Skip to main content

Advertisement

Log in

Unobserved Heterogeneity of Frailty in the Analysis of Socioeconomic Differences in Health and Mortality

  • Published:
European Journal of Population Aims and scope Submit manuscript

Abstract

The concepts of unobserved frailty and selection have been extensively analyzed with respect to phenomena like mortality deceleration at old ages and mortality convergence or cross overs between populations (for example American black and white populations, men and women). Despite the long-time observation of converging mortality risks in differential socioeconomic mortality research, the interest in the connection between frailty, selection, and health and mortality inequalities over a life course approach has increased only recently. This overview of the literature summarizes the main concepts of unobserved frailty and socioeconomic differences in mortality and how frailty and selection relate to these differences at old ages. It then reviews the evidence coming from the existing studies. Although the number of studies is still limited, the body of research on unobserved frailty and socioeconomic inequalities in health and mortality in a life course approach is growing. The results, however, are contradictory, and whether selection plays a major role in shaping the observed socioeconomic mortality patterns at old ages is still controversial.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Notes

  1. In the investigation of decreasing health inequalities at older ages, one should be aware that these inequalities might be displaying cohort effects and not just age effects as showed by Willson et al. (2007) and Masters (2012).

References

  • Aalen, O. (1988). Heterogeneity in survival analysis. Statistics in Medicine, 7(11), 1121–1137.

    Article  Google Scholar 

  • Aalen, O. (1994). Effects of frailty in survival analysis. Statistical Methods in Medical Research, 3(3), 227–243.

    Article  Google Scholar 

  • Aalen, O., Borgan, Ø., & Gjessing, H. (2008a). Unobserved heterogeneity: The odd effects of frailty. Survival and event history analysis, chapter 6 (pp. 231–270). New York: Springer.

    Chapter  Google Scholar 

  • Aalen, O., Borgan, Ø., & Gjessing, H. (2008b). Survival and event history analysis: A process point of view. Berlin: Springer.

    Book  Google Scholar 

  • Aldabe, B., Anderson, R., Lyly-Yrjänäinen, M., Parent-Thirion, A., Vermeylen, G., Kelleher, C., et al. (2011). Contribution of material, occupational, and psychosocial factors in the explanation of social inequalities in health in 28 countries in Europe. Journal of Epidemiology and Community Health, 65(12), 1123–1131.

    Article  Google Scholar 

  • Antonovsky, A. (1967). Social class, life expectancy and overall mortality. The Milbank Memorial Fund Quarterly, 45(2), 31–73.

    Article  Google Scholar 

  • Beckett, M. (2000). Converging health inequalities in later life-an artifact of mortality selection? Journal of Health and Social Behavior, 41(1), 106–119.

    Article  Google Scholar 

  • Beckett, M., Goldman, N., Weinstein, M., Lin, I., Chuang, Y., et al. (2002). Social environment, life challenge, and health among the elderly in Taiwan. Social Science & Medicine, 55(2), 191–209.

    Article  Google Scholar 

  • Betensky, R., Louis, D., & Gregory Cairncross, J. (2002). Influence of unrecognized molecular heterogeneity on randomized clinical trials. Journal of Clinical Oncology, 20(10), 2495–2499.

    Article  Google Scholar 

  • Black, D., Morris, J., Smith, C., & Townsend, P. (1980). Inequalities in health: Report of a Research Working Group. London: Department of Health and Social Security 19.

    Google Scholar 

  • Blakely, T., & Wilson, N. (2005). The contribution of smoking to inequalities in mortality by education varies over time and by sex: Two national cohort studies, 1981–84 and 1996–99. International Journal of Epidemiology, 34(5), 1054–1062.

    Article  Google Scholar 

  • Braveman, P. A., Cubbin, C., Egerter, S., Williams, D. R., & Pamuk, E. (2010). Socioeconomic disparities in health in the United States: What the patterns tell us. American Journal of Public Health, 100(S1), S186–S196.

    Article  Google Scholar 

  • Bretagnolle, J., & Huber-Carol, C. (1988). Effects of omitting covariates in cox’s model for survival data. Scandinavian Journal of Statistics, 15(2), 125–138.

    Google Scholar 

  • Cai, B. (2010). Bayesian semiparametric frailty selection in multivariate event time data. Biometrical Journal, 52(2), 171–185.

