世界各国の寿命の原因解明非線形解析による社会的決定要因の分析鈴木孝弘 a 田辺和俊 b Determinants of Life Expectancy of Many Countries in the World by Using Support Vector

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2 世界各国の寿命の原因解明非線形解析による社会的決定要因の分析鈴木孝弘 a 田辺和俊 b Determinants of Life Expectancy of Many Countries in the World by Using Support Vector Machine Takahiro SUZUKI a, Kazutoshi TANABE b Abstract Social determinants of life expectancy attract much attention worldwide, and several papers were presented on statistical analysis of determinants using linear regression method OLS. In this study, a large-scale experiment has been done to analyze determinants of life expectancy of 161 countries using 42 explanatory variables of 5 fields and a non-linear regression support vector machine SVM technique. The SVM model developed shows that just 13 factors represent life expectancy of 161 countries with a higher accuracy of determination coefficient of than previous works. It also shows that the health factors such as infant mortality rates and health expenditures most significantly contribute to life expectancy. Keywords: life expectancy; determinant analysis; support vector machine 1. はじめに WHO Natural Science Lab., Toyo University, Hakusan, Bunkyo-ku, Tokyo , JAPAN Institute of Social Sciences, Toyo University, Hakusan, Bunkyo-ku, Tokyo , JAPAN

3 68 Social Determinants of Health: The Solid Facts 2 WHO, Closing the gap in a generation: Health equity through action on the social determinants of health WHO, , Table 1 Christensen & Vaupeld, 1996;, 2005;, 2006; Skolnik, 2008;, 2010; 2012; Mehrara & Nasibparast, 2012, ordinary least squares, OLS Table 1 1 OECD Bergh & Nilsson GpC GDP GpC OLS ANN, 2000;, 2003;, 2006 ANN SVM Cristianini & Shaw- Taylor, 2000;, 2007;, 2011 ANN ANN ANN SVM

4 Life Expectancy of Many Countries 69 Table 1. Summary of literature review on statistical determinant analysis of life expectancy Countries analyzed Explanatory variable Authors 47 less developed countries economic variables, health expenditures, health personnel and facilities, social indicators, power and sanitation utilities Grosse & Perry developing countries GNP per capita, poverty rate, public health spending Anand & Ravallion developed and developing countries newspaper, electric power, protein intake, GDP, school life years, imports, mortality rate, hospital beds, physicians Furukawa recipient countries sanitary toilet facilities, safe drinking water, literacy, GDP, access to basic medicines, measles vaccine inoculation rate. 19 OECD countries GpC, pharmaceutical expenditure, health expenditure, senior population rate, tobacco consumption, alcohol consumption, butter consumption, vegetable consumption, dummy 91 developing countries GpC, literacy rate, health expenditure, urban population rate, total fertility rate, rate of population without access to water, number of physicians, undernourished people rate, area dummy 65 African countries GpC, undernourishment prevalence, safe water access, education, HIV prevalence, malaria risk, tuberculosis incidence Furukawa 2005 Shaw et al Kabir 2008 Desbordes & Azemar developed and developing countries 83 developed and developing countries 29 developed and developing countries globalization index, GpC, urban population, average year of education, number of physicians, nutritional status, dependency ratio, government consumption, Gini coefficient per capita income, human capital stock, infant mortality, hospital beds, urbanization, political instability, area dummy GpC, foreign direct investment, population density, education, hospital beds, employment rate, food supply Bergh & Nilsson 2009 Castello-Climent 2011 Doytch et al European countries GpC, health expenditure, food availability, employment ratio, education Index, immunization rate, urban population ratio, CO 2 emission Bayati et al SVM

5 70 2. 方法 2.1 平均寿命および各種指標のデータ 161 WHO UN WB 161 Table WB Table 2. Distribution of 161 countries LE range Developed countries Developing countries Africa America Asia Europe Oceania WHO Table 3 42 WHO 2003 Fig Table 4 0 1

