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Cohort Analysis in Epidemiology

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A Celebration of Statistics

Abstract

Epidemiologic cohort studies typically involve the follow-up of large population groups over many years to ascertain the effects of environmental exposures on the outbreak of illness and the age and cause of death. An efficient method of analysis is to fit Poisson regression models to grouped data consisting of a multidimensional classification of disease cases and person-years of observation by discrete categories of age, calendar period, and various aspects of exposure. Extension of these models for use with disease rates and exposure variables that vary continuously with age or time leads to the well-known proportional hazards model. Incorporation of external standard rates is more likely to improve the estimates of exposure effects in additive or excess risk models than in multiplicative or relative risk situations. Examples are provided of the maximum likelihood fitting of such models to data from cohort studies of British doctors and Montana smelter workers. The discussion considers the choice between models and certain problems that may arise when attempting to fit nonmultiplicative relationships.

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Bibliography

  • Aalen, O. (1978). “Nonparametric inference for a family of counting processes.” Ann. Statist., 6, 701–726.

    Article  MathSciNet  MATH  Google Scholar 

  • Andersen, P. K. and Gill, R. D. (1982). “Cox’s regression model for counting processes: A large sample study.” Ann. Statist., 10, 1100–1120.

    Article  MathSciNet  MATH  Google Scholar 

  • Aranda-Ordaz, F. J. (1983). “An extension of the proportional hazards model for grouped data.” Biometrics, 39, 109–117.

    Article  MathSciNet  MATH  Google Scholar 

  • Armitage, P. (1955). “Tests for linear trend in proportions and frequencies.” Biometrics, 11, 375–386.

    Article  Google Scholar 

  • Armitage, P. (1971). Statistical Methods in Medical Research. Oxford: Blackwell.

    Google Scholar 

  • Armitage, P. and Doll, R. (1961). “Stochastic models for carcinogenesis.” In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 4, 19–38.

    Google Scholar 

  • Baker, R. J. and Nelder, J. A. (1978). The GLIM System: Release 3. Oxford: Numerical Algorithms Group.

    Google Scholar 

  • Beaumont, J. J. and Breslow, N. E. (1981). “Power considerations in epidemiologic studies of vinyl chloride workers.” Amer. J. Epidemiology, 114, 725–734.

    Google Scholar 

  • Beebe, G. W. (1981). “The atomic bomb survivors and the problem of low dose radiation effects.” Amer. J. Epidemiology, 114, 761–783.

    Google Scholar 

  • Berry, G. (1980). “Dose-response in case-control studies.” Epidemiology and Community Health, 34, 217–222.

    Article  Google Scholar 

  • Berry, G. (1983). “The analysis of mortality by the subject-years method.” Biometrics, 39, 173–184.

    Article  Google Scholar 

  • Berry, G., Gilson, J. C., Holmes, S., Lewinsohn, H. C., and Roach, S. A. (1979). “Asbestosis: A study of dose-response relationship in an asbestos textile factory.” British J. Industrial Medicine, 36, 98–112.

    Google Scholar 

  • Breslow, N. E. (1972). “Contribution to discussion of paper by D. R. Cox.” J. Roy. Statist. Soc. Ser. B, 34, 216–217.

    MathSciNet  Google Scholar 

  • Breslow, N. (1981). “Odds ratio estimators when the data are sparse.” Biometrika, 68, 73–84.

    Article  MathSciNet  MATH  Google Scholar 

  • Breslow, N. (1982). “Design and analysis of case-control studies.” Annual Rev. Public Health, 3, 29–54.

    Article  Google Scholar 

  • Breslow, N. (1984). “Elementary methods of cohort analysis.” Internat. J. Epidemiology, 13, 112–115.

    Article  Google Scholar 

  • Breslow, N. E. and Day, N. E. (1980). Statistical Methods in Cancer Research I: The Analysis of Case-Control Studies. Lyon: International Agency for Research on Cancer.

    Google Scholar 

  • Breslow, N. E., Lubin, J. H., Marek, P., and Langholz, B. (1983). “Multiplicative models and cohort analysis.” J. Amer. Statist. Assoc., 78, 1–12.

    Article  MATH  Google Scholar 

  • Brown, C. C. and Chu, K. C. (1983). “Implications of the multistage theory of carcinogenesis applied to occupational arsenic exposure.” J. Natl. Cancer Inst., 70, 455–463.

    Google Scholar 

  • Clayton, D. G. (1982). “The analysis of prospective studies of disease aetiology.” Comm. Statist. A—Theory Methods, 11, No. 19, 2129–2155.

    Article  MathSciNet  Google Scholar 

  • Cochran, W. G. (1954). “Some methods for strengthening the common χ2 tests.” Biometrics, 10, 417–451.

    Article  MathSciNet  MATH  Google Scholar 

  • Cox, D. R. (1972). “Regression models and life tables (with discussion).” J. Roy. Statist. Soc. Ser. B, 34, 187–220.

    MathSciNet  MATH  Google Scholar 

  • Cox, D. R. (1975). “Partial likelihood.” Biometrika, 62, 269–276.