    Google Scholar 

  • Caselli, G., Vaupel, J., & Yashin, A. (2000). Longevity, heterogeneity and selection. In proceeding Atti della XL Riunione Scientifica della Società Italiana di Statistica, 49–72.

  • Chamberlain, G. (1985). Heterogeneity, omitted variable bias, and duration dependence. In J. J. Heckman, B. Singer (Eds.), Longitudinal analysis of labor market data (pp. 3–38). Cambridge: Cambridge University Press.

    Google Scholar 

  • Chen, J. T., Beckfield, J., Waterman, P. D., & Krieger, N. (2013). Can changes in the distributions of and associations between education and income bias temporal comparisons of health disparities? An exploration with causal graphs and simulations. American Journal of Epidemiology, 177(9), 870–881.

    Article  Google Scholar 

  • Coale, A., & Kisker, E. (1986). Mortality crossovers: Reality or bad data? Population Studies, 40(3), 389–401.

    Article  Google Scholar 

  • Congdon, P. (1994). Analysing mortality in London: Life-tables with frailty. Journal of the Royal Statistical Society Series D (The Statistician), 43(2), 277–308.

    Google Scholar 

  • Connolly, S., OReilly, D., & Rosato, M. (2009). House value as an indicator of cumulative wealth is strongly related to morbidity and mortality risk in older people: A census-based cross-sectional and longitudinal study. International Journal of Epidemiology. doi:10.1093/ije/dyp356.

    Google Scholar 

  • Dalstra, J., Kunst, A., Mackenbach, J., et al. (2006). A comparative appraisal of the relationship of education, income and housing tenure with less than good health among the elderly in Europe. Social Science & Medicine, 62(8), 2046–2060.

    Article  Google Scholar 

  • Decker, S., & Rapaport, C. (2002). Medicare and disparities in women’s health. In Technical Report on National Bureau of Economic Research.

  • Dor, A., Sudano, J., & Baker, D. (2006). The effect of private insurance on the health of older, working age adults: Evidence from the Health and Retirement Study. Health Services Research, 41(3p1), 759–787.

    Article  Google Scholar 

  • Duchateau, L., & Janssen, P. (2008). The frailty model. Berlin: Springer.

    Google Scholar 

  • Dupre, M. (2007). Educational differences in age-related patterns of disease: Reconsidering the cumulative disadvantage and age-as-leveler hypotheses. Journal of Health and Social Behavior, 48(1), 1–15.

    Article  Google Scholar 

  • Elo, I., Martikainen, P., & Smith, K. (2006). Socioeconomic differentials in mortality in Finland and the United States: The role of education and income. European Journal of Population/Revue Européenne de Démographie, 22(2), 179–203.

    Article  Google Scholar 

  • Elo, I., & Preston, S. (1996). Educational differentials in mortality: United states, 1979–1985. Social Science & Medicine, 42(1), 47–57.

    Article  Google Scholar 

  • Enroth, L., Raitanen, J., Hervonen, A., & Jylhä, M. (2013). Do socioeconomic health differences persist in nonagenarians? The Journals of Gerontology Series B: Psychological Sciences and Social Sciences. doi:10.1093/geronb/gbt067.

    Google Scholar 

  • Ferraro, K., & Farmer, M. (1996). Double jeopardy, aging as leveler, or persistent health inequality? A longitudinal analysis of white and black Americans. The Journals of Gerontology Series B: Psychological Sciences and Social Sciences, 51(6), S319.

    Article  Google Scholar 

  • Frijters, P., Haisken-DeNew, J. P., & Shields, M. A. (2011). The increasingly mixed proportional hazard model: An application to socioeconomic status, health shocks, and mortality. Journal of Business & Economic Statistics, 29(2), 271–281.

    Article  Google Scholar 

  • Gail, M., Wieand, S., & Piantadosi, S. (1984). Biased estimates of treatment effect in radomized experiments with nonlinear regressions and omitted covariates. Biometrika, 71(3), 431–444.

    Article  Google Scholar 

  • Gampe, J. (2010). Human mortality beyond age 110. Supercentenarians (pp. 219–230). Berlin: Springer.

    Chapter  Google Scholar 

  • Goldman, N., Korenman, S., & Weinstein, R. (1995). Marital status and health among the elderly. Social Science & Medicine, 40(12), 1717–1730.

