Generalizations of Current Status Data with Applications

  • Nicholas P. Jewell
  • Mark van der Laan
Chapter

Abstract

In estimation of a survival function, current status data arises when the only information available on individuals is their survival status at a single monitoring time. Here, we briefly review extensions of this form of data structure in two directions: (i) doubly censored current status data, where there is incomplete information on the origin of the failure time random variable, and (ii) current status information on more complicated stochastic processes. Simple examples of these data forms are presented for motivation.

Keywords

Human Immunodeficiency Virus Nonparametric Maximum Likelihood Current Status Data Partner Study Human Immunodeficiency Virus Infected Individual 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ayer, M, Brunk, H. D., Ewing, G. M., Reid, W. T., and Silverman, E. (1955), “An Empirical Distribution Function for Sampling with Incomplete Information,” Annals of Statistics, 26, 641–647.MathSciNetMATHCrossRefGoogle Scholar
  2. Barlow, R. E., Bartholomew, D. J., Bremner, J. M., and Brunk, H. D. (1972), Statistical Inference Under Order Restrictions, New York, NY: Wiley.MATHGoogle Scholar
  3. Bickel, P. J., Klaassen, A. J., Ritov, Y., and Wenner, J. A. (1993), Efficient and Adaptive Inference in Semi-Parametric Models, Baltimore, MD: Johns Hopkins University Press.Google Scholar
  4. DeGruttola, V., and Lagakos, S. W. (1989), “Analysis of Doubly-Censored Survival Data, With Application to AIDS,” Biometrics, 45, 1–11.MathSciNetCrossRefGoogle Scholar
  5. Diamond, I. D., and McDonald, J. W. (1991), “The Analysis of Current Status Data,” in Demographic Applications of Event History Analysis, Trussell, J., Hankinson, R., and Tilton, J. (eds.), Oxford, UK: Oxford University Press.Google Scholar
  6. Diamond, I. D., McDonald, J. W., and Shah, I. H. (1986), “Proportional Hazards Models for Current Status Data: Application to the Study of Differentials in Age at Weaning in Pakistan,” Demography, 23, 607–620.CrossRefGoogle Scholar
  7. Dinse, G. E., and Lagakos, S. W. (1982), “Nonparametric Estimation of Lifetime and Disease Onset Distributions from Incomplete Observations,” Biometrics, 38, 921–932.MATHCrossRefGoogle Scholar
  8. Groeneboom, P., and Wellner, J. A. (1992), Nonparametric Maximum Likelihood Estimators for Interval Censoring and Deconvolution, Boston, MA: Birkhaüser-Boston.CrossRefGoogle Scholar
  9. Huang, J. (1994), Estimation in Regression Models with Interval Censoring, Ph.D. Thesis, University of Washington.Google Scholar
  10. Jewell, N. P., and Shiboski, S. C. (1990), “Statistical Analysis of HIV Infectivity Based on Partner Studies,” Biometrics, 46, 1133–1150.CrossRefGoogle Scholar
  11. Jewell, N. P., and Shiboski, S. C. (1993), “The design and analysis of partner studies of HIV transmission,” in Methodological Issues in AIDS Behavioral Research, Ostrow, D. G, and Kessler, R. (eds.), New York, NY: Plenum Publishing Company.Google Scholar
  12. Keiding, N. (1991), “Age-specific Incidence and Prevalence (with discussion),” Journal of the Royal Statistical Society, Series A, 154, 371–412.MathSciNetMATHGoogle Scholar
  13. Klein, R. W., and Spadey, R. H. (1993), “An Efficient Semiparametric Estimator for Binary Response Models,” Econometrica, to appear.Google Scholar
  14. van der Laan, M., Bickel, P., and Jewell, N. P. (1994), “Singly and Doubly Censored Current Status Data: Estimation, Asymptotics and Regression,” submitted for publication.Google Scholar
  15. Rabinowitz, D., and Jewell, N. P. (1994), “Regression with Doubly Censored Current Status Data,” submitted for publication.Google Scholar
  16. Rabinowitz, D., Tsiatis, A and Aragon, J. (1994), “Regression with Interval Censored Data,” Biometrika, to appear.Google Scholar
  17. Shiboski, S. C., and Jewell, N. P. (1992), “Statistical analysis of the time dependence of HIV infectivity based on partner study data,” Journal of the American Statistical Association, 87, 360–372.CrossRefGoogle Scholar
  18. Vittinghoff, E., Malani, H.M., and Jewell, N. P. (1994), “Estimating Patterns of CD4 Lymphocyte Decline Using Data from a Prevalent Cohort of HIV Infected Individuals,” Statistics in Medicine, 13, 1101–1118.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Nicholas P. Jewell
    • 1
  • Mark van der Laan
    • 1
  1. 1.Division of Biostatistics and Department of StatisticsUniversity of CaliforniaBerkeleyUSA

Personalised recommendations