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Decrement tables and the measurement of morbidity: I

Published online by Cambridge University Press:  20 April 2012

S. Haberman
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1.1. In a recent paper, Pollard(1) introduced the morbidity-mortality table as a model for measuring the interaction between morbidity and mortality of chronic degenerative conditions like breast cancer and lung cancer. This device consists essentially of two double decrement tables: for example, persons either remain free of breast cancer for life or depart from the breast cancer-free group by incurring breast cancer or by dying from other causes; those who incur breast cancer either remain alive with it until they die from it or die from other causes. Clearly this model is very similar to the combined marriage-mortality table which is referred to briefly in U.K. actuarial texts(2). Neither of these models, however, allows for increments, for example recoveries from breast cancer in Pollard's morbidity-mortality table. In recent years one of the major advances in the theoretical development and practical construction of life tables has been the incorporation of increments. A guide to this methodology is provided here with particular emphasis on the measurement of incidence and prevalence of disease. Further applications are given in an accompanying paper, to appear in Volume 111(3).

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 110 , Issue 2 , September 1983 , pp. 361 - 381
Copyright
Copyright © Institute and Faculty of Actuaries 1983

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References

(1) Pollard, A. H. (1980) The interaction between morbidity and mortality. (with discussion). J.I.A., 107, 233.Google Scholar
(2) Neill, A. (1977) Life contingencies. Chapter 9. Heinemann. London.Google Scholar
(3) Haberman, S. (1984) Decrement tables and the measurement of morbidity II. To appear in J.I.A. 111.Google Scholar
(4) Hoem, J. M. & Funck Jensen, U. (1981) Multi-state Life Table Methodology: A Probabilist Critique. Laboratory of Actuarial Mathematics, University of Copenhagen, Working Paper no. 38.Google Scholar
(5) Du Pasquier, L. G. (1912, 1913) Mathematische theorie der invaliditatsverischerung. Mitteilungen der Vereinigung der Schweitzerische Verischerungs-mathematiker, 7, 1; 8, 1.Google Scholar
(6) Fix, E. & Neyman, J. (1951) A simple stochastic model of recovery, relapse death and loss of patients. Human Biology, 23, 205.Google Scholar
(7) Sverdrup, E. (1965) Estimates and test procedures in connection with stochastic models for deaths, recoveries and transfers between different states of health. Skand. Akt. 40, 184.Google Scholar
(8) Chiang, C. L. (1968) Introduction to Stochastic Processes in Biostatistics. J. Wiley, New York.Google Scholar
(9) Hoem, J. M. (1977) A Markov chain model of working life tables. Scand. Act. J. pp. 1–20.CrossRefGoogle Scholar
(10) Rogers, A. (1975) Introduction to Multi-Regional Mathematical Demography. J. Wiley, New York.Google Scholar
(11) Schoen, R. & Nelson, V. E. (1974) Marriage, divorce and mortality: a life table analysis. Demography, 11, 267.CrossRefGoogle ScholarPubMed
(12) Schoen, R. (1975) Constructing increment-decrement life tables. Demography, 12, 313.Google Scholar
(13) Schoen, R. & Land, K. C. (1979) A general algorithm for estimating a Markov-generated increment-decrement life table with applications to marital-status patterns. J. Amer. Stat. Assoc. 14, 761.Google Scholar
(14) Willekens, F. J., Shah, I., Shah, J. M. & Ramachandran, P. (1982) Multi-state analysis of marital status life tables: theory and application. Pop. Studies 36, 129.Google Scholar
(15) Preston, S. H., Keyfitz, N. & Schoen, R. (1973) Cause-of-death life tables: application of a new technique to world-wide data. Trans. Soc. Act. 25, 83.Google Scholar
(16) Heasman, M. A. & Lipworth, L. (1966) Accuracy of Certification of Cause of Death GRO Studies and Medical and Population Subjects No. 20. HMSO London.Google Scholar
(17) Benjamin, B. & Pollard, J. H. (1980) Analysis of Mortality and other Actuarial Statistics. Chapters 1–4. Heinemann, London.Google Scholar
(18) Matsumoto, N., Whisnant, J. P., Kurland, L. T. et al. (1973) Natural history of stroke in Rochester, Minnesota, 1955 through 1969: an extension of a previous study, 1945 through 1954. Stroke 4, 20.Google Scholar
(19) Haberman, S. (1978) Application of mathematical results to stroke incidence and prevalance data. Social Sci. and Med. 12, 153.Google ScholarPubMed
(20) Stallones, R., Dyken, M., Fang, H. et al. (1972) Epidemiology for stroke facilities planning. Stroke, 3, 360.CrossRefGoogle Scholar
(21) Registrar General (1968) Decennial Supplement. English Life Tables no. 12. HMSO, London.Google Scholar
(22) Abu Zeid, H. A. H., Choi, N. W., Hsu, P. H. et al. (1978) Prognostic factors in the survival of 1484 stroke cases observed for 30 to 48 months I diagnostic types and descriptive variables. Archives of Neurology, 35, 121.CrossRefGoogle Scholar
(23) Haberman, S. (1982) Statistical analysis of survival after stroke and the derivation of life assurance underwriting ratings. Ph.D. Thesis. The City University.Google Scholar
(24) Hoem, J. M. (1970) Point estimation of forces of transition in demographic models. J. Roy. Stat. Soc. B, 33, 275.Google Scholar
(25) Elandt Johnson, R. G. & Johnson, N. L. (1980) Survival Models and Data Analysis. J. Wiley, New York.Google Scholar