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Dependence Estimation for Marginal Models of Multivariate Survival Data

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Abstract

We have previously(Segal and Neuhaus, 1993) devised methods for obtaining marginal regression coefficients and associated variance estimates for multivariate survival data, using a synthesis of the Poisson regression formulation for univariate censored survival analysis and generalized estimating equations (GEE's). The method is parametric in that a baseline survival distribution is specified. Analogous semiparametric models, with unspecified baseline survival, have also been developed (Wei, Lin and Weissfeld, 1989; Lin, 1994).Common to both these approaches is the provision of robust variances for the regression parameters.

However, none of this work has addressed the more difficult area of dependence estimation. While GEE approaches ostensibly provide such estimates, we show that there are problems adopting these with multivariate survival data. Further, we demonstrate that these problems can affect estimation of the regression coefficients themselves. An alternate, ad hoc approach to dependence estimation, based on design effects, is proposed and evaluated via simulation and illustrative examples.

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References

  • Aitkin, M. and Clayton, D.G. “The fitting of exponential, Weibull and extreme value distributions to complex censored survival data using GLIM,” Applied Statistics vol. 29 pp. 156–163, 1980.

    Article  MATH  Google Scholar 

  • Baker, R.J. and Nelder, J.A. Generalized Linear Interactive Modelling, Release 3, Numerical Algorithms Group, Oxford, 1978.

    Google Scholar 

  • Cai, J. and Prentice, R.L. “Estimating equations for hazard ratio parameters based on correlated failure time data,” Biometrika vol. 82 pp. 151–164, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  • Chambers, J.M., Mallows, C.L. and Stuck, B.W. “A method for simulating stable random variables,” Journal of the American Statistical Association vol. 71 pp. 340–344, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  • Clayton, D.G. “A Monte Carlo method for Bayesian inference in frailty models,” Biometrics vol. 47 pp. 467–485, 1991.

    Article  Google Scholar 

  • Clayton, D.G. and Cuzick, J. “The EM algorithm for Cox's regression model using GLIM,” Applied Statistics vol. 34 pp. 148–156, 1985a.

    Article  Google Scholar 

  • Clayton, D.G and Cuzick, J. “Multivariate generalizations of the proportional hazards model (with discussion),” Journal of the Royal Statistical Society, Series A vol. 148 pp. 82–117, 1985b.

    Article  MATH  MathSciNet  Google Scholar 

  • Cox, D.R. “Regression models and life tables (with discussion),” Journal of the Royal Statistical Society, Series B vol. 34 pp. 187–220, 1972.

    MATH  Google Scholar 

  • Crowder, M. “On the use of a working correlation matrix in generalized linear models for repeated measures,” Biometrika vol. 82 pp. 407–410, 1995.

    Article  MATH  Google Scholar 

  • Diggle, P.J., Liang, K.-Y., and Zeger, S.L. The Analysis of Longitudinal Data, Oxford: Oxford University Press, 1993.

    Google Scholar 

  • Donner, A. and Koval, J.J. “The estimation of intraclass correlation in the analysis of family data,” Biometrics vol. 36 pp. 19–25, 1980.

    Article  MATH  Google Scholar 

  • Feinleib, M., Garrison, R.J., Fabsitz et al. “The NHLBI Twin Study of cardiovascular risk factors: Methodology and summary of results,” American Journal of Epidemiology vol. 106 pp. 284–295, 1977.

    Google Scholar 

  • Feller, W. An Introduction to Probability Theory and its Applications, Volume II, Wiley: New York, 1971.

    MATH  Google Scholar 

  • Fleming, T. and Harrington, D.P. Counting Processes and Survival Analysis, Wiley: New York, 1991.

    MATH  Google Scholar 

  • Hougaard, P. ‘Discussion of “Multivariate generalizations of the proportional hazards model” by D. Clayton and J. Cuzick’, Journal of the Royal Statistical Society, Series Avol. 148 pp. 82–117, 1985.

  • Hougaard, P. “A class of multivariate failure time distributions,” Biometrika vol. 73 pp. 671–678, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  • Hougaard, P. “Frailty models for survival data,” Lifetime Data Analysis vol. 1 pp. 255–273, 1995.

