Standard and Innovative Statistical Methods for Empirically Analyzing Cancer Morbidity and Mortality

  • K.G. Manton
  • Igor Akushevich
  • Julia Kravchenko
Part of the Statistics for Biology and Health book series (SBH)

In Chapter 2, we examined the substantive and mathematical basis of a number of theories and models of the mechanisms underlying human carcinogenesis and suggested some innovative modeling strategies to deal with various informational limitations of specific observational and measurement plans. In Chapter 3, we discussed the various types of controllable and uncontrollable risk factors that have been evaluated to determine if they increase cancer risk in humans. Both of these aspects are important to taken into account while modeling cancer risks and outcomes on population level, as well as for individualizing them. In this chapter, we discuss certain approaches to cancer analyses, such as the features of cancer survival and incidence and tumor growth models applied to national population cancer mortality and tumor registry data, and various techniques for assessing the quality and content of various types of data.

In the first section of this chapter, we describe the standard survival...


Life Table Hazard Function Female Breast Cancer Frailty Model Wait Time Distribution 
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  1. Akushevich I., Kulminski A., Manton K., 2005a. Life tables with covariates: life tables with covariates: dynamic model for nonlinear analysis of longitudinal data. Math Popul Stud 12(2):51–80.Google Scholar
  2. Akushevich I., Kulminski A., Manton K.G., 2005b. Human Mortality and Chronic Disease Incidence at Extreme Ages: New Data and Analysis. Talk given at Session “New Direction on Mortality Research” in the Population Association of America Annual Meeting, Philadelphia, March 31–April 2, 2005.Google Scholar
  3. Akushevich I., Kulminski A., Akushevich L., Manton K.G., 2006. Age Patterns of Disease Incidences in the U.S. Elderly: Population-Based Analysis. Trends Working Paper Series.Google Scholar
  4. Allison P.D., 1984. Event History Analysis. Beverly Hills, CA: SAGE Publications.Google Scholar
  5. Anderson D.E., 1974. Genetic study of breast cancer: identification of a high risk group. Cancer 34(4):1090–1097.CrossRefGoogle Scholar
  6. Armitage P., Doll R., 1954. The age distribution of cancer and a multi-stage theory of carcinogenesis. Br J Cancer 8(1):1–12.Google Scholar
  7. 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.Google Scholar
  8. Beard, R.E. (1959). Note on some mathematical mortality models. In: Wolstenholme, G.E.W., O’Connor, M. (Eds.). The Lifespan of Animals (pp. 302–311). Boston: Little, Brown.Google Scholar
  9. Beard, R.E. (1971). Some aspects of theories of mortality, cause of death analysis, forecasting and stochastic processes. In: Brass, W. (Ed.), Biological Aspects of Demography (pp. 57–68). London: Taylor and Francis.Google Scholar
  10. Bishop Y.M.M., Fienberg S.E. Discrete Multivariate Analysis: Theory and Practice, Cambridge, MA: The MIT Press, 1975.MATHGoogle Scholar
  11. Brown L.D., Cai T.T., DasGupta A., 2001. Interval Estimation for a Binomial Proportion. Stat Sci 16:101–117.MATHMathSciNetGoogle Scholar
  12. Chiang C.L., 1968. Introduction to Stochastic Processes in Biostatistics. New York : John WileyMATHGoogle Scholar
  13. Cox D., 1972. Regression models and life tables (with discussion). J R Stat Soc, Ser B 34:187–220.MATHGoogle Scholar
  14. De Waard F., Halewijn B., Huizinga J., 1964. The bimodal age distribution of patients with mammary carcinoma. Cancer 17:141–152.CrossRefGoogle Scholar
  15. Frier B., 1982. Roman life expectancy: Ulpian’s evidence. Harv Stud Classic Philol 86:213–251.CrossRefGoogle Scholar
  16. Gavrilov L.A., Gavrilova N.S., 2006a. Models of systems failure in aging. In: P. Michael Conn (Ed): Handbook of Models for Human Aging, Burlington, MA: Elsevier Academic Press, 45–68.Google Scholar
  17. 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. San Diego, CA, USA: Academic Press 3–42.Google Scholar
  18. Hebert P.L., Geiss L.C., Tierney E.F. et al., 1999. Identifying person with diabetes using medicare claims data. Am J Med Qual 14(6):270–277.CrossRefGoogle Scholar
  19. Hougaard P., 1988. A boundary modification of kernel function smoothing, with application to insulin absorption kinetics. In Compstat Lectures 31–36. Physica, Vienna.Google Scholar
