The Annals of Applied Statistics

Bayesian semiparametric inference for multivariate doubly-interval-censored data

Alejandro Jara, Emmanuel Lesaffre, Maria De Iorio, and Fernando Quintana

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Based on a data set obtained in a dental longitudinal study, conducted in Flanders (Belgium), the joint time to caries distribution of permanent first molars was modeled as a function of covariates. This involves an analysis of multivariate continuous doubly-interval-censored data since: (i) the emergence time of a tooth and the time it experiences caries were recorded yearly, and (ii) events on teeth of the same child are dependent. To model the joint distribution of the emergence times and the times to caries, we propose a dependent Bayesian semiparametric model. A major feature of the proposed approach is that survival curves can be estimated without imposing assumptions such as proportional hazards, additive hazards, proportional odds or accelerated failure time.

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Ann. Appl. Stat. Volume 4, Number 4 (2010), 2126-2149.

First available in Project Euclid: 4 January 2011

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Multivariate doubly-interval-censored data Bayesian nonparametrics linear dependent Poisson–Dirichlet prior linear dependent Dirichlet process prior


Jara, Alejandro; Lesaffre, Emmanuel; De Iorio, Maria; Quintana, Fernando. Bayesian semiparametric inference for multivariate doubly-interval-censored data. Ann. Appl. Stat. 4 (2010), no. 4, 2126--2149. doi:10.1214/10-AOAS368.

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Supplemental materials

  • Supplementary material A: MCMC schemes for posterior computation. A complete description of the full conditionals for marginal and conditional MCMC algorithms for fitting the LDPD survival model for doubly-interval-censored data is given.
  • Supplementary material B: The HIV-AIDS data. The analysis of the data set considered by De Gruttola and Lagakos (1989) is presented. This analysis allows for the comparison of the LDPD model with the one-sample nonparametric maximum likelihood estimator proposed by De Gruttola and Lagakos (1989). The data set considers information from a cohort of hemophiliacs at risk of human immunodeficiency virus (HIV) infection from infusions of blood they received periodically to treat their hemophilia in two hospitals in France. For this cohort both infection with HIV and the onset of acquired immunodeficiency syndrome (AIDS) or other clinical symptoms could be subject to censoring. Therefore, the induction time between infection and clinical AIDS are treated as doubly-censored.