Nonparametric Inference on Tumor Incidence with Partially Identified Cause-of-Death Data

Part of the ICSA Book Series in Statistics book series (ICSABSS)


The use of survival-sacrifice experiments with animals, primarily rodents, has long been an indispensable tool for gauging the possible carcinogenic effect of a new drug or pharmaceutical agent. Because the tumor induced in the animal is generally impalpable and non-lethal, the precise time to its occurrence is unobservable. The only information that can be gleaned is its presence or absence when the animal dies from tumor-related or accidental causes. Provided that the cause of death is ascertained by a pathologist, Gomes (Braz J Probab Stat 15:135–145, 2001) provides a computationally efficient approach to nonparametric estimation of the cumulative distribution function for tumor onset time. In this article, we develop an EM-type algorithm to extend this approach to the situation where the cause of death is unknown on a subset of the animals. Such a scenario often occurs in practice as certain cases of death may elude the expertise of the pathologist. We also propose a class of logrank-type tests to compare different treatment groups on tumor incidence. Simulation studies show that, by properly accounting for missing data, the proposed methods outperform the naive approaches of complete-case analysis and simple imputations. Real data from a large-scale study on pituitary tumor in rats are analyzed as an illustration.


  1. Ahn, H., Kodell, R.L.: Analysis of long-term carcinogenicity studies. In: Chow, S.C., Liu, J.P. (eds.) Design and Analysis of Animal Studies in Pharmaceutical Development, pp. 259–290. CRC Press, Boca Raton (1998)Google Scholar
  2. Archer, L.E., Ryan, L.M.: Accounting for misclassification in the cause-of-death test for carcinogenicity. J. Am. Stat. Assoc. 84, 787–791 (1989)CrossRefGoogle Scholar
  3. Chow, S.C., Liu, J.P. (eds.): Design and Analysis of Animal Studies in Pharmaceutical Development. CRC Press, Boca Raton (1998)Google Scholar
  4. Clifford, P.: Nonidentifiability in stochastic models of illness and death. Proc. Natl. Acad. Sci. 74, 1338–1340 (1977)MathSciNetCrossRefGoogle Scholar
  5. Dewanji, A., Kalbfleisch, J.D.: Nonparametric methods for survival/sacrifice experiments. Biometrics 42, 325–341 (1986)MathSciNetCrossRefGoogle Scholar
  6. Dinse, G.E.: Discussion of “Handling cause of death in equivocal cases using the em algorithm” by RL Kodell and JJ Chen. Commun. Stat. Theory Methods, 16, 2587–2592 (1987)CrossRefGoogle Scholar
  7. Dinse, G.E., Lagakos, S.W.: Nonparametric estimation of lifetime and disease onset distributions from incomplete observations. Biometrics 38, 921–932 (1982)CrossRefGoogle Scholar
  8. Fleming, T.R., Harrington, D.P.: Counting Processes and Survival Analysis. Wiley, New York (1991)zbMATHGoogle Scholar
  9. Gart, J.J.: Statistical Methods in Cancer Research: The Design and Analysis of Long-Term Animal Experiments. Oxford University Press, Oxford (1986)Google Scholar
  10. Gomes, A.E.: Characterization of the NPMPLE of the disease onset distribution function for a survival-sacrifice model. Braz. J. Probab. Stat. 15, 135–145 (2001)MathSciNetzbMATHGoogle Scholar
  11. Gomes, A.E.: Consistency of the non-parametric maximum pseudo-likelihood estimator of the disease onset distribution function for a survival-sacrifice model. J. Nonparametr. Stat. 20, 39–46 (2008)MathSciNetCrossRefGoogle Scholar
  12. Gray, R.J.: A class of K-sample tests for comparing the cumulative incidence of a competing risk. Ann. Stat. 16, 1141–1154 (1988)MathSciNetCrossRefGoogle Scholar
  13. Groeneboom, P., Jongbloed, G.: Nonparametric Estimation Under Shape Constraints. Cambridge University Press, Cambridge (2014)CrossRefGoogle Scholar
  14. Groeneboom, P., Wellner, J.A.: Information Bounds and Nonparametric Maximum Likelihood Estimation. Springer, Berlin (1992)CrossRefGoogle Scholar