  20. Jacquez J.A., 1972. Compartmental Analysis in Biology and Medicine, volume 50. New York: Elsevier.Google Scholar
  21. Jones H.W., 1945. John Graunt and His Bills of Mortality. Bull Med Libr Assoc 33(1):3–4.Google Scholar
  22. Kaplan E.L., Meier P., 1958. Nonparametric estimation from incomplete observations. J Am Stat Assoc 53:457–481.MATHCrossRefMathSciNetGoogle Scholar
  23. Kertzer D.I., Laslet P. (eds.), 1995. Aging in the Past. Berkley-Los Angeles-Oxford: University of California Press. At:
  24. Kestenbaum B.A., 1992. Description of extreme aged population based on improved medicare enrollment data. Demography 29(4):565–580.CrossRefGoogle Scholar
  25. Kestenbaum B., Ferguson B.R., 2002. Mortality of the extreme aged in the United States in the 1990s, based on improved medicare data. North Am Actua J 6(3):35–44.MathSciNetGoogle Scholar
  26. Kloeden P.E., Platen E., 1992. Numerical Solution of Stochastic Differential Equations. Application of Mathematics Series, volume 23. Heidelberg: Springer-Verlag.Google Scholar
  27. Kloeden P.E., Platen E., Schurz H., 1994. Numerical Solution of SDE Through Computer Experiments. Berlin: Springer.MATHGoogle Scholar
  28. Knudson A.G. Jr., 1971. Mutation and cancer: statistical study of retinoblastoma. Proc Natl Acad Sci USA 68:820–823.CrossRefGoogle Scholar
  29. Kulminski A., Akushevich I., Manton K., 2004. Modeling nonlinear effects in longitudinal survival data: implications for the physiological dynamics of biological systems. Front Biosci 9:481–493.CrossRefGoogle Scholar
  30. MacMahon B., Cole P., Brown J., 1973. Etiology of human breast cancer: a review. J Natl Cancer Inst, 50:21–42.Google Scholar
  31. Manton K.G., Stallard E., 1980. A two-disease model of female breast cancer: mortality in 1969 among white females in the United States. J Natl Cancer Inst. 64(1):9–16.MathSciNetGoogle Scholar
  32. Manton K.G., Stallard E., 1984. Recent Trends in Mortality Analysis. Orlando, Florida, USA: Academic Press.Google Scholar
  33. Manton K.G., Stallard E., 1988. Chronic Disease Modeling: Measurement and Evaluation of the Risks of Chronic Disease Processes. London: Charles Griffin.Google Scholar
  34. Manton K.G., Stallard E., 1996. Longevity in the United States: age and sex-specific evidence on life span limits from mortality patterns: 1960–1990. J Gerontol Ser A-Biol Sci Med Sci 51(5):B362–B375.Google Scholar
  35. Manton K.G., Land K.C., 2000a. Active life expectancy estimates for the U.S. elderly population: a multidimensional continuous-mixture model of functional change applied to completed cohorts, 1982 to 1996. Demography 37(3):253–265.Google Scholar
  36. Manton K.G., Land K.C., 2000b. Multidimensional disability/mortality trajectories at ages 65 and over: the impact of state dependence. Soc Indic Res 51(2):193–221.Google Scholar
  37. Manton K.G., Gu X., 2001. Changes in the prevalence of chronic disability in the United States black and non-black population above age 65 from 1982 to 1999. Proc Natl Acad Sci USA 98(11):6354–6359.CrossRefGoogle Scholar
  38. Manton K.G., Patrick C.H., Stallard E., 1980. Mortality model based on delays in progression of chronic diseases: alternative to cause elimination model. Public Health Rep. 95(6):580–588.Google Scholar
  39. Manton, K., Woodbury, M., Stallard, E. 1981. A variance components approach to categorical data models with heterogenous mortality rates in North Carolina counties, Biometrics 37:259–269.CrossRefGoogle Scholar
  40. Manton K.G., Stallard E., Vaupel J.W., 1986. Alternative models for the heterogeneity of mortality risks among the aged. J Am Stat Assoc. 81(395):635–644.CrossRefGoogle Scholar
  41. 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.CrossRefGoogle Scholar
  42. 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.CrossRefGoogle Scholar
  43. Manton K.G., Lowrimore G., Yashin A., 1993. Methods for combining ancillary data in stochastic compartment models of cancer mortality: generalization of heterogeneity models. Math Popul Stud 4(2):133–147.CrossRefGoogle Scholar
  44. Manton K.G., Woodbury M.A., Tolley H.D., 1994. Statistical Applications using Fuzzy Sets. New York: John Wiley and Sons.MATHGoogle Scholar
  45. Manton K.G., Corder L., Stallard E., 1997. Chronic disability trends in the U.S. elderly populations 1982 to 1994. Proc Natl Acad Sci USA 94:2593–2598.CrossRefGoogle Scholar