    Article  MathSciNet  MATH  Google Scholar 

  • Cox, D. R. and Hinkley, D. V. (1974). Theoretical Statistics. London: Chapman and Hall.

    MATH  Google Scholar 

  • Doll, R. and Hill, A. B. (1964). “Mortality in relation to smoking: Ten years’ observations on British doctors.” British Medical J., 1, 1399–1410, 1460–1467.

    Article  Google Scholar 

  • Doll, R. and Hill, A. B. (1966). “Mortality of British doctors in relation to smoking: Observations on coronary thrombosis.” Natl. Cancer Inst. Monogr., 19, 205–268.

    Google Scholar 

  • Doll, R. and Peto, R. (1976). “Mortality in relation to smoking: 20 years’ observations on male British doctors.” British Medical J., 2, 1525–1536.

    Article  Google Scholar 

  • Doll, R. and Peto, R. (1978). “Cigarette smoking and bronchial carcinoma: Dose and time relationships among regular smokers and lifelong non-smokers.” J. Epidemiology and Community Health, 32, 303–313.

    Article  Google Scholar 

  • Fienberg, S. E. (1980). The Analysis of Cross-Classified Data, 2nd edn. Cambridge, MA: MIT Press.

    MATH  Google Scholar 

  • Fienberg, S. E. and Mason, W. M. (1985). “Specification and implementation of age, period and cohort models.” In W. M. Mason and S. E. Fienberg (eds.), Cohort Analysis in Social Research: Beyond the Identification Problem. New York: Springer-Verlag, 45–88.

    Google Scholar 

  • Fox, A. J. and Collier, P. F. (1976). “Low mortality rates in industrial cohort studies due to selection for work and survival in the industry.” British. J. Preventive and Social Medicine, 30, 225–230.

    Google Scholar 

  • Frome, E. L. (1983). “The analysis of rates using Poisson regression models.” Biometrics, 39, 665–674.

    Article  MATH  Google Scholar 

  • Frost, W. H. (1939). “The age selection of mortality from tuberculosis in successive decades.” Amer. J. Hygiene A, 30, 91–96.

    Google Scholar 

  • Gilbert, E. S. (1983). “An evaluation of several methods for assessing the effects of occupational exposure to radiation.” Biometrics, 39, 161–171.

    Article  Google Scholar 

  • Gill, R. (1980). Censoring and Stochastic Integrals. Amsterdam: Mathematical Centre Tracts.

    MATH  Google Scholar 

  • Hammond, E. C. (1966). “Smoking in relation to the death rates of one million men and women.” Natl. Cancer Inst. Monogr., 19, 127–204.

    Google Scholar 

  • Hauck, W. W. (1979). “The large sample variance of the Mantel-Haenszel estimator of a common odds ratio.” Biometrics, 35, 817–820.

    Article  MathSciNet  MATH  Google Scholar 

  • Holford, T. R. (1980). “The analysis of rates and of survivorship using log-linear models.” Biometrics, 36, 299–306.

    Article  MATH  Google Scholar 

  • Johansen, S. (1981). “Discussion of paper by D. Oakes.” Internat. Statist. Rev., 49, 258–262.

    Google Scholar 

  • Kalbfleisch, J. D. and Prentice, R. L. (1980). The Statistical Analysis of Failure Time Data. New York: Wiley.

    MATH  Google Scholar 

  • Kleinbaum, D. G., Kupper, L. L., and Morgenstern, H. (1982). Epidemiologic Research. Belmont: Wadsworth.

    Google Scholar 

  • Knox, E. G. (1973). “Computer simulation of industrial hazards.” British J. Industrial Medicine, 30, 54–63.

    Google Scholar 

  • Laird, N. and Olivier, D. (1981). “Covariance analysis of censored survival data using log-linear analysis techniques.” J. Amer. Statist. Assoc., 76, 231–240.

    Article  MathSciNet  MATH  Google Scholar 

  • Lee, A. M. and Fraumeni, J. F. (1969). “Arsenic and respiratory cancer in man: An occupational study.” J. Natl. Cancer Inst., 42, 1045–1052.

    Google Scholar 

  • Lee-Feldstein, A. (1983). “Arsenic and respiratory cancer in humans: Follow-up of copper smelter employees in Montana.” J. Natl. Cancer Inst., 70, 601–610.

    Google Scholar 

  • Lehman, E. L. (1959). Testing Statistical Hypotheses. New York: Wiley.

    Google Scholar 

  • Lundin, F. E., Archer, V. E., and Wagoner, J. K. (1979). “An exposure-time-response model for lung cancer mortality in uranium miners: Effects of radiation exposure, age, and cigarette smoking.” In N. E. Breslow and A. Whittemore (eds.), Energy and Health. Philadelphia: SIAM, 243–264.

    Google Scholar 

  • Maahon, B. and Pugh, T. F. (1970). Epidemiology: Principles and Methods. Boston: Little, Brown.

