Abstract
Interval-censored survival data, in which the event of interest is not observed exactly but is only known to occur within some time interval, occur very frequently. In some situations, event times might be censored into different, possibly overlapping intervals of variable widths; however, in other situations, information is available for all units at the same observed visit time. In the latter cases, interval-censored data are termed grouped survival data. Here we present alternative approaches for analyzing intervalcensored data. We illustrate these techniques using a survival data set involving mango tree lifetimes. This study is an example of grouped survival data.
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REFERENCES
Aalen, O. O. (1989), “A Linear Regression Model for the Analysis of Lifetimes,” Statistics in Medicine, 8, 907–925.
— (1993), “Further Results on the Non-Parametric Linear Regression Model in Survival Analysis,” Statistics in Medicine, 12, 1569–1588.
Betensky, R. A., Lindsey, J. C., Ryan, L. M., and Wand, M. P. (1999), “Local EM Estimation of the Hazard Function for Interval-Censored Data,” Biometrics, 55, 238–245.
Collett, D. (1991), Modelling Binary Data, New York: Chapman & Hall.
Colosimo, E. A., Chalita, L. V. A. S., and Demétrio, C. G. B. (2000), “Tests of Proportional Hazards and Proportional Odds Models for Grouped Survival Data,” Biometrics, 56, 1233–1240.
Cox, D. R. (1972), “Regression Models and Life-Tables” (with discussion), Journal of the Royal Statistical Society, Ser. B, 34, 187–220.
— (1975), “Partial Likelihood,” Biometrika, 62, 269–276.
Cox, D. R., and Hinkley, D. V. (1974), Theoretical Statistics, London: Chapman & Hall.
Dorey, F. J., Little, R. J., and Schenker, N. (1993), “Multiple Imputation for Threshold-Crossing Data With Interval Censoring,” Statistics in Medicine, 12, 1589–1603.
Finkelstein, D. M. (1986), “A Proportional Hazards Model for Interval-Censored Failure Time Data,” Biometrics, 42, 845–854.
Giolo, S. R. (2004), “Turnbull’s Nonparametric Estimator for Interval-Censored Data: An R Code,” Technical Report 2004/01-C. Available at www.est.ufpr.br/rt.
Goetghebeur, E., and Ryan, L. (2000), “Semiparametric Regression Analysis of Interval-Censored Data,” Biometrics, 56, 1139–1144.
Goggins, W. B., Finkelstein, D. M., Schoenfeld, D. A., and Zaslavsky, A. M. (1998), “A Markov Chain Monte Carlo EM Algorithm for Analyzing Interval-Censored Data Under the Cox Proportional Hazards Model,” Biometrics, 54, 1498–1507.
Henschel, V., Heiss, C., and Mansmann, U. (2004), “The Intcox Package,” available at http://cran.r-project.org/ web/packages/ intcox/ index.html.
Hsu, C.-H., Taylor, J. M. G., Murray S., and Commenges, D. (2007), “Multiple Imputation for Interval Censored Data With Auxiliary Variables,” Statistics in Medicine, 26, 769–781.
Kaplan, E. L., and Meier, P. (1958), “Nonparametric Estimation From Incomplete Observations,” Journal of the American Statistical Association, 53, 457–481.
Kim, J. (2003), “Maximum Likelihood Estimation for the Proportional Hazards Model With Partly Interval-Censored Data,” Journal of the Royal Statistical Society, Ser. B, 65, 489–502.
Klein, J. P., and Moeschberger, M. L. (2003), Survival Analysis: Techniques for Censored and Truncated Data (2nd ed.), New York: Springer.
Komárek, A., Lesaffre, E., and Hilton, J. F. (2005), “Accelerated Failure Time Model for Arbitrarily Censored Data With Smoothed Error Distribution,” Journal of Computational & Graphical Statistics, 14 (3), 726–745.
Law, G., and Brookmeyer, R. (1992), “Effects of Midpoint Imputation on the Analysis of Doubly Censored Data,” Statistics in Medicine, 11, 1569–1578.
Lawless, J. F. (2002), Statistical Models and Methods for Lifetime Data (2nd ed.), New York: Wiley.
Lee, E. T., and Weissfeld, L. A. (1998), “Assessment of Covariates Effects in Aalen’s Additive Hazard Model,” Statistics in Medicine, 17, 983–998.
Lesaffre, E., Komárek, A., and Declerck, D. (2005), “An Overview of Methods for Interval-Censored Data With an Emphasis on Applications in Dentistry,” Statistical Methods in Medical Research, 14 (6), 539–552.
Martinussen, T., and Scheike, T. H. (2006), Dynamic Regression Models for Survival Data, New York: Springer.
Odell, P. M., Anderson, K. M., and D’Agostino, R. B. (1992), “Maximum Likelihood Estimation for Interval-Censored Data Using a Weibull-Based Accelerated Failure Time Model,” Biometrics, 48, 951–959.
Pan, W. (1999), “A Comparison of Some Two-Sample Tests With Interval Censored Data,” Journal of Nonparametric Statistics, 12, 133–146.
— (1999a), “Extending the Iterative Convex Minorant Algorithm to the Cox Model for Interval-Censored Data,” Journal of Computational & Graphical Statistics, 8 (1), 109–120.
— (2000), “A Multiple Imputation Approach to Cox Regression With Interval Censored Data,” Biometrics, 5, 192–203.
Peto, R. (1973), “Experimental Survival Curves for Interval Censored Data,” Applied Statistics, 22, 86–91.
R Development Core Team (2008), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. Available at http://www.R-project.org.
Rabinowitz, D., Tsiatis, A., and Aragon, J. (1995), “Regression With Interval-Censored Data,” Biometrika, 82, 501–513.
Rücker, G., and Messerer, D. (1988), “Remission Duration: An Example of Interval-Censored Observations,” Statistics in Medicine, 7, 1139–1145.
Sen, B., and Banerjee, M. (2007), “A Pseudolikelihood Method for Analyzing Interval-Censored Data,” Biometrika, 94, 71–86.
Sinha, D., Chen, M.-H., and Ghosh, S. K. (1999), “Bayesian Analysis and Model Selection for Interval-Censored Data,” Biometrics, 55, 585–590.
Therneau, T. M., and Grambsch, P. M. (2000), Modeling Survival Data: Extending the Cox Model, New York: Springer.
Turnbull, B.W. (1976), “The Empirical Distribution Function With Arbitrarily Grouped, Censored, and Truncated Data,” Journal of the Royal Statistical Society, Ser. B, 38, 290–295.
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Giolo, S.R., Colosimo, E.A. & Demétrio, C.G.B. Different approaches for modeling grouped survival data: A mango tree study. JABES 14, 154–169 (2009). https://doi.org/10.1198/jabes.2009.0010
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DOI: https://doi.org/10.1198/jabes.2009.0010