Sampling based approach for one-hit and multi-hit models in quantal bioassay

Statistics and Computing

Volumn 7, Issue 3, 1997, Pages 183-192

  Chu, Hui May ^a   Kuo, Lynn ^a  

^a UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Abbott's correction; Conditional predictive ordinate; Low dose extrapolation; Markov chain Monte Carlo; Metropolis algorithm; Risk analysis

Indexed keywords

EID: 0042230275     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1018586118882     Document Type: Article

References (27)

1. Abbott, W.S. (1925) Method of computing the effectiveness of an insecticide. Journal of Economic Entomology, 18, 265-7.
2. Albert, J. and Chib, S. (1993) Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88, 669-79.
3. Antoniak, C.E. (1974) Mixture of Dirichlet processes with application to Bayesian nonparametric problems. Annals of Statistics, 2, 1152-74.
4. Chu, H. and Kuo, L. (1996) Sampling based approach for one-hit and multi-hit models in quantal bioassay, Technical Report No. 96-11. Storrs, Connecticut: Statistics Department, University of Connecticut.
5. Cornfield, J. (1954) Measurement and comparison of toxicities: the quantal response. In O. Kempthorne, T.A. Bancroft, J.W. Gowen and J.L. Lush (eds) Statistics and Mathematics in Biology, p. 327-44. New York: Hafner.
6. Cornfield, J. and Mantel, M. (1977) A discussion of 'Estimation of safe doses in carcinogenic experiments' by Hartley and Sielken. Biometrics, 33, 21-24.
7. Dey, D.K., Kuo, L. and Sahu, S.K. (1995) A Bayesian predictive approach to determining the number of components in a mixture distribution. Statistics and Computing, 5, 297-305.
8. Geisser, S. and Eddy, W. (1979) A predictive approach to model selection. Journal of the American Statistical Association, 74, 153-60.
9. Gelfand, A.E., Dey, D.K. and Chang, H. (1992) Model determination using predictive distributions with implementation via sampling-based methods (with Discussion). In J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M. Smith (eds) Bayesian Statistics 4, pp. 147-69. Oxford: Oxford University Press.
10. Gelfand, A.E. and Kuo, L. (1991) Nonparametric Bayesian bioassay including ordered polytomous response. Biometrika, 78, 657-66.
11. Gelfand, A.E. and Smith, A.F.M. (1990) Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398-409.
12. Gelman, A.E. and Rubin, D. (1992) Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457-72.
13. Kuo, L. and Cohen, M.P. (1992) Bayesian analysis for linearized multi-stage models in quantal bioassay, Technical Report No. 92-31. Storrs, Connecticut: Statistics Department, University of Connecticut.
14. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953) Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087-92.
15. Morgan, B.J.T. (1992) Analysis of Quantal Response Data. London: Chapman and Hall.
16. Newton, M.A. and Raftery, A.E. (1994) Approximate Bayesian inference by the weighted likelihood bootstrap (with Discussion). Journal of the Royal Statistical Society, Series B, 56, 1-48.
17. Petrasovitas, A. and Cornell, R. (1975) Approximations to the Bayes estimate for a quantal assay with simple exponential tolerance distribution. Communications in Statistics, 4(9), 851-62.
18. Rai, K. and Van Ryzin, J. (1979) Risk assessment of toxic environmental substances using a generalized multi-hit dose response model. In N.B. Breslow, and A.S. Whittemore (eds) Energy and Health, pp. 99-117. Philadelphia: SIAM.
19. Rai, K. and Van Ryzin, J. (1981) A generalized multi-hit dose-response model for low-dose extrapolation. Biometrics, 37, 341-52.
20. Ramgopal, P., Laud, P.W. and Smith, A.F.M. (1993) Nonparametric Bayesian bioassay with prior constraints on the shape of the potency curve. Biometrika, 80, 489-98.
21. Ramsey, F.L. (1972) A Bayesian approach to bio-assay. Biometrics, 28, 841-58.
22. Schwarz, G. (1978) Estimating the dimension of a model. Annals of Statistics, 6, 461-4.
23. Shaked, M. and Singpurwalla, N.D. (1990) A Bayesian approach for quantile and response probability estimation with applications to reliability. Annals of the Institute of Statistical Mathematics, 42, 1-19.
24. Stone, M. (1974) Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, Series B, 38, 111-47.
25. Tanner, M. and Wong, W. (1987) The calculation of posterior distributions by data augmentation (with Discussion). Journal of the American Statistical Association, 81, 82-6.
26. Tierney, L. (1994) Markov chains for exploring posterior distributions. Annals of Statistics, 22, 1701-62.
27. Zellner, A. and Rossi, P.E. (1984) Bayesian analysis of dichotomous quantal response models. Journal of Econometrics, 25, 365-93.