    Article  Google Scholar 

  • Hambright, T. (1969). Comparison of information on death certificates and matching 1960 census records: Age, marital status, race, nativity and country of origin. Demography, 6(4), 413–423.

    Article  Google Scholar 

  • Henderson, R., & Oman, P. (1999). Effect of frailty on marginal regression estimates in survival analysis. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 61(2), 367–379.

    Article  Google Scholar 

  • Herd, P. (2006). Do functional health inequalities decrease in old age? Research on Aging, 28(3), 375–392.

    Article  Google Scholar 

  • Hoffmann, R. (2005). Do socioeconomic mortality differences decrease with rising age? Demographic Research, 13(2), 35–62.

    Article  Google Scholar 

  • Hoffmann, R. (2008). Socioeconomic differences in old age mortality. Berlin: Springer.

    Book  Google Scholar 

  • Hoffmann, R. (2011a). Illness, not age, is the leveler of social mortality differences in old age. The Journals of Gerontology Series B: Psychological Sciences and Social Sciences, 66(3), 374–379.

    Article  Google Scholar 

  • Hoffmann, R. (2011b). Socioeconomic inequalities in old-age mortality: A comparison of Denmark and the USA. Social Science & Medicine, 72(12), 1986–1992.

    Article  Google Scholar 

  • Hougaard, P. (1984). Life table methods for heterogeneous populations: Distributions describing the heterogeneity. Biometrika, 71(1), 75–83.

    Article  Google Scholar 

  • Hougaard, P. (1986). Survival models for heterogeneous populations derived from stable distributions. Biometrika, 73(2), 387–396.

    Article  Google Scholar 

  • House, J., Lepkowski, J., Kinney, A., Mero, R., Kessler, R., & Herzog, A. (1994). The social stratification of aging and health. Journal of Health and Social Behavior, 35(3), 213–234.

    Article  Google Scholar 

  • Huisman, M., Kunst, A., Andersen, O., Bopp, M., Borgan, J., Borrell, C., et al. (2004). Socioeconomic inequalities in mortality among elderly people in 11 European populations. Journal of Epidemiology and Community Health, 58(6), 468–475.

    Article  Google Scholar 

  • Huisman, M., Kunst, A. E., Bopp, M., Borgan, J. K., Borrell, C., Costa, G., et al. (2005). Educational inequalities in cause-specific mortality in middle-aged and older men and women in eight western European populations. The Lancet, 365(9458), 493–500.

    Article  Google Scholar 

  • Huisman, M., Kunst, A., & Mackenbach, J. (2003). Socioeconomic inequalities in morbidity among the elderly; a European overview. Social Science & Medicine, 57(5), 861–873.

    Article  Google Scholar 

  • Jaffe, D. H., Neumark, Y. D., Eisenbach, Z., & Manor, O. (2008). Educational inequalities in mortality among Israeli Jews: Changes over time in a dynamic population. Health & Place, 14(2), 287–298.

    Article  Google Scholar 

  • Kalwij, A. (2014). An empirical analysis of the importance of controlling for unobserved heterogeneity when estimating the income-mortality gradient. Demographic Research, 31(30), 913–940. doi:10.4054/DemRes.2014.31.30.

    Article  Google Scholar 

  • Kalwij, A. S., Alessie, R. J., & Knoef, M. G. (2013). The association between individual income and remaining life expectancy at the age of 65 in the Netherlands. Demography, 50(1), 181–206.

    Article  Google Scholar 

  • Kelley-Moore, J. (2010). Disability and ageing: The social construction of causality. The SAGE Handbook of social gerontology (pp. 96–110). London: Sage Publications Ltd.

    Chapter  Google Scholar 

  • Kim, J., & Durden, E. (2007). Socioeconomic status and age trajectories of health. Social Science & Medicine, 65(12), 2489–2502.

    Article  Google Scholar 

  • Kitagawa, E., & Hauser, P. (1973). Differential mortality in the United States: A study in socioeconomic epidemiology. MA: Harvard University Press Cambridge.

    Book  Google Scholar 

  • Kohler, H., & Kohler, I. (2000). Frailty modelling for adult and old age mortality: The application of a modified DeMoivre hazard function to sex differentials in mortality. Demographic Research, 3(8), 32.

    Google Scholar 

  • Koskinen, S., Joutsenniemi, K., Martelin, T., & Martikainen, P. (2007). Mortality differences according to living arrangements. International Journal of Epidemiology, 36(6), 1255–1264.

