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Modelling multi-state health transitions in China: a generalised linear model with time trends

Published online by Cambridge University Press:  02 July 2018

Katja Hanewald ,
Han Li  and
Adam W. Shao
Katja Hanewald
Affiliation:
ARC Centre of Excellence in Population Ageing Research (CEPAR), University of New South Wales, Sydney, NSW 2052, Australia
Han Li*
Affiliation:
Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, NSW 2109, AustraliaARC Centre of Excellence in Population Ageing Research (CEPAR), University of New South Wales, Sydney, NSW 2052, Australia
Adam W. Shao
Affiliation:
ARC Centre of Excellence in Population Ageing Research (CEPAR), University of New South Wales, Sydney, NSW 2052, Australia
*
*Correspondence to: Han Li, Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, Australia. Tel: +61 (2) 9850 6460. E-mail: [email protected]
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Abstract

Rapid population ageing in China has urged the need to understand health transitions of older Chinese to assist the development of social security programmes and financial products aimed at funding long-term care. In this paper, we develop a new flexible approach to modelling health transitions in a multi-state Markov model that allows for age effects, time trends and age-time interactions. The model is implemented in the generalised linear modelling framework. We apply the model to evaluate health transitions of Chinese elderly using individual-level panel data from the Chinese Longitudinal Healthy Longevity Survey for the period 1998–2012. Our results confirm that time trends and age–time interactions are important factors explaining health transitions in addition to the more commonly used age effects. We document that differences in disability and mortality rates continue to persist between urban and rural older Chinese. We also compute life expectancies and healthy life expectancies based on the proposed model as inputs for the development of aged care and financial services for older Chinese.

Keywords

Generalised linear models (GLMs)Multi-state health transitionsLong-term careHealthy life expectancyChina
Type
Paper
Information
Annals of Actuarial Science , Volume 13 , Issue 1 , March 2019 , pp. 145 - 165
Copyright
© Institute and Faculty of Actuaries 2018 