  46. Manton K.G., Akushevich I., Kulminski A., 2005. The Stochastic Linkage of Mortality Declines and Declines in Functional Disability. Invited paper for a meeting on “Projecting Mortality” at Brookings Institution, sponsored by the Office of Policy, Social Security Administration and the Center for Retirement Research at Boston College.Google Scholar
  47. Manton K.G., Gu X., Lamb V.L., 2006. Long term trends in life expectancy and active life expectancy in the United States. Popul Develop Rev 32(1):81–105.CrossRefGoogle Scholar
  48. Matis J.H., Wehrly T.E., 1979. Stochastic models of compartmental systems. Biometrics 35:199–220.MATHCrossRefGoogle Scholar
  49. McGeough K., 2004. The Romans: New Perspectives. Oxford: ABC-CLIO. 381 pp.Google Scholar
  50. Metzler R., Klafter J., 2000. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys Rep 339:1–77.MATHCrossRefMathSciNetGoogle Scholar
  51. Preston S.H., Elo I.T., Rosenwaike I. et al., Hill M. 1996 African–American mortality at older ages: results of a matching study. Demography 33(2):193–209.CrossRefGoogle Scholar
  52. Risken H., 1996. The Fokker-Planck Equation: Methods of Solution and Applications, 2nd edition, Berlin: Springer-Verlag.MATHGoogle Scholar
  53. Robine J-M., Jagger C., Mathers C.D. et al. (eds.), 2003a. Determining Health Expectancies. West Sussex, UK: John Wiley and Sons.Google Scholar
  54. Robine J-M., Romieu I., Michel J-P., 2003b. Trends in health expectancies. In: Robine J-M., Jagger C., Mathers C.D., Crimmins E.M., Suzman R.M. (eds.), Determining Health Expectancies. West Sussex, UK: John Wiley and Sons.Google Scholar
  55. Rosenwaike I., Stone L.F., 2003. Verification of the ages of super-centenarians in the United States: results of a matching study. Demography 40(4):727–739.CrossRefGoogle Scholar
  56. Simms H., 1942. The use of measurable causes of death (hemorrhage) for the evaluation of aging. J Gen Physiol 26:169–178.CrossRefGoogle Scholar
  57. Social Security Association, 2003. Life Tables for the United States Social Security Area 1900–2100. Actuarial Study No. 116. Distributed by Social Security Association.Google Scholar
  58. Strehler B., 1977. Time, Cells and Aging. New York: Academic Press.Google Scholar
  59. Sullivan D.F., 1971. A single index of mortality and morbidity. HSMHA Health Rep 86:347–354.CrossRefGoogle Scholar
  60. Tsiatis A., 1975. A nonidentifiability aspect of the problem of competing risks. Proc Natl Acad Sci USA 72(1):20–22.MATHCrossRefMathSciNetGoogle Scholar
  61. U.S. Bureau of the Census, 2001. 1999 LTC cross-sectional estimates: source and accuracy statement. Washington, DC: U.S. Census Bureau.Google Scholar
  62. Vaupel J.W., Manton K.G., Stallard E., 1979. The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16:439–454.CrossRefGoogle Scholar
  63. 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.CrossRefGoogle Scholar
  64. Wolf D., 2001. The role of microsimulation in longitudinal data analysis. Can Stud Popul 28:165–179.Google Scholar
  65. Wolter K.M., 1985. Introduction to variance estimation. New York: Springer-Verlag.MATHGoogle Scholar
  66. Woodbury M.A., Manton K.G., Stallard E., 1981. Longitudinal models for chronic disease risk: an evaluation of logistic multiple regression and alternatives. Int J Epidemiol 10: 187–197.CrossRefGoogle Scholar
  67. Woodbury M.A., Manton K.G., 1977. A random walk model of human mortality and aging. Theor Popul Biol 11:37–48.CrossRefMathSciNetGoogle Scholar
  68. Woodbury M.A., Manton K.G., 1983. A theoretical model of the physiological dynamics of circulatory disease in human populations. Hum Biol 55:417–441.Google Scholar
  69. Writing Group for the Women's Health Initiative Investigators, 2002. Risks and benefits of estrogen plus progestin in healthy postmenopausal women: principal results From the Women's Health Initiative randomized controlled trial. JAMA 288:321–333.CrossRefGoogle Scholar
  70. Yashin A.I., Manton K.G., Stallard E. (1986) Dependent competing risks: a stochastic process model. J Math Biol 24(2):119–40.MATHCrossRefMathSciNetGoogle Scholar
  71. 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.MATHCrossRefMathSciNetGoogle Scholar
  72. Yashin A.I., Iachine I.A., 1997. How frailty models can be used for evaluating longevity limits: taking advantage of an interdisciplinary approach. Demography 34(1):31–48.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • K.G. Manton
    • 1
  • Igor Akushevich
    • 1
  • Julia Kravchenko
    • 1
  1. 1.Duke UniversityDurhamUSA

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