The Statistical Analysis of Interval-Censored Failure Time Data with Applications

Affiliation(s)

University of Waterloo, Waterloo, Canada.

Formerly at University of Guelph, Guelph, Canada.

University of Waterloo, Waterloo, Canada.

Formerly at University of Guelph, Guelph, Canada.

ABSTRACT

The analysis of survival data is a major focus of statistics. Interval censored data reflect uncertainty as to the exact times the units failed within an interval. This type of data frequently comes from tests or situations where the objects of interest are not constantly monitored. Thus events are known only to have occurred between the two observation periods. Interval censoring has become increasingly common in the areas that produce failure time data. This paper explores the statistical analysis of interval-censored failure time data with applications. Three different data sets, namely Breast Cancer, Hemophilia, and AIDS data were used to illustrate the methods during this study. Both parametric and nonparametric methods of analysis are carried out in this study. Theory and methodology of fitted models for the interval-censored data are described. Fitting of parametric and non-parametric models to three real data sets are considered. Results derived from different methods are presented and also compared.

Cite this paper

R. Singh and D. Totawattage, "The Statistical Analysis of Interval-Censored Failure Time Data with Applications,"*Open Journal of Statistics*, Vol. 3 No. 2, 2013, pp. 155-166. doi: 10.4236/ojs.2013.32017.

R. Singh and D. Totawattage, "The Statistical Analysis of Interval-Censored Failure Time Data with Applications,"

References

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[1] J. C. Lindsey and L. M. Ryan, “Tutorial in Biostatistics Methods for Interval-Censored Data,” Statistics in Medicine, Vol. 17, No. 2, 1998, pp. 219-238. doi:10.1002/(SICI)1097-0258(19980130)17:2<219::AID-SIM735>3.0.CO;2-O

[2] J. K. Lindsey, “A Study of Interval Censoring in Parametric Regression Models,” Life Time Data Analysis, Vol. 4, No. 4, 1998, pp. 329-354. doi:10.1023/A:1009681919084

[3] D. M. Finkelstein and R. A. Wolfe, “A Semi-Parametric Model for Regression Analysis of Interval Censored Failure Time Data,” Biometrics, Vol. 41, No. 4, 1985, pp. 933-945. doi:10.2307/2530965

[4] D. M. Finkelstein, “A Proportional Hazards Model for Interval-Censored Failure Time Data”, Biometrics, Vol. 42, No. 4, 1986, pp. 845-854. doi:10.2307/2530698

[5] R. Peto, “Experimental Survival Curves for Interval-Censored Data,” Applied Statistics, Vol. 22, No. 1, 1973, pp. 86-91. doi:10.2307/2346307

[6] P. S. Rosenberg, “Hazard Function Estimation Using B-Splines,” Biometrics, Vol. 51, No. 3, 1995, pp. 874-887. doi:10.2307/2532989

[7] P. M. Odell, K. M. Anderson and R. B. Agostino, “Maximum Likelihood Estimation for Interval-Censored Data Using a Weibull-Based Accelerated Failure Time Model,” Biometrics, Vol. 48, No. 3, 1992, pp. 951-959. doi:10.2307/2532360

[8] B. W. Turnbull, “The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data”, Journal of the Royal Statistical Society, Series B, Vol. 38, No. 3, 1976, pp. 290-295.

[9] C. P. Farrington, “Interval Censored Survival Data: A Generalized Linear Modeling Approach,” Statistics in Medicine, Vol. 15, No. 3, 1996, pp. 283-292. doi:10.1002/(SICI)1097-0258(19960215)15:3<283::AID-SIM171>3.0.CO;2-T

[10] E. Goetghebeur and L. Ryan, “Semi-Parametric Regression Analysis of Interval-Censored Data,” Biometrics, Vol. 56, No. 4, 2000, pp. 1139-44.

[11] J. F. Lawless, “Statistical Models and Methods for Lifetime Data,” Wiley, 2003.

[12] D. Collett, “Modelling Survival Data in Medical Research,” Chapman and Hall, London, 2003.

[13] J. Sun “The Statistical Analysis of Interval-Censored Failure Time Data,” Springer, New York/Heidelberg, 2006.

[14] E. L. Kaplan and P. Meier, “Nonparametric Estimation from Incomplete Observations,” Journal of the American Statistical Association, Vol. 53, No. 282, 1958, pp. 457-481. doi:10.1080/01621459.1958.10501452

[15] G. Rucker and D. Messerer, “Remission Duration: An Example of Interval-Censored Observations,” Statistics in Medicine, Vol. 7, No. 11, 1988, pp. 1139-1145. doi:10.1002/sim.4780071106

[16] F. J. Dorey, R. J. Little and N. Schenker, “Multiple Imputation for Threshold-Crossing Data with Interval Censoring”, Statistics in Medicine, Vol. 12, No. 17, 1993, pp. 1589-1603. doi:10.1002/sim.4780121706

[17] R. Gentleman and C. J. Geyer, “Maximum Likelihood for Interval Censored Data: Consistency and Computation,” Biometrika, Vol. 81, No. 3, 1994, pp. 618-623. doi:10.1093/biomet/81.3.618

[18] C. Kooperberg and C. J. Stone, “Logspline Density Estimation for Censored Data,” Journal of Computational and Graphical Statistics, Vol. 1, No. 4, 1992, pp. 301-328.

[19] D. R. Cox, “Regression Models and Life Tables (with Discussion),” Journal of the Royal Statistical Society, Series B, Vol. 34, No. 2, 1972, pp. 187-220.

[20] V. De Gruttola and S. W. Lagakos, “Analysis of Doubly-Censored Survival Data, with Application to AIDS,” Biometrics, Vol. 45, No. 1, 1989, pp. 1-11. doi:10.2307/2532030

[21] S. G. Self and E. A. Grossman, “Linear Rank Tests for Interval-Censored Data with Application to PCB levels in Adipose Tissue of Transformer Repair Workers,” Biometrics, Vol. 42, No. 3, 1996, pp. 521-530. doi:10.2307/2531202

[22] R. G. Miller, “Least Squares Regression with Censored Data,” Biometrika, Vol. 63, No. 3, 1976, pp. 447-464. doi:10.1093/biomet/63.3.449

[23] J. Buckley and I. James, “Linear Regression with Censored Data,” Biometrika, Vol. 66, No. 3, 1979, pp. 429-436. doi:10.1093/biomet/66.3.429