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References

Alai, D.H., Chen, H., Cho, D., Hanewald, K. & Sherris, M. (2014). Developing equity release markets: risk analysis for reverse mortgages and home reversions. North American Actuarial Journal, 18(1), 217–241.Google Scholar
Aro, H., Djehiche, B. & Lofdahl, B. (2015). Stochastic modelling of disability insurance in a multi-period framework. Scandinavian Actuarial Journal, 2015(1), 88–106.Google Scholar
Brouhns, N., Denuit, M. & Vermunt, J.K. (2002). A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31(3), 373–393.Google Scholar
Cairns, A.J., Blake, D. & Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73(4), 687–718.Google Scholar
Cairns, A.J., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A. & Balevich, I. (2009). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal, 13(1), 1–35.Google Scholar
Derksen, S. & Keselman, H.J. (1992). Backward, forward and stepwise automated subset selection algorithms: frequency of obtaining authentic and noise variables. British Journal of Mathematical and Statistical Psychology, 45(2), 265–282.Google Scholar
Djehiche, B. & Lofdahl, B. (2018). A hidden Markov approach to disability insurance. North American Actuarial Journal, 22(1), 119–136.Google Scholar
Dowd, K., Cairns, A.J., Blake, D., Coughlan, G.D., Epstein, D. & Khalaf-Allah, M. (2010). Evaluating the goodness of fit of stochastic mortality models. Insurance: Mathematics and Economics, 47(3), 255–265.Google Scholar
Ferri, S. & Olivieri, A. (2000). Technical bases for LTC covers including mortality and disability projections. Proceedings of the 31st International ASTIN Colloquium, pp. 295–314, Porto Cervo, Italy, 17–20 September.Google Scholar
Fong, J.H. & Feng, J. (2016). Patterns of functional disability in the oldest adults in China. Journal of the American Geriatrics Society, 64(9), 1890–1894.Google Scholar
Fong, J.H., Shao, A.W. & Sherris, M. (2015). Multistate actuarial models of functional disability. North American Actuarial Journal, 19(1), 41–59.Google Scholar
Grafen, A., Hails, R., Hails, R. & Hails, R. (2002). Modern Statistics for the Life Sciences, volume 123. Oxford University Press, Oxford.Google Scholar
Guo, W. (2017). The changes of disability-free life expectancy and inter-generation support for the elderly in China: 2005-2010. In T. Samanta, (Ed.), Cross-Cultural and Cross-Disciplinary Perspectives in Social Gerontology (pp. 221–243). Springer, Singapore.Google Scholar
Haberman, S. & Renshaw, A. (2009). On age-period-cohort parametric mortality rate projections. Insurance: Mathematics and Economics, 45(2), 255–270.Google Scholar
Hinde, J. & Demetrio, C.G. (1998). Overdispersion: models and estimation. Computational Statistics & Data Analysis, 27(2), 151–170.Google Scholar
Hurvich, C.M. & Tsai, C.-L. (1990). The impact of model selection on inference in linear regression. The American Statistician, 44(3), 214–217.Google Scholar
Li, H., O’Hare, C. & Vahid, F. (2017). A flexible functional form approach to mortality modeling: Do we need additional cohort dummies? Journal of Forecasting 36(4), 357–367.Google Scholar
Li, H., O’Hare, C. & Zhang, X. (2015). A semiparametric panel approach to mortality modeling. Insurance: Mathematics and Economics, 61, 264–270.Google Scholar
Li, Z., Shao, A.W. & Sherris, M. (2017). The impact of systematic trend and uncertainty on mortality and disability in a multi-state latent factor model for transition rates. North American Actuarial Journal 21(4), 594–610.Google Scholar
Liu, J., Chen, G., Song, X., Chi, I. & Zheng, X. (2009). Trends in disability-free life expectancy among Chinese older adults. Journal of Aging and Health, 21(2), 266–285.Google Scholar
Lu, B., Liu, X. & Piggott, J. (2015). Informal long term care in China and population ageing: evidence and policy implications. Population Review, 54(2), 28–41.Google Scholar
Lu, B., Liu, X. & Yang, M. (2017). A budget proposal for China’s public long-term care policy. Journal of Aging & Social Policy, 29(1), 84–103.Google Scholar
Luo, H., Wong, G.H., Lum, T.Y., Luo, M., Gong, C.H. & Kendig, H. (2016). Health expectancies in adults aged 50 years or older in China. Journal of Aging and Health, 28(5), 758–774.Google Scholar
Majer, I.M., Stevens, R., Nusselder, W.J., Mackenbach, J.P. & van Baal, P.H. (2013). Modeling and forecasting health expectancy: theoretical framework and application. Demography, 50(2), 673–697.Google Scholar
McCullagh, P. & Nelder, J. (1989). Generalized Linear Models, 2nd edition. Monographs on Statistics and Applied Probability, volume 37, Chapman & Hall/CRC, Boca Raton.Google Scholar