    Article  Google Scholar 

  • Krieger, J., & Higgins, D. (2002). Housing and health: Time again for public health action. American Journal of Public Health, 92(5), 758–768.

    Article  Google Scholar 

  • Lauderdale, D. (2001). Education and survival: Birth cohort, period, and age effects. Demography, 38(4), 551–561.

    Article  Google Scholar 

  • Liang, J., Bennett, J., Krause, N., Kobayashi, E., Kim, H., Brown, J., et al. (2002). Old age mortality in Japan. The Journals of Gerontology Series B: Psychological Sciences and Social Sciences, 57(5), S294–S307.

    Article  Google Scholar 

  • Lindström, M., Hanson, B., & Östergren, P. (2001). Socioeconomic differences in leisure-time physical activity: The role of social participation and social capital in shaping health related behaviour. Social Science & Medicine, 52(3), 441–451.

    Article  Google Scholar 

  • Link, B. G., & Phelan, J. (1995). Social conditions as fundamental causes of disease. Journal of Health and Social Behavior, 35, 80–94.

    Article  Google Scholar 

  • Lin, D., Psaty, B., & Kronmal, R. (1998). Assessing the sensitivity of regression results to unmeasured confounders in observational studies. Biometrics, 54(3), 948–963.

    Article  Google Scholar 

  • Lynch, S. (2003). Cohort and life-course patterns in the relationship between education and health: A hierarchical approach. Demography, 40(2), 309–331.

    Article  Google Scholar 

  • Mackenbach, J., Commission, E., & Britain, C. C. A. G. (2006). Health inequalities: Europe in profile. In Produced by COI for the Department of Health.

  • Mackenbach, J., Huisman, M., Andersen, O., Bopp, M., Borgan, J., Borrell, C., et al. (2004). Inequalities in lung cancer mortality by the educational level in 10 European populations. European Journal of Cancer, 40(1), 126–135.

    Article  Google Scholar 

  • Mackenbach, J., Stirbu, I., Roskam, A., Schaap, M., Menvielle, G., Leinsalu, M., et al. (2008). Socioeconomic inequalities in health in 22 European countries. New England Journal of Medicine, 358(23), 2468–2481.

    Article  Google Scholar 

  • Mackenbach, J., Stronks, K., & Kunst, A. (1989). The contribution of medical care to inequalities in health: Differences between socio-economic groups in decline of mortality from conditions amenable to medical intervention. Social Science & Medicine, 29(3), 369–376.

    Article  Google Scholar 

  • Manton, K., & Stallard, E. (1981). Methods for evaluating the heterogeneity of aging processes in human populations using vital statistics data: Explaining the black/white mortality crossover by a model of mortality selection. Human Biology, 53(1), 47–67.

    Google Scholar 

  • Manton, K., Stallard, E., & Vaupel, J. (1981). Methods for comparing the mortality experience of heterogeneous populations. Demography, 18(3), 389–410.

    Article  Google Scholar 

  • Manton, K., Stallard, E., & Vaupel, J. (1986). Alternative models for the heterogeneity of mortality risks among the aged. Journal of the American Statistical Association, 81(395), 635–644.

    Article  Google Scholar 

  • Manton, K., Woodbury, M., & Stallard, E. (1995). Sex differences in human mortality and aging at late ages: The effect of mortality selection and state dynamics. The Gerontologist, 35(5), 597–608.

    Article  Google Scholar 

  • Marmot, M., & Shipley, M. (1996). Do socioeconomic differences in mortality persist after retirement? 25 year follow up of civil servants from the first Whitehall study. BMJ, 313(7066), 1177–1180.

    Article  Google Scholar 

  • Martelin, T. (1994). Mortality by indicators of socioeconomic status among the Finnish elderly. Social Science & Medicine, 38(9), 1257–1278.

    Article  Google Scholar 

  • Martikainen, P., Valkonen, T., & Martelin, T. (2001). Change in male and female life expectancy by social class: Decomposition by age and cause of death in Finland 1971–95. Journal of Epidemiology and Community Health, 55(7), 494–499.

    Article  Google Scholar 

  • Martikainen, P., Valkonen, T., & Moustgaard, H. (2009). The effects of individual taxable income, household taxable income, and household disposable income on mortality in Finland, 1998–2004. Population Studies, 63(2), 147–162.