  15. Harrington, D.P., Fleming, T.R.: A class of rank test procedures for censored survival data. Biometrika 69, 553–566 (1982)MathSciNetCrossRefGoogle Scholar
  16. Huang, J.: Efficient estimation for the proportional hazards model with interval censoring. Ann. Stat. 24, 540–568 (1996)MathSciNetCrossRefGoogle Scholar
  17. Huang, J., Wellner, J.A.: Interval censored survival data: a review of recent progress. In: Lin, D.Y., Fleming, T.R. (eds.) Proceedings of the First Seattle Symposium in Biostatistics: Survival Analysis, pp. 123–169. Springer, New York (1997)CrossRefGoogle Scholar
  18. Jewell, N.P., van der Laan, M.: Current status data: review, recent developments and open problems. In: Handbook of Statistics, vol. 23, pp. 625–642. Elsevier, Amsterdam (2003)Google Scholar
  19. Kodell, R.L., Chen, J.J.: Handling cause of death in equivocal cases using the EM algorithm. Commun. Stat. Theory Methods 16, 2565–2585 (1987)CrossRefGoogle Scholar
  20. Kodell, R.L., Nelson, C.J.: An illness-death model for the study of the carcinogenic process using survival/sacrifice data. Biometrics 36, 267–277 (1980)CrossRefGoogle Scholar
  21. Kodell, R.L., Shaw, G.W., Johnson, A.M.: Nonparametric joint estimators for disease resistance and survival functions in survival/sacrifice experiments. Biometrics. 43–58 (1982)CrossRefGoogle Scholar
  22. Kodell, R.L., Chen, J.J., Moore, G.E.: Comparing distributions of time to onset of disease in animal tumorigenicity experiments. Commun. Stat. Theory Methods 23, 959–980 (1994)CrossRefGoogle Scholar
  23. Malani, H.M., Van Ryzin, J.: Comparison of two treatments in animal carcinogenicity experiments. J. Am. Stat. Assoc. 83, 1171–1177 (1988)MathSciNetCrossRefGoogle Scholar
  24. Mao, L., Lin, D.Y.: Efficient estimation of semiparametric transformation models for the cumulative incidence of competing risks. J. R. Stat. Soc. Ser. B 79, 573–587 (2017)MathSciNetCrossRefGoogle Scholar
  25. Mao, L., Lin, D.Y., Zeng, D.: Semiparametric regression analysis of interval-censored competing risks data. Biometrics 73, 857–865 (2017)MathSciNetCrossRefGoogle Scholar
  26. McKnight, B., Crowley, J.: Tests for differences in tumor incidence based on animal carcinogenesis experiments. J. Am. Stat. Assoc. 79, 639–648 (1984)MathSciNetCrossRefGoogle Scholar
  27. Peto, R.: Guidelines on the analysis of tumour rates and death rates in experimental animals. Br. J. Cancer 29, 101–105 (1974)CrossRefGoogle Scholar
  28. Peto, R., Pike, M.C., Day, N.E., Gray, R.G., Lee, P.N., Parish, S., Peto, J., Richards, S., Wahrendorf, J.: Guidelines for simple, sensitive significance tests for carcinogenic effects in long-term animal experiments. IARC Monogr. Eval. Carcinog. Risk Chem. Hum. Supplement, 311–426 (1980)Google Scholar
  29. Peto, R., Gray, R., Brantom, P., Grasso, P.: Nitrosamine carcinogenesis in 5120 rodents: chronic administration of sixteen different concentrations of NDEA, NDMA, NPYR and NPIP in the water of 4440 inbred rats, with parallel studies on NDEA alone of the effect of age of starting (3, 6 or 20 weeks) and of species (rats, mice or hamsters). IARC Sci. Publ. 57, 627–665 (1984)Google Scholar
  30. Turnbull, B.W.: The empirical distribution function with arbitrarily grouped, censored and truncated data. J. R. Stat. Soc. Ser. B 38, 290–295 (1976)MathSciNetzbMATHGoogle Scholar
  31. Turnbull, B.W., Mitchell, T.J.: Nonparametric estimation of the distribution of time to onset for specific diseases in survival/sacrifice experiments. Biometrics 40, 41–50 (1984)CrossRefGoogle Scholar
  32. van der Laan, M.J., Jewell, N.P., Peterson, D.R.: Efficient estimation of the lifetime and disease onset distribution. Biometrika 84, 539–554 (1997)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Biostatistics and Medical Informatics, School of Medicine and Public HealthUniversity of Wisconsin-MadisonMadisonUSA

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