Models for Degradation Processes and Event Times Based on Gaussian Processes

  • Kjell A. Doksum
  • Sharon-Lise T. Normand


We present two stochastic models that describe the relationship between marker process values at random time points, event times, and a vector of covariates. In both models the marker processes are degradation processes that represent the decay of systems over time. In the first model the degradation process is a Wiener process whose drift is a function of the covariate vector; in the second model the degradation process is taken to be the difference between a stationary Gaussian process and a time drift whose drift parameter is a function of the covariates. For both models we present statistical methods for estimation of the regression coefficients. The first model is useful for predicting the residual time from study entry to the time a critical boundary is reached while the second model is useful for predicting the latency time from the event initiating degradation until the time the presence of degradation is detected. We present our methods principally in the context of conducting inference in a population of HIV infected individuals.


Latency Time Degradation Process Gaussian Process Wiener Process Residual Time 
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  1. Berman SM. (1990). A stochastic model for the distribution of HIV latency time based on T4 counts. Biometrika 77, 733–741.zbMATHCrossRefGoogle Scholar
  2. CDC (1993). Revision of the HIV classification system and the AIDS surveillance definition. Center for Disease Control and Prevention (Atlanta).Google Scholar
  3. Chhikara RS, Folks L. (1989). The Inverse Gaussian Distribution. Theory, Methodology and Applications. Marcel Dekker, New York.Google Scholar
  4. Doksum KA, Hóyland A. (1992). Models for variable-stress accelerated life testing experiments based on Wiener processes and the inverse Gaussian distribution. Technometrics 34, 74–82.zbMATHCrossRefGoogle Scholar
  5. Jewell NP, Kalbfleisch JD. (1992). Marker models in survival analysis and applications to issues associated with AIDS. In: Jewell NP, Dietz K, Farewell VT, eds. AIDS Epidemiology: Methodological Issues, Birkhäuser, Boston, 211–230.CrossRefGoogle Scholar
  6. Jewell NP, Dietz K, Farwell VT. (1992). AIDS Epidemiology: Methodological Issues, Birkhäuser, Boston.CrossRefGoogle Scholar
  7. Lefkopoulou M, Zelen M. (1992). Intermediate clinical events, surrogate markers and survival. Technical Report 742Z, Dana-Farber Cancer Institute.Google Scholar
  8. Normand S-L, and Doksum K.A. (1994). Nonparametric calibration methods for longitudinal data. Technical Report #HCP-1994–3, Department of Health Care Policy, Harvard Medical School, Boston, MA.Google Scholar
  9. Winkelstein W Jr, Lyman DM, Padian N, Grant R, Samuel M, Anderson RE, Lang W, Riggs J, Levy JA (1987). Sexual practices and risk of infection by the human immunodeficiency virus. J Am Med Assoc. 257, 321–325.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Kjell A. Doksum
    • 1
    • 2
  • Sharon-Lise T. Normand
    • 1
    • 2
  1. 1.Department of StaticsUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of Health Care PolicyHarvard Medical SchoolBostonUSA

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