Optimal designs for estimating the percentiles of the risk in multistage models of carcinogenesis

Biometrical Journal

Volumn 41, Issue 1, 1999, Pages 33-43

  Kitsos, Christos P ^a  

^a ATHENS UNIVERSITY OF ECONOMICS AND BUSINESS   (Greece)

Author keywords

Experimental carcinogenesis; Optimal designs; Stochastic approximation; Virtual safe dose estimation

Indexed keywords

APPROXIMATION THEORY; OPTIMAL SYSTEMS; PATHOLOGY; RISK PERCEPTION;

CARCINOGENESES; D-OPTIMAL; DOSE ESTIMATIONS; DOSE LEVELS; EXPERIMENTAL CARCINOGENESIS; MULTI STAGE MODELING; MULTISTAGE CARCINOGENESIS; OPTIMAL DESIGN; STOCHASTIC APPROXIMATIONS; VIRTUAL SAFE DOSE ESTIMATION;

STOCHASTIC SYSTEMS;

EID: 0033481375     PISSN: 03233847     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1521-4036(199903)41:1<33::AID-BIMJ33>3.0.CO;2-K     Document Type: Article

References (58)

1. ANBAR, D., 1978: A Stochastic Newton-Raphson. J. Stat. Planning and Inference 2, 153-163.
2. ARMITAGE, P. and DOLL, R., 1954: The Age Distribution of Cancer and a Multi-Stage Theory of Carcinogenesis. Brit. J. Cancer 8, 1-12.
3. ARMITAGE, P., 1982: The Assessment of Low Dose Carcinogenecity. Biometrics 28 (sup.), 119-129.
4. ARMITAGE, P., 1985: Multistage Models of Carcinogenesis. Environmental Health Perspectives 63, 195-201.
5. BARD, Y., 1974: Nonlinear Parametric Estimation. Academic Press.
6. BOFINGER, E., HAYTER, A. J., and LIU, W., 1993: The Construction of Upper Confidence Bounds on the Range of Several Location Parameters. JASA 88, 906-911.
7. BÖHNING, D., 1993: Acceleration techniques in fixed-point method for finding percentage points. Statistics and Computing 3, 1-5.
8. BUCCHI, A. R., GABRIELLE, M., LUPI, C., and ZAPPONI, G. A., 1988: Dose-response Relationships in Rodents of Promoter Carcinogens: A Tentative Interpretation of Some Downward Trends. Biomedical and Environmental Sciences 1, 184-193.
9. CHUNG, K. L., 1954: On a Stochastic Approximation Method. Ann. Math. Stat. 25, 463-469.
10. CORNISH, E. A. and FISHER, R. A., 1937: Moments and cummulants in the specification of distribution. Rev. Internat. Stat. Inst. 5, 307-320.
11. CORNFIELD, J., 1977: Carcinogenic risk assessment. Science 198, 693-699.
12. COX, D. R., 1970: Analysis of Binary Data. Medhvems Monographs.
13. COX, D. R., 1972: Regression Models and Life Tables (with discussion). JRSS B 74, 187-220.
14. CRUMP, K. S., GUESS, H. A., and DEAL, K. L., 1977: Confidence Internals and tests of Hypotheses concerning Dose Response Relations Inferred from Animal Carcinogenecity Data. Biometrics 33, 437-445.
15. DEWANJII, A., KREWSKI, D., and GODDARD. M. J., 1993: A Weibull Model for the Estimation of Tumourogenic Potency. Biometrics 49, 367-377.
16. DOLL, R., 1971: The Age Distribution of Cancer: Implications for Models of Carcinogenesis. JRSS A 134, 133-166.
17. DOLL, R., 1978: An Epidemiological Perspective on the Biology of Cancer. Cancer Res. 38, 3573-3583.
18. FINKELSTEIN, D. M., 1991: Modelling the Effect of Dose in the Lifetime Tumour Rate from an Animal Carcinogenecity Experiment. Biometrics 47, 669-680.
19. EFRON, B., 1991: Regression Percentiles Using Asymmetric Squared Error Loss. Statistica Sinica 1, 93-125.
20. FORD, I., KITSOS, C. P., and TITTERINGTON, D. M., 1989: Recent Advances in Nonlinear Experimental Design. Technometrics 31, 49-60.
21. GRAY, H. L. and WANG, S., 1991: A General Method for Approximating Tail Probabilities. JASA 86, 160-166.
22. HARTLEY, H. O. and SIELKEN, R. L., 1977: Estimation of 'Safe Dose' in Carcinogenic Experiments. Biometrics 33, 1-30.
23. HOTHORN, L. A., NEUHÄUSER, M., and KOCH, H.-F., 1997: Analysis of Randomized Dose-Finding-Studies: Closure Test Modifications Based on Multiple Contrast Tests. Biometrical Journal 39, 467-479.
24. JENSEN, S. T., JOHANSEN, S., and LAURITZEN, S. L., 1991: Globally Convergent Algorithms for Maximizing a Likelihood Function. Biometrica 78, 867-877.
25. KENDALL, M. G. and STUART, A., 1977: The Advanced Theory of Statistics. Vol. 1, 4th edition, Macmillan, New York.
26. KITSOS, C. P., 1986: Design and Inference in Nonlinear Problems. Ph.D. Thesis, Glasgow University.
27. KITSOS, C. P., TITTERINGTON, D. M., and TORSNEY, B., 1988: An Optimal Design Problem in Rhythmometry. Biometrics 44, 657-671.