6 Life Expectancy of Many Countries 71 Table 3. Dependent and explanatory variables No Variable Definition and unit Field Source Life expectancy Expected number of years of life remaining at birth WHO, UN, WB 1 Infant mortality rate Number of infants dying before reaching one year of age, per 1,000 live births in a year 2 Birth rate Average annual number of births during a year per 1,000 persons 3 Suicide rate Total rate deaths officially recorded as suicides per 100,000 population Health Health Health UN, WB WB, OECD WHO, OECD 4 Health expenditure Sum of public and private health Health WHO, WB expenditures per capita 5 Hospital beds Number of hospital beds per 1,000 Health WHO, WB population 6 Physicians Number of physicians per 1,000 population Health WHO, WB 7 Smoking prevalence Percentage of men and women ages 15 and Health WHO, WB over who smoke daily 8 Alcohol consumption Alcohol consumption among adults age Health WHO, OECD 15+ in litres per capita per year 9 Calorie intake Daily calorie intake per capita in 10 3 kcal Health FAO 10 Fat intake Average daily fat intake per capita in gram Health FAO 11 Obesity Rate of adults of body mass index over 30 Health WHO, OECD 12 Marriage rate Number of marriages per 1,000 population Health UN, OECD 13 Divorce rate Number of divorces per 1,000 population Health UN, OECD 14 Religion Rate of population who say religion is important Health Gallup 15 Gross domestic Per capita gross domestic product in 10 3 $ Economy IMF, WB product 16 GDP growth rate Annual percentage growth rate of GDP at Economy IMF, WB market prices based on constant local currency 17 Tax rates Total taxation as of GDP Economy IMF, WB 18 Wealth Wealth per capita in 10 3 $ Economy Credit Suisse 19 Household consumption expenditure Household final consumption expenditure per capita in 10 3 $ Economy WB, OECD 20 Gini coefficient Measure of inequality of income Economy UN, WB 21 Poverty rate Poverty headcount ratio at national poverty Economy UN, WB line per population 22 Unemployment rate Rate of the number of unemployed Economy IMF, UN individuals to all individuals currently in the labor force 23 Senior worker Rate of economically active population ages Economy ILO 65 and over 24 Grain self-sufficiency rate Proportion of domestic grains among those consumed in the country Economy FAO

7 72 Table 3. continued No Variable Definition and unit Field Source 25 Motor vehicle Motor vehicles including cars, buses, and freight vehicles per 1,000 population Economy UN, WB 26 Military expenditure Military expenditure per capita in $ Political CIA, WB 27 Armed forces Rate of armed forces personnel to total Political WB labor force 28 Murder Rate Murder rate per 100,000 population Social UN, WHO 29 Crime rate Crime rate per 100,000 population Social UN, ICPO 30 Education expenditure Public expenditure on education per capita in $ Education UN, WB 31 Literacy rate Literacy rate of people ages 15 and above Education UN, WB 32 Intelligence quotient Ratio of tested mental age to chronological Education Eutimes age 33 School life expectancy School life expectancy, primary to tertiary education Education UN 34 School enrollment, tertiary Percentage of high school graduates that successfully enroll into university Education UN, WB 35 Internet Internet users per 100 population Culture UN, WB 36 Latitude Average latitude of country Geography WB 37 Urban population Rate of people living in urban areas Environment UN, WB 38 Terrestrial protected Rate of terrestrial protected areas to total Environment UN, WB area land area 39 Forest area Forest areas per capita in m 2 Environment FAO, WB 40 Water access Rate of population with access to improved Environment WHO, WB water source 41 Electricity access Rate of population with access to electricity Environment UN, WB 42 Air pollution Country level of PM10 in μg/m 3 Environment WHO, WB For more detailed definition of variables, see homepages of data sources Life expectancy Infant mortality rate Fig. 1. Scatter plot of life expectancy versus infant mortality rate

