Essays in modeling health care expenditures with a focus on singapore

ESSAYS IN MODELING HEALTH CARE EXPENDITURES WITH A FOCUS ON SINGAPORE HIMANI AGGARWAL B.A.(Hons.), M.A., M.Phil. A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ECONOMICS NATIONAL UNIVERSITY OF SINGAPORE 2010 i Acknowledgements First and foremost, I would like to thank my thesis advisor Associate Prof. Tilak Abeysinghe for his invaluable guidance, patience and support rendered during the past four years. It has been a real pleasure working with him. I would especially like to thank Dr. Jeremy Lim (Senior Consultant, Singapore General Hospital) for his grant support in getting access to the patient data and for giving a health service provider’s perspective. I am extremely thankful to Prof. Ake G. Blomqvist for the numerous discussions that I had with him during the course of my PhD work. I have learnt a lot from him. I am also thankful to Associate Prof. Chia Ngee Choon for insightful suggestions on Singapore’s health care system. I am grateful to Prof. Willard Manning (University of Chicago) who promptly replied to emails from a stranger that were full of queries on modeling health expenditure distributions. My thanks are also due to the three examiners of the thesis for their valuable comments that led to this revised version of the thesis. Last but not the least, I wish to thank my family, friends and fellow students at the Department of Economics for their love, care and support. This journey would not have been as enjoyable without them. i Table of Contents Acknowledgements i Table of Contents ii Summary iv List of Tables vii List of Figures ix Chapter 1: Introduction . 1.1 Background . 1.2 Singapore’s Health Care Delivery System . 1.3 Singapore’s Health Care Financing System . 1.3.1 Medical Savings Accounts (Medisave) . 1.3.2 Government Health Insurance (MediShield) . 1.3.3 Medifund 1.3.4 Government Subsidies . 1.4 Ageing Population 1.4.1 Policy Measures in Response to Ageing Population . 12 1.4.2 Financing of Health Care of the Elderly 14 1.5 The Focus of the Thesis 15 Chapter 2: How the Elderly Singaporeans Pay for their Hospitalization in Singapore? 17 2.1 Introduction . 17 2.2 Description of Data . 24 2.3 Results and Analysis . 25 2.3.1 Government Subsidies . 25 2.3.2 Inpatient Expenditure . 26 2.3.2 Length of Stay (LOS) . 28 2.3.4 Financing of Inpatient Expenditure . 29 2.4 Concluding Remarks and Limitations 37 Chapter 3: Modeling Skewed and Heavy-Tailed Inpatient Expenditure of the Elderly in Singapore 42 3.1 Introduction . 42 3.2 Objective . 46 3.3 Modeling Techniques 47 3.3.1 Ordinary Least Square (OLS) on ln(Yi) Model 47 3.3.2 Generalized Linear Model (GLM) . 50 3.3.3 Extended Estimating Equation (EEE) Model 54 3.4 Description of Data and Variables 57 3.5 Overview of Model Selection Procedure 59 3.6 Estimation Results 61 3.6.1 Ordinary Least Square (OLS) on ln(Yi) Model 63 3.6.2 Generalized Linear Model (GLM) . 67 3.6.3 Extended Estimating Equation (EEE) Model 69 3.7 Split-Sample Cross-Validation . 72 3.8 Comparison of Different Models 73 3.9 Marginal and Incremental Effects 75 ii 3.10 Conclusion 79 Chapter 4: Modeling Risk of Catastrophic Inpatient Expenditure of the Elderly in Singapore 81 4.1 Introduction . 81 4.2 Statistical Methodology 85 4.2.1 Pareto Distribution . 85 4.2.2 Lognormal Distribution . 87 4.3 Description of Data . 90 4.4 Estimation Results 93 4.4.1 Fitting Univariate Distribution . 93 4.4.2 Conditional Shape Parameters . 99 4.4.3 Probabilities of Catastrophic Expenditure by Insurance Status and Primary Diagnosis . 105 4.4.4 Probability of Catastrophic Expenditure for Some Most Expensive DiseasesDisaggregated Analysis 108 4.5 Conclusion 115 Chapter 5: Optimal Deductible: A Simulation Approach . 118 5.1 Introduction . 118 5.2 The Theoretical Model 125 5.3 Optimal Deductible for Non-elderly Families under Rand HIE . 132 5.3.1 Description of Rand HIE . 132 5.3.2 Operational Implementation 133 5.3.3 Numerical Results 136 5.4 Optimal Deductible for the Elderly, Singapore 139 5.4.1 Description of Data 139 5.4.2 Operational Implementation 139 5.4.3 Numerical Results 141 5.5 Conclusion 145 Appendix A . 147 A.1 Picking a Model: Box-Cox test . 147 A.2 Checking for Heteroscedasticity: Park test- GLM version 147 A.3 Checking Model Fit for Linearity: Modified Hosmer-Lemeshow Test 148 A.4 Test of Overfitting: Copas Test 148 A.5 Marginal and Incremental Effects 149 Appendix B . 151 B.1 Results: OLS on ln(Yi) 151 B.2 Results: GLM Model with Log link and Gamma family . 153 B.3 Results: EEE model 155 B.4: Results: GLM with Power Link and Gamma Family . 157 Appendix C . 159 Appendix D . 161 D.1 Calibration of Parameters, Rand Data 161 Appendix E . 163 E.1 Simulation Methodology for the Optimal Deductible Values, Rand Data . 163 Bibliography . 