28. KITSOS, C. P., 1989: Fully sequential procedures in nonlinear design problems. Comp. Stat. Data Analysis 8, 13-19.
29. KITSOS, C. P., 1992: Adopting Sequential Procedures for Biological Experiments. In: Muller, Wynn, Zhigljavsky (eds): Model Oriented Data Analysis. Physica-Verlag, 3-9.
30. KITSOS, C. P. and MULLER, C. H., 1995: Robust Estimation of Non-linear Aspects. In: C. Kitsos, W. Muller (eds): Model Oriented Data Analysis. Physica-Verlag, 223-233.
31. KITSOS, C. P., 1995: Sequential Assays for Experimental Carginogenesis. In: ISI 50th Session, Book 1, Beijing, 625-626.
32. KODELL, L. R. and PARK, N. C., 1995: Linear Extrapolation in Cancer Risk Assessment. In: W. Farland, S. Olin, C. Park, L. Phomber, R. Scheuplein, T. Starr, and J. Wilson (eds.): Low-Dose Extrapolation of Cancer Risks: Issues and Perspectives. ILSI Press, Leetsdale, PA.
33. KOPP-SCHNEIDER, A., 1997: Carcinogenesis models for risk assessment. To appear in Statistical Methods in Medical Research.
34. KOPP, A. and PORTIER, C., 1989: A Note on Approximating the Cumulative Distribution Function of the Time to Tumour Onset in Multistage Models. Biometrics 45, 1259-1263.
35. LUEBECK, G. E. and MOOLGAVKAR, S. H., 1992: Multistage Carcinogenesis: Population-Based Model for Colon Cancer. Journal of National Institute, 610-618.
36. LUEBECK, G. E. and MOOLGAVKAR, S. H., 1991: Stochastic Analysis of Intermediate Lesions in Carcinogenesis Experiments. Risk Analysis 11, 149-157.
37. LUEBECK, G. E. and MOOLGAVKAR, S. H., 1989: Two-Event Model for Carcinogenesis: Biological, Mathematical and Statistical Considerations. Risk Analysis 10, 323-341.
38. MANTEL, N. and BRYAN, W. R., 1961: "Safety" Testing of Carcinogenic Agents. Journal of the National Cancer Institute 27, 455-470.
39. MCLEISH, D. L. and TOSH, D., 1990: Sequential Designs in Bioassay. Biometrics 46, 103-116.
40. MINKIN, S., 1994: Statistical Analysis of Aberrant Crypt Assays for Colon Cancer Promotion Studies. Biometrics 50, 279-288.
41. MOOLGAVKAR, S. and KNUDSON, A., 1981: Mutation and Cancer: A Model for Human Carcinogenesis. Journal of National Cancer Institute 66, 1037-1052.
42. MOOLGAVKAR, S. and VENZON, D., 1979: Two-Event Models for Carcinogenesis: Incidence Cures for Childhood and Adult Tumours. Mathematical Bioscience 47, 55-77.
43. MOSER, B. K. and FEI, W., 1991: A New Sequential Design Based on the Robbins-Monro Procedure. Metrika 38, 321-333.
44. PUKELSHEIM, F., 1993: Optimal Design of Experiments. John Wiley & Sons, New York.
45. RENAN, M. J., 1993: How Many Mutations Are Required for Tumourogenesis? Implications for Human Cancer Data. Molecular Carcinogenesis 7, 139-146.
46. RIBOUT, M. S., FENLON, J. S., and HUGHES, P. R., 1993: A Generalised One-Hit Model for Bioassays of Insect Viruses. Biometrics 49, 1136-1141.
47. ROBBINS, H. and MONRO, S., 1951: A Stochastic Approximation Method. Ann. Math. Stat. 22, 400-407.
48. ROBERTS, E. A., 1992: Sequential Data in Biological Experiment. Chapman and Hall, London.
49. SILVAPULLE, M. J., 1981: On the Existence of the Maximum Likelihood Estimators for the Bionomial Response Models. JRSS Series B 43, 310-313.
50. SILVEY, S. D., 1980: Optimal Design. Chapman and Hall, London.
51. TAN, W. Y., 1991: Stochastic Models in Carcinogenesis. Marchel Dekker, Inc., New York.
52. TRAVIS, C. D., 1988: Carcinogenic Risk Assessment. New York Plenum Press.
53. TRAVIS, C. C., 1989: Research Needs for Biologically Based Risk Assessment. In: C. Curtis (ed.): Biologically Based Methods for Cancer Risk Assessment. NATO ASI Series 109, 1-7.
54. US EPA, 1980: Water Quality Criteria Documents. Federal Register 45, 231, 79319-79378.
55. WHO, 1992: Revision of Drinking Water Guidelines (Summary Report). WHO, Geneva.
56. WU, C. F., 1985: Efficient Sequential Designs with Binary Data. JASA 80, 974-984.
57. ZAPPONI, G. A., BUCCHI, A. R., and LUPI, C., 1988: Reproducibility of Low-Dose Extrapolation Procedure: Comparison of Estimates Obtained Using Different Rodent Species and Strains. Biomedical and Environment Sciences 1, 160-170.
58. ZAPPONI, G. A., LOIZZO, A., and VALENTE, P., 1989: Carcinogenic Risk Assessment: Some Comparisons between Risk Estimates Derived from Human and Animal Data. Experimental Pathology 37, 210-218.