8 Life Expectancy of Many Countries 73 Table 4. Descriptive statistics of explanatory variables No Explanatory variable Mean St. Dev. Min Max Skewness 1 Infant mortality rate Birth rate Suicide rate Health expenditure Hospital beds Physicians Smoking prevalence Alcohol consumption Calorie intake Fat intake Obesity Marriage rate Divorce rate Religion Gross domestic product GDP growth rate Tax rates Wealth Household consumption expenditure Gini coefficient Poverty rate Unemployment rate Senior worker Grain self-sufficiency rate Motor vehicle Military expenditure Armed forces Murder Rate Crime rate Education expenditure Literacy rate Intelligence quotient School life expectancy School enrollment, tertiary Internet Latitude Urban population Terrestrial protected area Forest area Water access Electricity access Air pollution

9 Life expectancy Life expectancy Military expenditure Log(Military expenditure) Fig. 2. Scatter plot of life expectancy versus militar y expenditure before and after logarithmic transformation Fig SVM OLS 2.2 サポートベクターマシンによる解析 SVM LIBSVM ver.2.89 Chang & Lin εsvr RBF SVM 3 g RBF gamma c cost p loss function ε Leave-One-Out Cross-Validation Test LOOCVT Tanabe et al., 2013 SVM RMSE LOOCVT 3 g c p RMSE 2 RMSE

10 Life Expectancy of Many Countries 75 g c p RMSE 3 結果と考察 42 SVM 13 RMSE Fig RMSE 2.39 R RMSE 3 90 Predicted life expectancy Observed life expectancy Fig. 3. Scatter plot of observed versus predicted life expectancy of developed countries filled circle and developing countries open circle

11 76 SVM OLS R SVM OLS R OLS SVM Table Table Shaw et al OECD19 Kabir , 2005;, 2006;, 2010 Fig GpC , Fig GpC

12 Life Expectancy of Many Countries 77 Table 5. Sensitivities of 42 explanatory variables No Explanatory variable Field Sensitivity 1 Infant mortality rate Health GDP growth rate Economy Wealth Economy Suicide rate Health Hospital beds Health Urban population Environment Health expenditure Health Birth rate Health Tax rates Economy Physicians Health Intelligence quotient Education Military expenditure Political Terrestrial protected area Environment Marriage rate Health Divorce rate Health Water access Environment Calorie intake Health Fat intake Health Electricity access Environment Armed forces Political Grain self-sufficiency rate Economy Air pollution Environment Forest area Environment Poverty rate Economy Crime rate Social Household consumption expenditure Economy Senior worker Economy Gross domestic product Economy Literacy rate Education Murder Rate Social Unemployment rate Economy School life expectancy Education Internet Culture Education expenditure Education Obesity Health Latitude Geography Alcohol consumption Health Religion Health Smoking prevalence Health Gini coefficient Economy Motor vehicle Economy School enrollment, tertiary Education Bold letters : Determinants of life expectancy.

13 78 Life expectancy Log(GpC) Life expectancy Log(Gini) Fig. 4. Scatter plot of life expectancy versus Log GpC left and Log Gini right 4 結論 SVM R WHO, 2005;, 2006;, 2010

