Abstract
Interval censoring appears when the event of interest is only known to have occurred within a random time interval. Estimation and hypothesis testing procedures for interval-censored data are surveyed. We distinguish between frequentist and Bayesian approaches. Computational aspects for every proposed method are described and solutions with S-Plus, whenever are feasible, are mentioned. Three real data sets are analyzed.
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Best, N.G., Cowles, M.K. and Vines, S.K. (1995)CODA Manual version 0.30, MRC Biostatistics unit, Cambridge, UK.
Böhning, D., Schlattmann, P. and Dietz, E. (1996) Interval-censored data: A note on the nonparametric maximum likelihood estimator of the distribution function.Biometrika 83, 462–466.
Brookmeyer, R. and Goedert, J.J. (1989) Censoring in an epidemic with an application to hemophilia-associated AIDS.Biometrics 45, 325–335.
Calle, M.L. and Gómez, G. (2001) Nonparametric Bayesian estimation from interval-censored data using Monte Carlo methods.Journal of Statistical Planning and Inference 98, 73–87.
Chang, M. N. and Yang, G. L. (1987) Strong consistency of a nonparametric estimator of the survival function with doubly censored data.Annals of Statistics 16, 1536–1547.
Courgeau, D. and Najim, J. (1996) Interval-censored event history analysis.Population: An English Selection,8, 191–298.
De Gruttola, V. and Lagakos, S.W. (1989) Analysis of doubly censored survival data, with application to AIDS.Biometrics 45, 1–11.
Doksum, K. (1974) Tailfree and neutral random probabilities and their posterior distributions.Ann. Probab. 2, 183–201.
Doss, H. (1994) Bayesian nonparametric estimation for incomplete data via successive substitution sampling.Ann. Statist. 22, 1763–1786.
Doss, H. and Narasimhan (1998) Dynamic diplay of changing posterior in Bayesian survival analysis, inPractical Nonparametric and Semiparametric Bayesian Statistics (eds. Dey, D. Müller, P. and Sinha, D.), New York: Springer-Verlag, 63–87.
Fay, M.P. (1996) Rank invariant tests for interval-censored data under the grouped continuous model.Biometrics 52, 811–822.
Fay, M.P. (1999) Comparing several score tests for interval-censored data.Statistics in Medicine 18, 273–285.
Fay, M.P. and Shih, J.H. (1998) Permutation tests using estimated distribution functions.Journal of the American Statistical Association 93, 387–396.
Ferguson, T.S. (1973) A Bayesian analysis of some nonparametric problems.Annals of Statistics 1, 209–230.
Finkelstein, D.M. (1986) A proportional hazards models for interval-censored failure time data.Biometrics 42, 845–854.
Fleming, T.R. and Harrington, D.P. (1991)Counting processes and survival analysis. New York: John Wiley and Sons.
Gehan, E.A. (1965) A generalized Wilcoxon test for comparing arbitrarily singly censored samples.Biometrika 52 203–223.
Gelfand, A.E. and Smith, F.M. (1990) Sampling-based approaches to calculating marginal densities.Journal of the American Statistical Association 85, 398–409.
Gentleman, R. and Geyer, C.J. (1994). Maximum-likelihood for interval-censored data: Consistency and computation.Biometrika 81, 618–623.
Goetghebeur, E. and Ryan, L. (2000) Semiparametric regression analysis of interval-censored data.Biometrics 56, 1139–1144.
Goggins, W. B. and Finkelstein, D.M. (2000) A proportional hazards models for multivariate interval-censored failure time data.Biometrics 56, 940–943.
Gómez, G. and Calle, M.L. (1999). Nonparametric estimation with doubly censored data.Journal of Applied Statistics 26 (1), 45–58.
Gómez, G., Calle, M.L., Muga, R. and Egea, J. M. (2000) Estimation of the risk of HIV Infection as a function of the length of intravenous drug use. A nonparametric Bayesian approach.Statistics in Medicine.19, 2641–2656
Gómez, G. and Julià, O. (1990) Estimation and asymptotic properties of the distribution of time-to-tumour in carcinogenesis experiments.IMA Journal of Mathematics Applied in Medicine and Biology 7, 109–123.
Gómez, G., Julià, O. and Utzet, F. (1992) Survival Analysis for Left Censored Data.Survival Analysis: State of the Art. Editors: J.P. Klein and P.K. Goel. Kluwer Academic Publishers. ISBN 0-7923-1634-7.
Gómez, G., Julià, O. and Utzet, F. (1994) Asymptotic properties of the left Kaplan-Meier estimator.Communications in Statistics: Theory and Methods 23, 123–135.
Gómez, G. and Lagakos, S. (1994) Estimation of the infection time and latency distribution of AIDS with doubly censored data.Biometrics 50, 204–212.
