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References
Akushevich I., Kulminski A., Manton K.G., 2005. Life tables with covariates: life tables with covariates: dynamic model for nonlinear analysis of longitudinal data. Math Popul Stud, 12(2):51–80.
Akushevich I., Manton K.G., Kulminski A., Kovtun M., Kravchenko J., Yashin A., 2006. Population models for the health effects of ionizing radiation. Radiats Biol Radioecol 46(6):663–674.
Akushevich I., Kravchenko J. S., Manton K.G., 2007. Health based population forecasting: effects of smoking on mortality and fertility. Risk Anal 27(2):467–82.
Akushevich I., Kovtun M., Manton K.G., Yashin A.I., 2008. Linear latent structure analysis and modeling of multiple categorical variables. Comput Math Methods Med (in press)
Armitage P., Doll R., 1954. The age distribution of cancer and a multistage theory of carcinogenesis. Br J Cancer 8:12.
Armitage P., Doll R., 1961. Stochastic models for carcinogenesis. In: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA: University of California Press.
Bartholomew D.J., Knott M., 1999. Latent Variable Models and Factor Analysis, 2nd edition. New York: Oxford University Press.
Berkman L., Singer B., Manton K.G., 1989. Black-white differences in health status and mortality among the elderly. Demography 26(4):661–678.
Blot W.J., Fraumeni J.F., Mason T.J., Hoover R., 1979. Developing clues to environmental cancer: a stepwise approach with the use of cancer mortality data. Environ Health Perspect 32:53–58.
Clogg, C.C., 1995. Latent Class Models. Handbook of Statistical Modeling for the Social and Behavioral Sciences. New York: Plenum Press, pp. 311–360.
Efron B., Morris C., 1973. Combining possibly related estimation problems. J R Statist Soc B 35:379–421.
Erosheva, E.A., 2005. Comparing Latent Structures of the Grade of Membership, Rasch, and Latent Class Models. Psychometrika 70:619–628.
Everitt B., 1984. An introduction to latent variable models. London, New York: Chapman and Hall.
Frank S., 2007. Dynamics of Cancer. Incidence, Inheritance, and Evolution. Princeton and Oxford: Princeton University Press 378 pages.
Gaver D.P., O’Muircheartaigh I.G., 1987. Robust empirical Bayes analyses of event rates. Technometrics 29:1–15.
Gavrilov L.A., Gavrilova N.S. 2006a Models of Systems Failure in Aging. In: Michael Conn P. (Editor): Handbook of Models for Human Aging, Burlington, MA: Elsevier Academic Press. 45–68.
Gavrilov L.A., Gavrilova N.S., 2006b. Reliability Theory of Aging and Longevity. In: Masoro E.J., Austad S.N. (Eds.): Handbook of the Biology of Aging, 6th edition. Academic Press. San Diego, CA, USA, 3–42.
Gilbert N., Troitszch K.G., 1999. Simulation for the Social Scientist. Buckingham: Open University Press.
Gompertz B., 1825. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philos Trans R Soc Lond 115(1825):513–585.
Goodman L.A., 1974. Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika 61:215–231.
Goodman L.A., 1978. Analyzing qualitative/categorical data: log-linear models and latent-structure analysis. Cambridge, MA: Abt Books.
Haenszel W., Kurihara M., 1968. Studies of Japanese migrants. I. Mortality from cancer and other diseases among Japanese in the United States. J Natl Cancer Inst 40:43–68.
Heinen T., 1996. Latent class and discrete latent trait models: similarities and differences. Thousand Oaks, CA: SAGE Publications.
Kossenko M.M., Thomas T.L., Akleyev A.V. et al., 2005. The Techa River Cohort: study design and follow-up methods. Radiat Res. 164(5):591–601.
Kovtun, M., Akushevich, I., Manton, K.G. et al., 2006. Grade of membership analysis: one possible approach to foundations. In: Focus on Probability Theory, pp. 1–26, Hauppauge, NY: Nova Science Publishers.
Kovtun, M., Akushevich, I., Manton, K.G., Tolley, H.D., 2007. Linear latent structure analysis: mixture distribution models with linear constrains. Stat Methodol 4:90–110.