165 iii Summary Modeling and predicting both average and extreme hospitalization expenditures and financing health care expenditures within the Singapore context are the key issues addressed in this thesis. As a precursor to modeling, the first essay (second chapter) examines how the elderly Singaporeans offset their hospital bill. The government subsidy that a patient receives, on average, covers 60% of the total charges of a hospitalization episode. After accounting for the government subsidy, medical savings accounts of the patient and family member, together, offset about 68% of the subsidized hospital bill. The contribution of insurance (both the government and private) is small, covering only 15% of the subsidized bill. Direct out-of-pocket payment comprises 6.3% of the subsidized bill. The second essay (third chapter) explores the best model to predict the mean inpatient expenditure incurred by the elderly Singaporeans and estimates the impact of various covariates such as demographic characteristics, clinical factors, outcome of hospitalization, length of stay, insurance status on mean expenditure via marginal and incremental effects. The findings show that, compared to ward C, the average bill of a hospitalization episode in ward A is higher by S$8,241 and the bill in ward B1 is higher by S$5,686. The difference between ward B2 and ward C bills narrows down to S$657. In case of a surgical operation, the average bill per episode is approximately S$1,043 more than the episodes without any operation and the difference in case of an implant is S$2,411. The average bill is S$876 more in the event of death of a patient in the hospital. iv For patients who had payouts from the government insurance, other things being equal, the mean expense per admission is S$288 higher than for patients without payout. In case of private health insurance, the difference is S$395. If slope parameters remain the same, the model can be used for out-of-sample predictions through intercept adjustments as the expenditure profile shifts over time. In the third essay (fourth chapter), the probabilities of incurring catastrophic health care expenditures by the elderly Singaporeans are predicted and factors that increase the likelihood of facing such expenditures are determined. The results show that the probability of incurring hospitalization expenditure more than S$10,000 by the elderly with the government insurance varies from 1.7 to 8.8% while the corresponding probability range for the elderly without the government insurance is 0.9 to 4.9%. This difference is more pronounced for private insurance (2.9-10.8% versus 0.9-5.3%). Among different diseases afflicting the elderly, the probability of catastrophic expenditure is highest for musculoskeletal diseases. The oldest old face the lowest probability of catastrophic expenditure. As in the second essay, the model can be adapted for out-of-sample predictions through intercept adjustments. A significant proportion of the elderly are not covered by any health insurance in Singapore. One of the reasons cited for low uptake of the catastrophic illness insurance offered by the government is that it is characterized by high deductibles. In the fourth essay (fifth chapter), a simulation model is developed to estimate the size of optimal deductible for the government insurance in Singapore. The result shows that the optimal v deductible is S$1000 (in 2007 dollars) for the base case scenario which matches the deductible component of the government health insurance. vi List of Tables Table 1.1: Comparison of Hospital Ward Classes in Singapore . Table 1.2: Projected Use of Acute Care Services in the Public Sector by Older Persons 11 Table 2.1: Health Spending and Health Status Indicators across Singapore and Selected OECD Countries . 18 Table 2.2: Distribution of Gross Inpatient Expenditure in Different Ward Classes . 27 Table 2.3: Distribution of Net Inpatient Expenditure in Different Ward Classes 27 Table 2.4: Distribution of LOS in Different Ward Classes 28 Table 3.1: Summary Statistics on Inpatient Expenditures of the Elderly Singaporeans (S$, Year 2007) 62 Table 3.2: Summary Statistics on Logarithm of Inpatient Expenditures 63 Table 3.3: Result of Box-Cox Test . 64 Table 3.4: Result of Jarque-Bera Normality Test on ln(Yi) 65 Table 3.5: Result of Breusch-Pagan Test of Heteroscedasticity . 65 Table 3.6: Result of Park Test (GLM Version) of Heteroscedasticity . 65 Table 3.7: Result of Modified Park Test . 68 Table 3.8: Estimates of Link and Variance Function . 69 Table 3.9: Model Performance based on Out-of-Sample Forecasts . 73 Table 3.10: Comparison of Models: Goodness-of-Fit Tests . 74 Table 3.11: Comparison of Models: Test of Overfitting 74 Table 3.12: EEE Model: Marginal Effects (S$, Year 2007) . 78 Table 3.13: EEE Model: Incremental Effects (S$, Year 2007) 78 Table 4.1: Maximum Likelihood Estimate of Shape Parameter of Univariate Pareto Distribution . 