.45 Prob > chi = This is a two-tailed test. The p-value is less than.011, thus we can reject the alternative hypothesis that the right slope is zero. () Sasabuchi test for true U shape: The true alternative of a U-shape is that the slope at the left extreme is not negative (slope >=0) and/or the slope at the right extreme is not positive (slope <=0). To test this, we need to perform one-tailed tests of the alternative hypothesis for each extreme point separately. Note that the square-root of the chi distribution is equivalent to the standard normal distribution. The z statistic is then equivalent to the square_root of chi, multiplied by the sign of the expression being tested (β+γx low has a negative sign, β+γx high has a positive sign). Left side extreme point (x low = 0) Test H0: β+γx low >= 0. test (reort1+(*sq_reort1*0))=0 ( 1) [innovt]reort1 = 0 chi( 1) = 6.98 Prob > chi = display normal(-1*sqrt(r(chi))) This is a one-tailed test; -1 represents the sign of the expression β+γx low. The p- value is less than.004, thus we can reject the alternative hypothesis that the left slope is positive. Right side extreme point (x high = 6) Test H0: β+γx high <= 0