Kravchenko J., Goldschmidt-Clermont P.J., Powell T. et al., 2005. Endothelial progenitor cell therapy for atherosclerosis: the philosopher's stone for an aging population ? Effect of therapy on human life span is predicted to be comparable to that caused by eliminating cancer. Sci Aging Knowl Environ 25:18.
Krestinina L.Y., Preston D.L., Ostroumova E.V. et al., 2005. Protracted radiation exposure and cancer mortality in the extended Techa river cohort. Radiat Res 164:602–611.
Langeheine, R., Rost, J. (Eds.), 1988. Latent Trait and Latent Class Models. New York, NY: Plenum Press.
Lazarsfeld P.F., Henry N.W., 1968. Latent Structure Analysis. Boston, MA: Houghton Mifflin Company.
Little M.P., 2003. Risks associated with ionizing radiation. Br Med Bull 68:259–275.
Manton K.G., Stallard E., 1981. Methods for the analysis of mortality risks across heterogeneous small populations: examination of space-time gradients in cancer mortality in NC counties. Demography 18:217–230.
Manton K.G., Stallard E., 1988. Chronic Disease Modeling: Measurement and Evaluation of the Risks of Chronic Disease Processes. London: Griffin.
Manton K.G., Land K.C., 2000 Active life expectancy estimates for the U.S. elderly population: a multidimensional continuous-mixture model of functional change applied to completed cohorts, 1982–1996. Demography 37(3):253–265.
Manton K.G., Yashin A.I., 2000. Mechanisms of Aging and Mortality: Searches for New Paradigms. Monographs on Population Aging, 7, Odense, Denmark: Odense University Press.
Manton K.G., Woodbury M.A., Stallard E., 1981. A variance components approach to categorical data models with heterogeneous cell populations: analysis of spatial gradients in county lung cancer mortality rates in North Carolina counties. Biometrics 37:259–269.
Manton K.G., Stallard E., Creason J P. et al., 1985. U.S. cancer mortality 1950–1978: a strategy for analyzing spatial and temporal patterns. Environ Health Perspect 60:369–380.
Manton K.G., Stallard E., Woodbury M.A. et al., 1987. Statistically adjusted estimates of geographic mortality profiles. J Natl Cancer Inst 78:805–815.
Manton K.G., Woodbury M.A., Stallard E. et al., 1989. Empirical Bayes procedures for stabilizing maps of U.S. cancer mortality rates. J Am Stat Assoc 84(407):637–650.
Manton K.G., Stallard E., Singer B.H., 1992. Projecting the future size and health status of the U.S. elderly population. Int J Forecast 8:433–458.
Manton K.G., Woodbury M.A., Tolley H.D., 1994. Statistical applications using fuzzy sets. New York: John Wiley and Sons.
Manton K.G., Gu X., Huang H. et al., 2004 Fuzzy set analyses of genetic determinants of health and disability status. Stat Methods Med Res. 13(5):395–408.
Manton K.G., Gu X., Lamb V.L. 2006. Change in chronic disability from 1982 to 2004/2005 as measured by long-term changes in function and health in the U.S. elderly population. Proc Natl Acad Sci USA. 103(48):18374–18379.
Manton K.G., Akushevich I., Kulminski A., 2008. Human mortality at extreme ages: data from the national long term care survey and linked medicare records, Math Popul Stud. 15(2):137–159.
Marcoulides G.A., Moustaki I. (Eds.), 2002. Latent Variable and Latent Structure Models. Methodology for Business and Management. Mahwah, NJ: Lawrence Erlbaum Associates.
Mason T.J., McKey F.W., Hoover R. et al., 1975. Atlas of cancer mortality for U.S. counties, 1950–1969. Department of Health, Education, and Welfare, publication 75–780, Washington, DC: U.S Government Printing Office.
Mason T.J., McKey F.W., Hoover R. et al., 1976. Atlas of cancer mortality among U.S. nonwhites: 1950–1969. Department of Health, Education, and Welfare, publication 76–1204, Washington, DC: U.S. Government Printing Office.
Mislevy R.J., 1984. Estimating latent distributions. Psychometrika 49:359–381.
Morris C.N., 1983. Parametric empirical Bayes inference: theory and applications. J Am Stat Assoc 78:47–55.
NCI (National Cancer Institute), 1987. Research contributions made possible by the NCI Cancer Atlases published in the 1970s. Office of Cancer Communications Report (Backgrounder series), June 9, Bethesda, MD.