    Article  Google Scholar 

  • Martínez, C., Regidor, E., Sánchez, E., Pascual, C., & De La Fuente, L. (2009). Heterogeneity by age in educational inequalities in cause-specific mortality in women in the Region of Madrid. Journal of Epidemiology and Community Health, 63(10), 832–838.

    Article  Google Scholar 

  • Masters, R. (2012). Uncrossing the us black–white mortality crossover: The role of cohort forces in life course mortality risk. Demography, 49(3), 773–796.

    Article  Google Scholar 

  • McGilchrist, C., & Aisbett, C. (1991). Regression with frailty in survival analysis. Biometrics, 47(2), 461–466.

    Article  Google Scholar 

  • McMunn, A., Nazroo, J., & Breeze, E. (2009). Inequalities in health at older ages: A longitudinal investigation of the onset of illness and survival effects in England. Age and Ageing, 38(2), 181–187.

    Article  Google Scholar 

  • Merlo, J., Gerdtham, U. G., Lynch, J., Beckman, A., Norlund, A., & Lithman, T. (2003). International journal for equity in health. International Journal for Equity in Health, 2, 2.

    Article  Google Scholar 

  • Missov, T., & Finkelstein, M. (2011). Admissible mixing distributions for a general class of mixture survival models with known asymptotics. MPIDR Working Papers, WP 2011-004.

  • Olausson, P. (1991). Mortality among the elderly in Sweden by social class. Social Science & Medicine, 32(4), 437–440.

    Article  Google Scholar 

  • Phelan, J. C., Link, B. G., Diez-Roux, A., Kawachi, I., & Levin, B. (2004). Fundamental causes of social inequalities in mortality: A test of the theory. Journal of Health and Social Behavior, 45(3), 265–285.

    Article  Google Scholar 

  • Preston, S., Elo, I., Rosenwaike, I., & Hill, M. (1996). African-American mortality at older ages: Results of a matching study. Demography, 33(2), 193–209.

    Article  Google Scholar 

  • Rahkonen, O., Laaksonen, M., Martikainen, P., Roos, E., & Lahelma, E. (2006). Job control, job demands, or social class? The impact of working conditions on the relation between social class and health. Journal of Epidemiology and Community Health, 60(1), 50–54.

    Article  Google Scholar 

  • Riley, M. (1973). Aging and cohort succession: Interpretations and misinterpretations. Public Opinion Quarterly, 37(1), 35–49.

    Article  Google Scholar 

  • Riley, M. (1987). On the significance of age in sociology. American Sociological Review, 52(1), 1–14.

    Article  Google Scholar 

  • Rodriguez, G. (1994). Statistical issues in the analysis of reproductive histories using hazard models. Annals of the New York Academy of Sciences, 709(1), 266–279.

    Article  Google Scholar 

  • Ross, C., & Wu, C. (1996). Education, age, and the cumulative advantage in health. Journal of Health and Social Behavior, 37(1), 104–120.

    Article  Google Scholar 

  • Rostad, B., Deeg, D. J., & Schei, B. (2009). Socioeconomic inequalities in health in older women. European Journal of Ageing, 6(1), 39–47.

    Article  Google Scholar 

  • Schmoor, C., & Schumacher, M. (1997). Effects of covariate omission and categorization when analysing randomized trials with the Cox model. Statistics in Medicine, 16(3), 225–237.

    Article  Google Scholar 

  • Schrijvers, C., van de Mheen, H., Stronks, K., & Mackenbach, J. (1998). Socioeconomic inequalities in health in the working population: The contribution of working conditions. International Journal of Epidemiology, 27(6), 1011–1018.

    Article  Google Scholar 

  • Schumacher, M., Olschewski, M., & Schmoor, C. (1987). The impact of heterogeneity on the comparison of survival times. Statistics in Medicine, 6(7), 773–784.

    Article  Google Scholar 

  • Shkolnikov, V. M., Scholz, R., Jdanov, D. A., Stegmann, M., & Von Gaudecker, H. M. (2008). Length of life and the pensions of five million retired German men. The European Journal of Public Health, 18(3), 264–269.

    Article  Google Scholar 

  • Smith, G., Brunner, E., et al. (1997). Socio-economic differentials in health: The role of nutrition. Proceedings of the Nutrition Society, 56(1), 75–90.