    Article  Google Scholar 

  • Hsu, L. and Prentice, R.L. “On assessing the strength of dependency between failure time variates,” Biometrika vol. 83 pp. 491–506, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  • Huster, W.J., Brookmeyer, R. and Self, S.G. “Modelling paired survival data with covariates,” Biometrics vol. 45 pp. 145–156, 1989.

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  • Kanter, M. “Stable densities under change of scale and total variation inequalities,” Annals of Probability vol. 3 pp. 697–707, 1975.

    MATH  MathSciNet  Google Scholar 

  • Liang, K.-Y., Self, S.G. and Chang, Y.-C. “Modeling marginal hazards in multivariate failure-time data,” Journal of the Royal Statistical Society Series B vol. 55 pp. 441–53, 1993.

    MATH  MathSciNet  Google Scholar 

  • Liang, K.-Y. and Zeger, S.L. “Longitudinal data analysis using generalized linear models,” Biometrika vol. 73 pp. 13–22, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  • Lin, D.Y. “Cox regression analysis of multivariate failure data: The marginal approach,” Statistics in Medicine vol. 13 pp. 2233–2247, 1994.

    Google Scholar 

  • Lin, D.Y. “MULCOX2: A general computer program for the Cox regression analysis of multivariate failure data,” Computer Methods and Programs in Biomedicine vol. 40 pp. 279–293, 1993.

    Article  Google Scholar 

  • McCullagh, P. and Nelder, J.A. Generalized Linear Models, Chapman and Hall: London, 1983.

    MATH  Google Scholar 

  • Neuhaus, J.M. “Estimation efficiency and tests of covariate effects with clustered binary data,” Biometrics vol. 49 pp. 989–996, 1993.

    Article  Google Scholar 

  • Neuhaus, J.M. and Segal, M.R. “Design effects for generalized linear models,” Statistics in Medicine vol. 12 pp. 1259–1268, 1993.

    Google Scholar 

  • Oakes, D. “Bivariate survival models induced by frailties,” Journal of the American Statistical Association vol. 84 pp. 487–493, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  • Oakes, D. “Use of frailty models for multivariate survival data,” in Proceedings of the XVIIth International Biometrics Conference, McMaster University, Hamilton, Ontario, 1994.

    Google Scholar 

  • Prentice, R.L. and Cai, J. “Covariance and survivor function estimation using censored multivariate failure time data,” Biometrika vol. 79 pp. 495–512, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  • Rao, J.N.K. and Scott, A.J. “A simple method for the analysis of clustered binary data,” Biometrics vol. 48 pp. 577–585, 1992.

    Article  Google Scholar 

  • Royall, R.M. “Model robust confidence intervals using maximum likelihood estimators,” International Statistical Review vol. 54 pp. 221–226, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  • Scott, A.J. and Holt, D. “The effect of two–stage sampling on ordinary least squares methods,” Journal of the American Statistical Association vol. 77 pp. 485–497, 1990.

    Google Scholar 

  • Segal, M.R. and Neuhaus, J.M. “Robust inference for multivariate survival data,” Statistics in Medicine vol. 12 pp. 1019–1031, 1993.

    Google Scholar 

  • Shih, J.H. and Louis, T.A. “Inferences on the association parameter in copula models for bivariate survival data,” Biometrics vol. 51 pp. 1384–1399, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  • Vaupel, J.W., Manton, K.G. and Stallard, E. “The impact of heterogeneity in individual frailty on the dynamics of mortality,” Demography vol. 16 pp. 439–454, 1979.

    Google Scholar 

  • Wei, L.J., Lin, D.Y. and Weissfeld, L. “Regression analysis of multivariate incomplete failure time data by modeling marginal distributions,” Journal of the American Statistical Association vol. 84 pp. 1065–1073, 1989.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Division of Biostatistics, University of California, San Francisco, CA, 94143-0560, USA

    Mark R. Segal & John M. Neuhaus

  2. Department of Mathematics, Murdoch University, Murdoch, W.A., 6150, AUSTRALIA

    Ian R. James

Authors
  1. Mark R. Segal
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  2. John M. Neuhaus
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  3. Ian R. James
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Segal, M.R., Neuhaus, J.M. & James, I.R. Dependence Estimation for Marginal Models of Multivariate Survival Data. Lifetime Data Anal 3, 251–268 (1997). https://doi.org/10.1023/A:1009601031424

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