Multivariate Interval-Censored Survival Data: Parametric, Semi-parametric and Non-parametric Models

  • Philip HougaardEmail author
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


Interval censoring means that an event time is only known to lie in an interval (L,R], with L the last examination time before the event, and R the first after. In the univariate case, parametric models are easily fitted, whereas for non-parametric models, the mass is placed on some intervals, derived from the L and R points. Asymptotic results are simple for the former and complicated for the latter. This paper is a review describing the extension to multivariate data, like eruption times for teeth examined at visits to the dentist. Parametric models extend easily to multivariate data. However, non-parametric models are intrinsically more complicated. It is difficult to derive the intervals with positive mass, and estimated interval probabilities may not be unique. A semi-parametric model makes a compromise, with a parametric model, like a frailty model, for the dependence and a non-parametric model for the marginal distribution. These three models are compared and discussed. Furthermore, extension to regression models is considered. The semi-parametric approach may be sensible in many cases, as it is more flexible than the parametric models, and it avoids some technical difficulties with the non-parametric approach.


Bivariate survival Frailty models Interval censoring Model choice 


  1. Hougaard, P. (2014). Analysis of interval-censored survival data. Book manuscript (in preparation).Google Scholar
  2. Jewell, N., Van der Laan, M., & Lei, X. (2005). Bivariate current state data with univariate monitoring times. Biometrika, 92, 847–862.CrossRefzbMATHMathSciNetGoogle Scholar
  3. Peto, R. (1973). Experimental survival curves for interval-censored data. Applied Statistics, 22, 86–91.CrossRefGoogle Scholar
  4. Sun, J. (2006). The statistical analysis of interval-censored failure time data. New York: Springer.zbMATHGoogle Scholar
  5. Wang, W., & Ding, A. (2000). On assessing the association for bivariate current status data. Biometrika, 87, 879–883.CrossRefzbMATHMathSciNetGoogle Scholar
  6. Yu, Q., Wong, G., & He, Q. (2000). Estimation of a joint distribution function with multivariate interval-censored data when the nonparametric mle is not unique. Biometrical Journal, 42, 747–763.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Biostatistics, LundbeckValbyDenmark

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