94 Table 4.2: Summary Statistics of Fitted Univariate Pareto Distribution 94 Table 4.3: Maximum Likelihood Estimates of Parameters of Univariate Lognormal Distribution . 94 Table 4.4: Summary Statistics of Fitted Univariate Lognormal Distribution . 94 Table 4.5: Results from Fitting Conditional Lognormal Distribution 100 Table 4.6: Conditional σ and α and Probability (%) of Incurring Catastrophic Expenditures . 107 Table 4.7: Probability (%) of Incurring Catastrophic Expenditures for Musculoskeletal Diseases . 110 Table 4.8: Probability (%) of Incurring Catastrophic Expenditures for Malignant Neoplasm 111 Table 4.9: Probability (%) of Incurring Catastrophic Expenditures for Other Circulatory System Diseases 112 Table 4.10: Probability (%) of Incurring Catastrophic Expenditures for Ischemic Heart Diseases . 113 Table 4.11: Probability (%) of Incurring Catastrophic Expenditures for Injuries 114 Table 5.1: Distribution of s from Health Expenditure Distribution under Rand free Plan . 138 Table 5.2: Optimal Annual Deductible for Different Relative Risk Aversion Coefficients, Rand HIE 138 vii Table 5.3: Distributions of s for Different Medical Care Price Elasticites, Singapore. 143 Table 5.4: Optimal Annual Deductible under Different Parameter Assumptions, Singapore 144 Table B.1: Jarque-Bera Normality Test on Residuals 151 Table B.2: Regression Results 151 Table B.3: Goodness-of-Fit Tests . 152 Table B.4: Copas Test . 152 Table B.5: Regression Results 153 Table B.6: Goodness-of-Fit Tests . 154 Table B.7: Copas Test . 154 Table B.8: Regression Results 155 Table B.9: Goodness-of-Fit Tests . 156 Table B.10: Copas Test . 156 Table B.11: Regression Results 157 Table B.12: Goodness-of-Fit Tests . 158 Table B.13: Copas Test . 158 Table C.1: Results from Fitting Conditional Pareto Distribution to Inpatient Expenditure . 159 viii List of Figures Figure 1.1: The Structure of Singapore’s Health Care Financing System Figure 2.1: Government Subsidy by Ward Class 25 Figure 2.2: Shares of Means of Financing Net Inpatient Expenditure . 29 Figure 2.3: Percentage of Elderly who have a Payout from MediShield by Age . 31 Figure 2.4: Percentage of Bill Covered by MediShield for Hospitalization Episodes with a Positive Payout by Ward Class 32 Figure 2.5: Hospitalization Episodes with Payout from Insurance versus Hospitalization Episodes without any Payout: A Comparison of Means of Financing . 33 Figure 2.6: Hospitalization Episodes with Payment from Family Members’ MSA versus Hospitalization Episodes without any such Payment: A Comparison of Means of Financing . 37 Figure 3.1: CDF Plot of Inpatient Expenditures of the Elderly Singaporeans 62 Figure 3.2: Histogram of Logarithm of Inpatient Expenditure of the Elderly Singaporeans . 64 Figure 3.3: Heteroscedasticity in Log-Scale OLS Residuals. . 66 Figure 3.4: Modified Hosmer-Lemeshow Residuals by Deciles of Prediction, OLS on ln(Yi) model . 67 Figure 3.5: Modified Hosmer-Lemeshow Residuals by Deciles of Prediction, GLM with Log Link 68 Figure 3.6: Modified Hosmer-Lemeshow Residuals by Deciles of Prediction, EEE model . 70 Figure 3.7: Modified Hosmer-Lemeshow Residuals by Deciles of Prediction, GLM with Power Link and Gamma Family . 72 Figure 4.1: Histogram Plot of Inpatient Expenditure . 92 Figure 4.2: Kernel Density Plot of Inpatient Expenditure 92 Figure 4.3: Q-Q Plot of Fitted Pareto Distribution . 95 Figure 4.4: Q-Q Plot of Fitted Lognormal Distribution 96 Figure 4.5: Empirical, Fitted Pareto and Lognormal Cumulative Distribution Functions 98 Figure 4.6: Empirical, Fitted Pareto and Lognormal Probability Density Functions . 98 Figure 4.7: Kernel density plot, Fitted Pareto and Lognormal Probability Density Functions . 99 Figure 5.1: An Insurance Plan with Deductible d . 130 ix n  T   f i mi  d  i r where f is the frequency with which a particular  occurs, n is the total number of s and (n-r+1) is the number of s for which the household exceeds the deductible. (d) Since the insurance is assumed to be actuarially fair, the expected value of payout from the insurer should be equal to the premium . If the computed T is not close to the value of  chosen in Step (a) then pick another value of  (keeping the value of d fixed) and repeat Steps (a)-(c) until the difference between T and  falls below the chosen cutoff.99 (e) Repeat steps (a)-(d) for different values of d. n (f) Compute the expected utility for each deductible, i.e., Eu   f i ui where n is i 1 the total number of s. (g) Compare the expected utility associated with each deductible and choose the deductible that generates the highest expected utility. This would constitute the optimal deductible. We use a cutoff point of 3. Thus, T is considered close to  if the difference between them is less than or equal to 3. 99 164 Bibliography 1. Arrow, K.J., 1963. Uncertainty and the welfare economics of medical care. American Economic Review 53 (5), 941-973. 