14 Life Expectancy of Many Countries 79 参考文献 Anand, S., Ravallion, M Human development in poor countries: on the role of private incomes and public services. J. Econ. Perspect, 7, Bayati, M., Akbarian, R., Kavosi, Z Determinants of life expectancy in eastern Mediterranean region: a health production function. Int. J. Health Policy Manage., 1, Bergh, A., Nilsson, T Good for living? On the relation between globalization and life expectancy. World Dev., 38, Castello-Climent, A Channels through which human capital inequality influences economic growth. J. Hum. Cap. 4, Chang C.C., Lin C.J. LIBSVM: a library for support vector machines, edu.tw/ cjlin/libsvm/, accessed 2011/12/1. Christensen, K., Vaupeld, J.W Determinants of longevity: genetic, environmental and medical factors. J. Intern. Med., 240, CIA, United States Central Intelligence Agency Factbook, publications/the-world-factbook/rankorder/rankorderguide.html, accessed 2013/2/1. Credit Suisse, Global Wealth Databook, publications/contributed/pages/global_wealth_databook_2012_-_credit_suisse.aspx, accessed 2013/2/1. Cristianini, N., Shaw-Taylor, J An introduction to support vector machines and other kernel-based learning methods. London : Cambridge University Press:.., 2005 Desbordes, R., Azemar, C Public governance, health and foreign direct investment in sub-saharan Africa. J. Afr. Econ., 18, Doytch, N., Kelly, I.R., Dave, D.M Global health and the economy. Hum. Biol. Rev. 1, Eutimes, The European Union Times, accessed 2013/2/1. FAO, United Nations Food and Agriculture Organization Statistics Division, fao.org/site/567/default.aspx#ancor, accessed 2013/2/1. Gallup, Gallup Global Reports, accessed 2013/2/1. Grosse, R.N., Perry, B.H Correlated of life expectancy in less developed countries. Health Policy Educ., 2, ICPO, International Criminal Police Organization Online Databases, or/en/ , accessed 2013/2/1. ILO, International Labour Union LABORSTA, accessed 2013/2/1. IMF, International Monetary Fund World Economic Outlook Database, external/pubs/ft/weo/2013/01/weodata/index.aspx, accessed 2013/2/1.

15 80 Kabir, M Determinants of life expectancy in developing countries. J. Dev. Areas, 41, Mehrara, M., Nasibparast, S Determinants of health status in developing countries: a Bayesian econometric approach. Int. J. Soc. Sci Tom., 1, 1-7. OECD, Organisation for Economic Co-operation and Development Statistics, oecd.org/statistics/, accessed 2013/2/1. Shaw J.W., Horrace W.C., Vogel R.J The determinants of life expectancy: an analysis of the OECD health data. South Econ. J., 71, Skolnik R Essentials of global health. Chapter 2: Health determinants, measurements, and trends. Sudbury MA, USA: Jones and Bartlett Publishers. Tanabe, K., Kurita, T., Nishida, K., Lu i, B., Ami, D., Suzuki, T Improvement of carcinogenicity prediction performances based on sensitivity analysis in variable selection of SVM models. SAR QSAR Environ Res., 24, UN, United Nations Development Program Human Development Report, org/en/, accessed 2013/2/1. WB, World Bank World Development Indicators, World Bank Global Development Network Growth Database WBSITE/EXTERNAL/EXTDEC/EXTRESEARCH/0,,contentMDK: pagepk: pipk: thesitepk:469382,00.html, accessed 2013/2/1. WHO, World Health Organization World Health Statistics, publications/world_health_statistics/en/index.html, accessed 2013/2/1. World Health Organization, Social determinants of health: the solid facts, who.int/ data/assets/pdf_file/0005/98438/e81384.pdf: 2, accessed 2013/8/1. World Health Organization The World Health Report 2003: Shaping the future. Geneve: World Health Organization. World Health Organization, Closing the gap in a generation: health equity through action on the social determinants of health, CSDH_08.1_eng.pdf, accessed 20138/8/ AI ,, : , 80,

16 Life Expectancy of Many Countries , 48, , 50, Neurosim/L ,., 60,

自然科学篇第61号_鈴木・田辺.indd

自然科学篇第61号_鈴木・田辺.indd 東洋大学紀要自然科学篇第 61 号 :105-118(2017) 105 非線形回帰分析による世界各国の平均寿命健康寿命の要因分析鈴木孝弘 a 田辺和俊 b Analysis of Determinants of Life Expectancy and Healthy Life Expectancy of Many Countries Using Nonlinear Regression Takahiro

世界各国の寿命の原因解明 非線形解析による社会的決定要因の分析 鈴木孝弘 a 田辺和俊 b Determinants of Life Expectancy of Many Countries in the World by Using Support Vector

世界各国の寿命の原因解明非線形解析による社会的決定要因の分析鈴木孝弘 a 田辺和俊 b Determinants of Life Expectancy of Many Countries in the World by Using Support Vector