    Article  Google Scholar 

  • Stringhini, S., Sabia, S., Shipley, M., Brunner, E., Nabi, H., Kivimaki, M., et al. (2010). Association of socioeconomic position with health behaviors and mortality. JAMA: The Journal of the American Medical Association, 303(12), 1159–1166.

    Article  Google Scholar 

  • Trussell, J., & Rodriguez, G. (1990). Heterogeneity in demographic research. In: Convergent issues in genetics and demography. USA: Oxford University Press.

  • Vallin, J. (1980). Socio-economic determinants of mortality in industrialized countries. Population Bulletin of the United Nations, 13, 26.

    Google Scholar 

  • Van Doorslaer, E., Masseria, C., & Koolman, X. (2006). Inequalities in access to medical care by income in developed countries. Canadian Medical Association Journal, 174(2), 177–183.

    Article  Google Scholar 

  • van Raalte, A., Kunst, A., Deboosere, P., Leinsalu, M., Lundberg, O., Martikainen, P., et al. (2011). More variation in lifespan in lower educated groups: Evidence from 10 European countries. International Journal of Epidemiology, 40(6), 1703–1714.

    Article  Google Scholar 

  • Vaupel, J. (2010). Biodemography of human ageing. Nature, 464(7288), 536–542.

    Article  Google Scholar 

  • Vaupel, J., Manton, K., & Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16(3), 439–454.

    Article  Google Scholar 

  • Vaupel, J., & Yashin, A. (1983). The deviant dynamics of death in heterogeneous populations. Austria: International Institute for Applied Systems Analysis.

    Google Scholar 

  • Vaupel, J., & Yashin, A. (1985). Heterogeneity’s ruses: Some surprising effects of selection on population dynamics. American Statistician, 39(3), 176–185.

    Google Scholar 

  • Wienke, A. (2010). Frailty models in survival analysis (Vol. 37). Boca Raton, FL: Chapman & Hall/CRC.

    Book  Google Scholar 

  • Wilkinson, R. (1997). Socioeconomic determinants of health: Health inequalities: Relative or absolute material standards? BMJ, 314(7080), 591.

    Article  Google Scholar 

  • Willson, A., Shuey, K., & Elder, G, Jr. (2007). Cumulative advantage processes as mechanisms of inequality in life course health1. American Journal of Sociology, 112(6), 1886–1924.

    Article  Google Scholar 

  • Wing, S., Manton, K., Stallard, E., Hames, C., & Tryoler, H. (1985). The black/white mortality crossover: Investigation in a community-based study. Journal of Gerontology, 40(1), 78–84.

    Article  Google Scholar 

  • Xue, X., & Brookmeyer, R. (1996). Bivariate frailty model for the analysis of multivariate survival time. Lifetime Data Analysis, 2(3), 277–289.

    Article  Google Scholar 

  • Yashin, A., Iachine, I., Begun, A., & Vaupel, J. (2001). Hidden frailty: Myths and reality. Research Report 34, Department of Statistics and Demography, Odense University.

  • Zajacova, A., & Burgard, S. (2013). Healthier, wealthier, and wiser: A demonstration of compositional changes in aging cohorts due to selective mortality. Population Research and Policy Review, 32(3), 1–14.

    Article  Google Scholar 

  • Zajacova, A., Goldman, N., & Rodriguez, G. (2009). Unobserved heterogeneity can confound the effect of education on mortality. Mathematical Population Studies, 16(2), 153–173.

    Article  Google Scholar 

  • Zarulli, V., Jasilionis, D., & Jdanov, D. (2012). Changes in educational differentials in old-age mortality in Finland and Sweden between 1971–1975 and 1996–2000. Demographic Research, 26(19), 489–510.

    Article  Google Scholar 

  • Zarulli, V., Marinacci, C., Costa, G., & Caselli, G. (2013). Mortality by education level at late-adult ages in turin: A survival analysis using frailty models with period and cohort approaches. BMJ Open, 3(7). http://bmjopen.bmj.com/citmgr?gca=bmjopen%3B3%2F7%2Fe002841.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Virginia Zarulli.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zarulli, V. Unobserved Heterogeneity of Frailty in the Analysis of Socioeconomic Differences in Health and Mortality. Eur J Population 32, 55–72 (2016). https://doi.org/10.1007/s10680-015-9361-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10680-015-9361-1

Keywords

Navigation