    Google Scholar 

  • Mantel, N. and Haenszel, W. (1959). “Statistical aspects of the analysis of data from retrospective studies of disease.” J. Natl. Cancer Inst., 22, 719–748.

    Google Scholar 

  • Moolgavkar, S. H., Lustbader, E. D., and Venzon, D. J. (1984). “A geometric approach to nonlinear regression diagnostics with application to matched case-control studies.” Ann. Statist., 12, 816–826.

    Article  MathSciNet  MATH  Google Scholar 

  • Nelder, J. A. and Wedderburn, R. W. M. (1972). “Generalized linear models.” J. Roy. Statist. Soc. A, 135, 370–384.

    Article  Google Scholar 

  • Oakes, D. (1977). “The asymptotic information in censored survival data.” Biometrika, 64, 441–448.

    Article  MathSciNet  MATH  Google Scholar 

  • Oakes, D. (1981). “Survival times: Aspects of partial likelihood.” Internat. Statist. Rev., 49, 235–264.

    Article  MathSciNet  MATH  Google Scholar 

  • Pregibon, D. (1981). “Logistic regression diagnostics.” Ann. Statist., 9, 705–724.

    Article  MathSciNet  MATH  Google Scholar 

  • Prentice, R. L. and Self, S. (1983). “Asymptotic distribution theory for Cox-type regression models with general relative risk form.” Ann. Statist., 11, 804–813.

    Article  MathSciNet  MATH  Google Scholar 

  • Rao, C. R. (1965). Linear Statistical Inference and its Applications. New York: Wiley.

    MATH  Google Scholar 

  • Richards, F. S. G. (1961). “A method of maximum likelihood estimation.” Roy. Statist. Soc. Ser. B, 23, 469–473.

    MathSciNet  MATH  Google Scholar 

  • Rothman, K. J. (1974). “Synergy and antagonism in cause-effect relationships.” Amer. J. Epidemiology, 99, 385–388.

    Google Scholar 

  • Rothman, K. J. and Boice, J. D. (1979). Epidemiologic Analysis with a Programmable Calculator. NIH Publication 79–1649. Washington: U.S. Government Printing Office.

    Google Scholar 

  • Roueché, B. (1967). Annals of Epidemiology. Boston: Little, Brown.

    Google Scholar 

  • Schlesselman, J. J. (1982). Case-Control Studies: Design, Conduct and Analysis. New York: Oxford U.P.

    Google Scholar 

  • Selikoff, I. J., Hammond, E. C., and Seidman, H. (1980). “Latency of asbestos disease among insulation workers.” Cancer, 46, 2736–2740.

    Article  Google Scholar 

  • Storer, B. E., Wacholder, S., and Breslow, N. E. (1983). “Maximum likelihood fitting of general risk models to stratified data.” Appl. Statist., 32, 177–181.

    Article  Google Scholar 

  • Tarone, R. E. (1982). “The use of historical control information in testing for a trend in Poisson means.” Biometrics, 38, 457–462.

    Article  Google Scholar 

  • Thomas, D. C. (1977). “Addendum to a paper by Liddel, F. D. K., McDonald, J. C. and Thomas, D. C.” J. Roy. Statist. Soc. Ser. A, 483–485.

    Google Scholar 

  • Thomas, D. C. (1981). “General relative risk models for survival time and matched case-control analysis.” Biometrics, 37, 673–686.

    Article  Google Scholar 

  • Thomas, D. C. (1982). “Temporal effects and interactions in cancer: Implications of carcinogenic models.” In R. L. Prentice and A. S. Whittemore (eds.), Environmental Health: Risk Assessment, Philadelphia: SIAM, 107–121.

    Google Scholar 

  • Thompson, R. and Baker, R. (1981). “Composite link functions in generalized linear models.” Appl. Statist., 30, 125–131.

    Article  MathSciNet  MATH  Google Scholar 

  • Wall, W. D. and Williams, H. L. (1970). Longitudinal Studies and the Social Sciences. London: Heinemann.

    Google Scholar 

  • White, E. (1982). “A two stage design for the study of the relationship between a rare exposure and a rare disease.” Amer. J. Epidemiology, 115, 119–128.

    Google Scholar 

  • Whitehead, J. (1980). “Fitting Cox’s regression model to survival data using GLIM.” Appl. Statist., 29, 268–275.

    Article  MathSciNet  MATH  Google Scholar 

  • Whittemore, A. and Altshuler, B. (1976). “Lung cancer incidence in cigarette smokers: Further analysis of Doll and Hill’s data on British physicians.” Biometrics, 32, 805–816.

    Article  Google Scholar 

  • Yule, G. U. (1934). “On some points relating to vital statistics, more especially statistics of occupational mortality.” J. Roy. Statist. Soc., 94, 1–84

    Article  Google Scholar 

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Breslow, N.E. (1985). Cohort Analysis in Epidemiology. In: Atkinson, A.C., Fienberg, S.E. (eds) A Celebration of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8560-8_6

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  • DOI: https://doi.org/10.1007/978-1-4613-8560-8_6

  • Publisher Name: Springer, New York, NY

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