Meng, Q., Xu, L., Zhang, Y., Qian, J., Cai, M., Xin, Y., Gao, J., Xu, K., Boerma, J.T. & Barber, S.L. (2012). Trends in access to health services and financial protection in China between 2003 and 2011: a cross-sectional study. The Lancet, 379(9818), 805–814.Google Scholar
National Bureau of Statistics of China (2013). China Statistical Yearbook 2013. Available online at the address http://www.stats.gov.cn/tjsj/ndsj/2013/indexeh.htm [accessed 23-Apr-2018].Google Scholar
Olivieri, A. & Pitacco, E. (2001). Facing LTC risks. Proceedings of the 32nd ASTIN Colloquium, Washington, DC, 8–11 July.Google Scholar
Peng, R., Ling, L. & He, Q. (2010). Self-rated health status transition and long-term care need of the oldest Chinese. Health Policy, 97(2), 259–266.Google Scholar
Peng, R. & Wu, B. (2015). Changes of health status and institutionalization among older adults in China. Journal of Aging and Health, 27(7), 1223–1246.Google Scholar
Pitacco, E. (1995). Actuarial models for pricing disability benefits: towards a unifying approach. Insurance: Mathematics and Economics, 16(1), 39–62.Google Scholar
Plat, R. (2009). On stochastic mortality modeling. Insurance: Mathematics and Economics, 45(3), 393–404.Google Scholar
Renshaw, A. & Haberman, S. (1995). On the graduations associated with a multiple state model for permanent health insurance. Insurance: Mathematics and Economics, 17(1), 1–17.Google Scholar
Renshaw, A.E. & Haberman, S. (2000). Modelling the recent time trends in UK permanent health insurance recovery, mortality and claim inception transition intensities. Insurance: Mathematics and Economics, 27(3), 365–396.Google Scholar
Rickayzen, B.D. & Walsh, D.E. (2002). A multi-state model of disability for the United Kingdom: implications for future need for long-term care for the elderly. British Actuarial Journal, 8(2), 341–393.Google Scholar
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464.Google Scholar
Shao, A.W., Hanewald, K. & Sherris, M. (2015). Reverse mortgage pricing and risk analysis allowing for idiosyncratic house price risk and longevity risk. Insurance: Mathematics and Economics, 63, 76–90.Google Scholar
Shao, A.W., Sherris, M. & Fong, J.H. (2017). Product pricing and solvency capital requirements for long-term care insurance. Scandinavian Actuarial Journal, 2017(2), 175–208.Google Scholar
Melorose, J., Perroy, R. & Careas, S. (2015). World population prospects: the 2015 revision, key findings and advance tables. United Nations Working Paper No. ESA/P/WP. 241, 1–59.Google Scholar
Wang, H. & Yu, Y. (2016). Increasing health inequality in China: an empirical study with ordinal data. The Journal of Economic Inequality, 14(1), 41–61.Google Scholar
Whittingham, M.J., Stephens, P.A., Bradbury, R.B. & Freckleton, R.P. (2006). Why do we still use stepwise modelling in ecology and behaviour? Journal of Animal Ecology, 75(5), 1182–1189.Google Scholar
Yang, H., Browning, C. & Thomas, S. (2013). Challenges in the provision of community aged care in China. Family Medicine and Community Health, 1(2), 32–42.Google Scholar
Yang, W., He, A.J., Fang, L. & Mossialos, E. (2016). Financing institutional long-term care for the elderly in China: a policy evaluation of new models. Health Policy and Planning, 31(10), 1391–1401.Google Scholar
Yi, Z., Vaupel, J.W., Zhenyu, X., Chunyuan, Z. & Yuzhi, L. (2001). The healthy longevity survey and the active life expectancy of the oldest old in China. Population: An English selection, 13(1), 95–116.Google Scholar
Zeng, Y. (2012). Toward deeper research and better policy for healthy aging-using the unique data of Chinese Longitudinal Healthy Longevity Survey. China Economic Journal, 5(2–3), 131–149.Google Scholar
Zeng, Y., Feng, Q., Hesketh, T., Christensen, K. & Vaupel, J.W. (2017). Survival, disabilities in activities of daily living, and physical and cognitive functioning among the oldest-old in China: a cohort study. The Lancet, 389(10079), 1619–1629.Google Scholar
Zhen, Z., Feng, Q. & Gu, D. (2015). The impacts of unmet needs for long-term care on mortality among older adults in China. Journal of Disability Policy Studies, 25(4), 243–251.Google Scholar
Zhou, M., Wang, H., Zhu, J., Chen, W., Wang, L., Liu, S., Li, Y., Wang, L., Liu, Y., Yin, P. & Liu, J. (2016). Cause-specific mortality for 240 causes in China during 1990-2013: a systematic subnational analysis for the Global Burden of Disease Study 2013. The Lancet, 387(10015), 251–272.Google Scholar
Zhu, H. (2015). Unmet needs in long-term care and their associated factors among the oldest old in China. BMC Geriatrics, 15(1), 1.Google Scholar