2. Arrow, K.J., 1976. 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Journal of Political Economy 97, 305-346. 179 [...]... premiums are deducted from Medisave The insurance scheme is only available to Singaporeans aged 40-69 years As with any insurance plan, a person with pre-existing disability is not eligible for ElderShield coverage (Ministry of Health, Singapore website13) The structure of Singapore s health care financing system is presented in Figure 1.1 Figure 1.1: The Structure of Singapore s Health Care Financing System... “Check Your Health was launched in 2000 It is a screening program for diabetes, hypertension and high blood cholesterol for people aged 55 years and above These conditions can lead to heart disease and stroke, the major causes of ill health and mortality in Singapore (Ministry of Health, Annual Report 2001, Singapore) (d) Other programs such as Comprehensive Chronic Care Program and Primary Care Partnership... (2001) and Shortt (2002) are made in absence of any data which cast doubt on their reliability In fact, the lack of primary data has been an issue in Singapore case The paper by Chia and Tsui (2005) deserves a special mention in this regard since it uses survey results of a longitudinal study of transition in health and wealth of the elderly to assess the adequacy of Medisave to finance medical expenses... public and private sectors operate on a fee-for-service basis Voluntary welfare organizations are the main suppliers of step-down care Most of these organizations are funded by the government for their services rendered to patients 1.3 Singapore s Health Care Financing System The National Health Plan (NHP) of 1983 and the White paper on affordable health care of 1993 are identified as two key health. .. health care system has attracted enormous attention from academicians and policymakers looking for solutions to contain rising health costs in the developed world Many (Massaro and Wong, 1995; Ham, 1996; Pauly, 2001; Eiff et al., 2002) attribute Singapore s success to its medical savings accounts (Medisave) program which is considered to be the core feature of a multi-pillared health care financing system... illness insurance than it would have been if the country had instituted more comprehensive insurance without personal savings account 19 Another argument advanced by the advocates of MSA (Ham, 1996; Prescott and Nichols, 199826; Phua and Yap, 1998) is that the saving approach resolves the problem of intergenerational transfers that a rapidly ageing society poses in a tax-financed system A major concern in. .. in a pay-as-you go social security system for an ageing society is that the increasing tax burden on a proportionately smaller number of working people to support greater number of the elderly would not be sustainable in the long run In the MSA system, individuals save during their working years in order to finance medical care needs in old age (intertemporal savings) rather than relying on uncertain... the Inter-Ministerial Committee on Health Care for the Elderly (IMCHE, 1997) “rapidly ageing population and the elderly’s growing health care needs are of increasing national concern.” Since the incidence of chronic illnesses and disabilities is higher in older age, the elderly utilize health care at a greater rate than the general population For OECD 10 countries, health expenditure on those aged... Hospitalization in Singapore? 2.1 Introduction Total spending on health care in Singapore accounts for less than 4% of the city-state's GDP, the lowest in comparison to all OECD countries, yet medical services and health outcomes are comparable to most OECD countries (Refer Table 2.1) The government expenditure on health care services is only 0.9% of GDP This outstanding performance of Singapore s health. .. (2000) ranked Singapore' s health care system sixth in the world in terms of the overall performance The ranking of Japan is 10, U.K 18, Sweden 23, Germany 25, Canada 30, Australia 32, and U.S 37 This outstanding performance of Singapore s health care system merits an in- depth analysis of the system However, due to paucity of space, it is only briefly described in the following sections, Singapore s health . Rand Data 163 Bibliography 165 iv Summary Modeling and predicting both average and extreme hospitalization expenditures and financing health care expenditures within the Singapore context. Canada 6 and U.S. 8. What makes Singapore s achievement laudable is that it has done so at a fraction of the cost of OECD countries. Total health care spending of Singapore has been less than. Singapore s Health Care Financing System The National Health Plan (NHP) of 1983 and the White paper on affordable health care of 1993 are identified as two key health policy documents in Singapore