Advertisement

Modeling The Relationship Between Progression Of CD4-Lymphocyte Count And Survival Time

  • Victor DeGruttola
  • Xin Ming Tu

Abstract

In models for repeated observations of a measured response, the length of the response vector may be determined by a survival process related to the response. If the measurement error is large, and probability of death depends on the true, unobserved value of the response, then the survival process must be modelled. Wu and Carroll (1988) proposed a random effects model for a two-sample longitudinal data in the presence of informative censoring, in which the individual effects included only slopes and intercepts. We propose methods for fitting a broad class of models of this type, in which both the repeated measures and the survival time are modelled using random effects. These methods permit us to estimate parameters describing the relationship between measures of disease progression and survival time; and we apply them to results of AIDS clinical trials.

Keywords

Survival Time American Statistical Association Growth Curve Model Middle Curve Informative Censoring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. DeGruttola, V., Wulfsohn, M. and Tsiatis, A. (1990) “Modeling the relationship between survival after AIDS diagnosis and progression of markers of HIV disease,” Technical Report, Harvard School of Public Health.Google Scholar
  2. Dempster, A.P., Rubin, D.B. and Laird, N.M. (1977) “Maximum likelihood with incomplete data via the E-M algorithm,” Journal of the Royal Statistical Society, Series B 39, 1–38.Google Scholar
  3. Dempster, A.P., Rubin, D.B. and Tsutakawa, R.K. (1981) “Estimation in covariance component models,” Journal of the American Statistical Association, 76, 341–353.CrossRefGoogle Scholar
  4. Fischl, M., Parker, C., Pettinelli, C., Wulfsohn, M., Hirsch, M., Collier, AC., et al. (1990) “A randomized controlled trial of a reduced daily dose of zidovudine in patients with the Acquired Immunodeficiency Syndrome,” New England Journal of Medicine, 323, 107–114.CrossRefGoogle Scholar
  5. Gelfand, A.E. and Smith, A.F.M. (1990), “Sampling-based approaches to calculating marginal densities,” Journal of the American Statistical Association, 85, 398–409.CrossRefGoogle Scholar
  6. Geman, S. and Geman, D. (1984), “Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741.PubMedCrossRefGoogle Scholar
  7. Harville, D.A. (1977), “Maximum likelihood approaches to variance component estimation and to related problems,” Journal of the American Statistical Association, 72, 320–340.CrossRefGoogle Scholar
  8. Laird, N.M. and Ware, J.H. (1982), “Random-effects models for longitudinal data” Biometrics, 38, 963–974.PubMedCrossRefGoogle Scholar
  9. Meng and Rubin (1990) “Using EM to obtain asymptotic variance-covar iance matrices: the SEM algorithm,” Journal of the American Statistical Association, to appear.Google Scholar
  10. Rubin, D.B. (1976) “Inference and missing data,” Biometrika, 63, 57–67.CrossRefGoogle Scholar
  11. Rubin, D.B. (1987a) Multiple Imputation for nonresponse in surveys. John Wiley and Sons, New York.CrossRefGoogle Scholar
  12. Rubin, D.B. (1987b), Comment on “The calculation of posterior distributions by data augmentation,” by M.A. Tanner and W.H. Wong, Journal of the American Statistical Association, 82, 543–546.Google Scholar
  13. Tanner, M. and Wong, W. (1987), “The calculation of posterior distributions by data augmentation,” Journal of the American Statistical Association, 82, 528–550.CrossRefGoogle Scholar
  14. Turnbull (1976), “The empirical distribution function with arbitrarily grouped, censored, and truncated data,” Journal of the Royal Statistical Society, Series B, 38, 290–295.Google Scholar
  15. Wu, M.C. and Carroll R.J. (1988), “Estimation and comparison of changes in the presence of Informative right censoring by modeling the censoring process,” Biometrics, 44, 175–188.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Victor DeGruttola
    • 1
  • Xin Ming Tu
    • 1
  1. 1.Department of BiostatisticsHarvard School of Public HealthBostonUSA

Personalised recommendations