Pickle L.W., Mason T.J., Howard N. et al., 1987. Atlas of U.S. cancer mortality among whites, 1950–1980. Department of Health and Human Services, Publication 87–2900, Washington, DC: U.S. Government Printing Office.
Press W.H., Flannery B.P., Teukolsky S.A. et al., 1999. Numerical recipes in FORTRAN, the art of scientific computing. Cambridge: Cambridge University Press.
Qu Y., Tan M., Kutner M.H., 1996 Random effects models in latent class analysis for evaluating accuracy of diagnostic tests. Biometrics 52:797–810.
Riggan W.B., Creason J.P., Nelson W.C. et al., 1987. U.S. cancer mortality rates and trends, 1950–1979. Volume IV: Maps. Environmental Protection Agency, Health Effects Research Laboratory, Publication 600/1-83/015e, Washington, DC: U.S. Government Printing Office.
Riggan W.B., Manton K.G., Creason J.P. et al., 1991. Assessment of spatial variation of risks in small populations. Environ Health Perspect 96:223–238.
Robbins H., 1955. The empirical Bayes approach to statistics. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability Volume 1. Berkely, CA: University of California Press. pp. 157–164.
Robbins H., 1964. The empirical Bayes approach to statistical decision problems. Ann Math Stat 35:49–68.
Sacher G.A., Trucco E., 1962 The stochastic theory of mortality. Ann NY Acad Sci 96:985–1007.
Singer, B. 1989. Grade of membership representations: concepts and problems. In: T.W. Andersen, K.B. Athreya, and D.L. Iglehart (Eds.), Probability, Statistics, and Mathematics: Papers in Honor of Samuel Karlin. New York: Academic Press, Inc. pp. 317–334.
Stallard E., 2007. Trajectories of disability and mortality among the U. S. elderly population: evidence from the 1984–1999 NLTCS. North Am Actuar J 11(3):16–53.
Strehler B.L., Mildvan A.S., 1960. General theory of mortality and aging. Science 132:14–21.
Tolley H.D., Manton K.G., 1992. Large sample properties of estimates of a discrete grade of membership model. Ann Inst Stat Math, 44:85–95.
Tsutakawa R.K., 1988. Mixed model for analyzing geographic variability in mortality rates. J Am Stat Assoc 83:37–42.
Tsutakawa R.K., Shoop G.L., Marienfeld C.J., 1985. Empirical Bayes estimation of cancer mortality rates. Stat Med 4:201–212.
Uebersax J.S., 1997. Analysis of student problem behaviors with latent trait, latent class, and related probit mixture models. In: Rost J., Langeheine R., (Eds). Applications of Latent Trait and Latent Class Models in the Social Sciences. New York, NY: Waxmann. pp. 188–195.
Uebersax, J.S., Grove, W.M. 1993. A latent trait finite mixture model for the analysis of rating agreement. Biometrics 49:823–835
UNSCEAR 2000, published 2001. United Nations Scientific Committee on the Effects of Atomic Radiation. Health Phys. 80(3):291.
Wachter K.W., 1999. Grade of membership models in low dimensions. Stat Papers 40:439–458.
Witteman J.C.M., Grobbee D.E., Valkenburg H.A. et al., 1994. J-shaped relation between change in diastolic blood pressure and aortic atherosclerosis. Lancet 343:504–507.
Woodbury M.A., Clive J., 1974. Clinical pure types as a fuzzy partition. J Cybernetics 4:111–121.
Woodbury M.A., Manton K.G. 1977. A random walk model of human mortality and aging. Theor Popul Biol 11:37–48.
Yashin A.I., Manton K.G., 1997: Effects of unobserved and partially observed covariate processes on system failure: a review of models and estimation strategies. Stat Sci 12(1):20–34.
Yashin A.I., Iachine I.A., Begun A.S., 2000. Mortality modeling: a review. Math Popul Stud 8(4):305–332.
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Manton, K., Akushevich, I., Kravchenko, J. (2009). Stochastic Methods of Analysis. In: Cancer Mortality and Morbidity Patterns in the U.S. Population. Statistics for Biology and Health. Springer, New York, NY. https://doi.org/10.1007/978-0-387-78193-8_5
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