Volume 41 - Article 4 | Pages 83–102
The threshold age of the lifetable entropy
By Jose Manuel Aburto, Jesús-Adrián Alvarez, Francisco Villavicencio, James W. Vaupel
References
Aburto, J.M. and Beltrán-Sánchez, H. (2019). Upsurge of homicides and its impact on life expectancy and life span inequality in Mexico, 2005–2015. American Journal of Public Health 109(3): 483–489.
Aburto, J.M. and van Raalte, A.A. (2018). Lifespan dispersion in times of life expectancy fluctuation: The case of Central and Eastern Europe. Demography 55(6): 2071–2096.
Aburto, J.M., Wensink, M., van Raalte, A., and Lindahl-Jacobsen, R. (2018). Potential gains in life expectancy by reducing inequality of lifespans in Denmark: An international comparison and cause-of-death analysis. BMC Public Health 18(1): 831.
Archer, C.R., Basellini, U., Hunt, J., Simpson, S.J., Lee, K.P., and Baudisch, A. (2018). Diet has independent effects on the pace and shape of aging in Drosophila melanogaster. Biogerontology 19(1): 1–12.
Arriaga, E.E. (1984). Measuring and explaining the change in life expectancies. Demography 21(1): 83–96.
Baudisch, A. (2011). The pace and shape of ageing. Methods in Ecology and Evolution 2(4): 375–382.
Baudisch, A., Salguero-Gómez, R., Jones, O.R., Wrycza, T., Mbeau-Ache, C., Franco, M., and Colchero, F. (2013). The pace and shape of senescence in angiosperms. Journal of Ecology 101(3): 596–606.
Beltrán-Sánchez, H., Preston, S.H., and Canudas-Romo, V. (2008). An integrated approach to cause-of-death analysis: Cause-deleted life tables and decompositions of life expectancy. Demographic Research 19(35): 1323–1350.
Beltrán-Sánchez, H. and Soneji, S. (2011). A unifying framework for assessing changes in life expectancy associated with changes in mortality: The case of violent deaths. Theoretical Population Biology 80(1): 38–48.
Brønnum-Hansen, H. (2017). Socially disparate trends in lifespan variation: A trend study on income and mortality based on nationwide danish register data. BMJ Open 7(5): e014489.
Burger, O., Baudisch, A., and Vaupel, J.W. (2012). Human mortality improvement in evolutionary context. Proceedings of the National Academy of Sciences 109(44): 18210–18214.
Colchero, F., Rau, R., Jones, O.R., Barthold, J.A., Conde, D.A., Lenart, A., Németh, L., Scheuerlein, A., Schoeley, J., Torres, C., Zarulli, V., Altmann, J., Brockman, D.K., Bronikowski, A.M., Fedigan, L.M., Pusey, A.E., Strier, K.B., Baudisch, A., Alberts, S.C., and Vaupel, J.W. (2016). The emergence of longevous populations. Proceedings of the National Academy of Sciences 113(48): e7681–e7690.
Demetrius, L. (1978). Adaptive value, entropy and survivorship curves. Nature 275: 213–214.
Demetrius, L. (1974). Demographic parameters and natural selection. Proceedings of the National Academy of Sciences 71(12): 4645–4647.
Demetrius, L. (1979). Relations between demographic parameters. Demography 16(2): 329–338.
Edwards, R.D. and Tuljapurkar, S. (2005). Inequality in life spans and a new perspective on mortality convergence across industrialized countries. Population and Development Review 31(4): 645–674.
Fernández, O.E. and Beltrán-Sánchez, H. (2015). The entropy of the life table: A reappraisal. Theoretical Population Biology 104: 26–45.
Gigliarano, C., Basellini, U., and Bonetti, M. (2017). Longevity and concentration in survival times: The log-scale-location family of failure time models. Lifetime Data Analysis 23(2): 254–274.
Gillespie, D.O., Trotter, M.V., and Tuljapurkar, S.D. (2014). Divergence in age patterns of mortality change drives international divergence in lifespan inequality. Demograph 51(3): 1003–1017.
Goldman, N. and Lord, G. (1986). A new look at entropy and the life table. Demograph 23(2): 275–282.
Hakkert, R. (1987). Life table transformations and inequality measures: Some noteworthy formal relationships. Demography 24(4): 615–622.
Hill, G. (1993). The entropy of the survival curve: An alternative measure. Canadian Studies in Population 20(1): 43–57.
Human Mortality Database (2018). Human mortality database [electronic resource]. Berkeley and Rostock: University of California and Max Planck Institute for Demographic Research.
Keyfitz, N. (1968). Introduction to the mathematics of populations. Reading: Addison–Wesley.
Keyfitz, N. (1977). What difference would it make if cancer were eradicated? An examination of the Taeuber paradox. Demography 14(4): 411–418.
Missov, T.I. and Lenart, A. (2013). Gompertz–Makeham life expectancies: Expressions and applications. Theoretical Population Biology 90: 29–35.
Mitra, S. (1978). A short note on the Taeuber paradox. Demography 15(4): 621–623.
Pollard, J.H. (1988). On the decomposition of changes in expectation of life and differentials in life expectancy. Demography 25(2): 265–276.
Shkolnikov, V.M., Andreev, E.M., and Begun, A.Z. (2003). Gini coefficient as a life table function: Computation from discrete data, decomposition of differences and empirical examples. Demographic Research 8(11): 305–358.
Shkolnikov, V.M., Andreev, E.M., Zhang, Z., Oeppen, J., and Vaupel, J.W. (2011). Losses of expected lifetime in the United States and other developed countries: Methods and empirical analyses. Demography 48(1): 211–239.
Smits, J. and Monden, C. (2009). Length of life inequality around the globe. Social Science and Medicine 68(6): 1114–1123.
Tuljapurkar, S. and Edwards, R.D. (2011). Variance in death and its implications for modeling and forecasting mortality. Demographic Research 24(21): 497–526.
van Raalte, A.A. and Caswell, H. (2013). Perturbation analysis of indices of lifespan variability. Demography 50(5): 1615–1640.
van Raalte, A.A., Martikainen, P., and Myrskylä, M. (2014). Lifespan variation by occupational class: compression or stagnation over time? Demography 51(1): 73–95.
van Raalte, A.A., Sasson, I., and Martikainen, P. (2018). The case for monitoring lifespan inequality. Science 362(6418): 1002–1004.
Vaupel, J.W. (1986). How change in age-specific mortality affects life expectancy. Population Studies 40(1): 147–157.
Vaupel, J.W. and Canudas-Romo, V. (2003). Decomposing change in life expectancy: A bouquet of formulas in honor of Nathan Keyfitz’s 90th birthday. Demography 40(2): 201–216.
Vaupel, J.W., Zhang, Z., and van Raalte, A.A. (2011). Life expectancy and disparity: An international comparison of life table data. BMJ Open e000128: 1–6.
Wagner, P. (2010). Sensitivity of life disparity with respect to changes in mortality rates. Demographic Research 23(3): 63–72.
Wrycza, T. (2014). Entropy of the Gompertz–Makeham mortality model. Demographic Research 30(49): 1397–1404.
Wrycza, T.F., Missov, T.I., and Baudisch, A. (2015). Quantifying the shape of aging. PLoS ONE 10(3): e0119163.
Zhang, Z. and Vaupel, J.W. (2009). The age separating early deaths from late deaths. Demographic Research 20(29): 721–730.