- Volume 23 Issue 5
In animal tumorigenicity data, the occurrence time of tumor is not observed because the existence of a tumor is examined only at either time of natural death or time of sacrifice for the animal. A three-state model (Health-Tumor onset-Death) is widely used to model the incomplete data. In this paper, we employed a frailty effect into the three-state model to incorporate the dependency of death on tumor occurrence when the time of natural death works as an informative censoring against the tumor onset time. For the inference of parameters, then the EM algorithm is considered in order to deal with missing quantities of tumor onset time and random frailty. The proposed method is applied to the bladder tumor data taken from Lindsey and Ryan (1993, 1994) and a simulation study is performed to show the behavior of the proposed estimators.
Bladder cancer data;EM algorithm;gamma frailty effect;Gauss-Laguerre method;three-state model;tumorigenicity experiment
- Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood for incomplete data via the EM algorithms (with discussion), Journal of the Royal Statistical Society, Series B, 39, 1-38.
- French, J. L. and Ibrahim, J. G. (2002). Bayesian methods for a three-state model for rodent carcinogenicity studies, Biometrics, 58, 906-916. https://doi.org/10.1111/j.0006-341X.2002.00906.x
- Golub, G. H. and Welsch, J. H. (1969). Calculation of Gauss quadrature rules, Mathematics of Computation, 23, 221-230. https://doi.org/10.2307/2004418
- Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97-109. https://doi.org/10.1093/biomet/57.1.97
- Huang, X. and Wolfe, R. A. (2002). A frailty model for informative censoring, Biometrics, 58, 510-520. https://doi.org/10.1111/j.0006-341X.2002.00510.x
- Kim, J., Kim, Y., Nam, C., Choi, E. and Kim, Y. J. (2010). A analysis of tumorigenicity data using a normal frailty effect, Proceedings for the Spring Conference, 2010, The Korean Statistical Society, 13.
- Lagakos, S. W. and Louis, T. A. (1988). Use of tumor lethality to interpret tumorigenicity experiments lacking cause-of-death data, Applied Statistics, 37, 169-179. https://doi.org/10.2307/2347336
- Lindsey, J. C. and Ryan, L. M. (1993). A three-state multiplicative model for rodent tumorigenicity experiments, Applied Statistics, 42, 283-300. https://doi.org/10.2307/2986233
- Lindsey, J. C. and Ryan, L. M. (1994). A comparison of continuous - and discrete time three state models for rodent tumorigenicity experiments, Environmental Health Perspective Supplements, 102, 9-17.
- Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953). Equations of state calculations by fast computing machines, Journal of Chemical Physics, 21, 1087-1091. https://doi.org/10.1063/1.1699114
- Sun, J. (2006). The Statistical Analysis of Interval-Censored Failure Time Data, Springer, New York.
Supported by : 한국연구재단