Gómez, G. and van Ryzin, J. (1992) Estimation of the subsurvival function for time-to-tumor in survival/sacrifice experiments.Statistics and Probability Letters 13, 5–13.
Groeneboom, P. and Wellner, J.A. (1992),Information bounds and nonparametric maximum likelihood estimation Basel: Birkhäuser Verlag.
Ibrahim, J.G., Chen, M.H. and Sinha, D. (2001)Bayesian Survival analysis. New York: Springer-Verlag.
Johnson, W. and Christensen, R. (1986) Bayesian nonparametric survival analysis for grouped data.The Canadian Journal of Statistics 14, 307–314.
Kooperberg, C. and Clarkson, D.B. (1997) Hazard regression with intervalcensored data.Biometrics 53, 1485–1494.
Lindsey, J.C. (1998) A study of interval censoring in parametric regression models.Lifetime Data Analysis 4, 329–354.
Lindsey, J.C. and Ryan, L.M. (1998) Tutorial in Biostatistics. Methods for interval-censored data.Statistics in Medicine 17, 219–238
Mantel, N. (1967) Ranking procedures for arbitrarily restricted observation.Biometrics 23, 65–78.
Muñoz, A. and Xu, F. (1996) Models for the incubation of AIDS and variations according to age and period.Statistics in Medicine 15, 2459–2473.
Ng, M.P. (2002) A modification of Peto's nonparametric estimation of survival curves for interval-censored data.Biometrics 58, 439–442.
Pan, W. and Chappell, R. (2002) Estimation in the Cox proportional hazards models with left-truncated and interval-censored data.Biometrics 58, 64–70.
Pepe, M.S. and Fleming, T.R. (1989) Weighted Kaplan-Meier statistics: a class of distance tests for censored survival data.Biometrics 45, 497–507.
Peto, R. and Peto, J. (1972) Asymptotically efficient rank invariant test procedures.Journal of the Royal Statistical Society, Series A, General 135, 185–207.
Peto, R. (1973) Experimental survival curves for interval-censored Data.Journal of the Royal Statistical Society, Series C 22, 86–91.
Petroni, G.R. and Wolfe, A. (1994) A two sample test for stochastic ordering with interval-censored data.Biometrics 50, 77–87.
Rai, K., Susarla, V. and van Ryzin, J. (1980) Shrinkage estimation in nonparametric Bayesian survival analysis: A simulation study.Communications in Statistics: Simulation and Computation 3, 271–298.
Schick, A. and Yu, Q. (2000) Consistency of the GMLE with mixed case intervalcensored data.Scandinavian Journal of Statistics 27, 45–55.
Sinha, D. and Dey, D.K. (1997) Semiparametric Bayesian analysis of survival data.Journal of the American Statistical Association 92, 1195–1212.
Smith, A.F.M. and Roberts, G.O. (1993) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods.J. Roy. Statist. Soc. Ser. B,55, 3–23.
Smith, P.J., Thompson, T.J. and Jereb, J.A. (1997) A model for intervalcensored tuberculosis outbreak data.Statistics in Medicine 16, 485–496.
Spiegelhalter, D.et al. (1996) Bayesian Inference Using Gibbs Sampling, Version 0.5, (version ii).MRC Biostatistics Unit, Cambridge.
Susarla, V. and van Ryzin, J. (1976) Nonparametric Bayesian estimation of survival curves from incomplete observations.Journal of the American Statistical Association 71, 897–902.
Tanner, M. A. and Wong, W.H. (1987) The calculation of posterior distributions by data augmentation.Journal of the American Statistical Association 82, 528–540.
Turnbull, B.W. (1976) The Empirical distribution function with arbitrarily grouped, censored and truncated data.Journal of the Royal Statistical Society, Series B 38, 290–295.
Volberding, P.A., Lagakos, S.W., Grimes, J.M.,et al. (1995) A comparison of immediate with deferred zidovudine therapy for asymptomatic HIV-infected adults with CD4 cell counts of 500 or more per cubic millimeter.New England Journal of Medicine 333, 401–451.
Younes, N. and Lachin, J. (1997) Link-based models for survival data with interval and continous time censoring.Biometrics 53, 1199–1211.
Yu, Q., Schick, A., Li, L. and Wong, G.Y.C. (1998) Asymptotic properties of the GMLE with case 2 interval-censored data.Statistics and Probability Letters 37, 223–228.
Yu, Q., Li, L. and Wong, G.Y.C. (2000) On consistency of the self-consistent estimator of survival functions with interval-censored data.Scandinavian Journal of Statistics 27, 35–44.
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Gómez, G., Calle, M.L. & Oller, R. Frequentist and Bayesian approaches for interval-censored data. Statistical Papers 45, 139–173 (2004). https://doi.org/10.1007/BF02777221
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DOI: https://doi.org/10.1007/BF02777221