Lifetime Data Analysis

, Volume 1, Issue 1, pp 7–18

Multiple time scales in survival analysis

  • David Oakes


In some problems in survival analysis there may be more than one plausible measure of time for each individual. For example mileage may be a better indication of the age of a car than months. This paper considers the possibility of combining two (or more) time scales measured on each individual into a single scale. A collapsibility condition is proposed for regarding the combined scale as fully informative regarding survival. The resulting model may be regarded as a generalization of the usual accelerated life model that allows time-dependent covariates. Parametric methods for the choice of time scale, for testing the validity of the collapsibility assumption and for parametric inference about the failure distribution along the new scale are discussed. Two examples are used to illustrate the methods, namely Hyde's (1980) Channing House data and a large cohort mortality study of asbestos workers in Quebec.


accelerated life model aging bivariate hazard function equivalency time-dependent covariates 


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  1. D. R. Cox, “Regression models and life-tables” (with discussion),J. Roy. Statist. Soc. B, vol. 34 pp. 187–220, 1972.Google Scholar
  2. D. R. Cox and D. Oakes,Analysis of Survival Data, Chapman and Hall: London, 1984.Google Scholar
  3. V. T. Farewell and D. R. Cox, “A note on multiple time scales in life testing,”Appl. Statist., vol. 28 pp. 73–75, 1979.Google Scholar
  4. J. Hyde, “Survival analysis with incomplete observations,” inBiostatistics Casebook, R. G. Miller, B. Efron, B. W. Brown, L. E. Moses (eds.), New York: Wiley, 1980, pp. 31–46.Google Scholar
  5. F. D. K. Liddell, J. C. McDonald, and D. C. Thomas, “Methods of cohort analysis: appraisal by application to asbestos mining” (with discussion),J. Roy. Statist. Soc. A, vol. 140 pp. 469–491, 1977.Google Scholar
  6. J. C. McDonald, F. D. K. Liddell, A. Dufresne, and A. D. McDonald, “The 1891–1920 birth cohort of Quebec chrysotile miners and millers: mortality 1976–88,”Brit. J. Ind. Med., vol. 50 pp. 1073–1081, 1993.Google Scholar
  7. J. C. McDonald, F. D. K. Liddell, G. W. Gibbs, G. E. Eyssen, and A. D. McDonald, “Dust exposure and mortality in chrysotile mining, 1910–1975,”Brit. J. Ind. Med., vol. 37 pp. 11–24, 1980.Google Scholar
  8. W. Nelson, “Hazard plotting for incomplete failure data,”J. Qual. Technology, vol. 1 pp. 27–42, 1969.Google Scholar
  9. J. Robins, “Estimation of the time-dependent accelerated failure time model in the presence of confounding factors,”Biometrika, vol. 79 pp. 321–334, 1992.Google Scholar
  10. J. Robins and A. A. Tsiatis, “Semiparametric estimation of an accelerated failure time model with time-dependent covariates,”Biometrika, vol. 79 pp. 311–320, 1992.Google Scholar
  11. D. C. Thomas, “General relative risk models for survival time and matched case-control analysis,”Biometrics, vol. 37 pp. 673–686, 1981.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • David Oakes
    • 1
  1. 1.Departments of Statistics and BiostatisticsUniversity of RochesterRochester

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