Estimation and testing with overdispersed proportions using the beta- logistic regression model of Heckman and Willis

Biometrics

Volumn 56, Issue 1, 2000, Pages 125-133

  Slaton, Terra L ^a,b   Piegorsch, Walter W ^a   Durham, Stephen D ^a  

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

^b and Associates ^*  (United States)

Author keywords

Beta binomial distribution; Correlated binary data; Developmental toxicology; Extra binomial variability; Hierarchical model; Intralitter correlation; Litter effect; Logistic regression; Overdispersion; Teratology

Indexed keywords

HIERARCHICAL SYSTEMS; REGRESSION ANALYSIS; TOXICITY;

BETA-BINOMIAL DISTRIBUTIONS; BINARY DATA; CORRELATED BINARY DATA; DEVELOPMENTAL TOXICOLOGY; EXTRA-BINOMIAL VARIABILITY; HIERARCHICAL MODEL; INTRALITTER CORRELATION; LITTER EFFECT; LOGISTICS REGRESSIONS; OVERDISPERSION; TERATOLOGY;

EXPONENTIAL FUNCTIONS;

ARTICLE; DOSE RESPONSE; STATISTICAL MODEL; TERATOLOGY; TOXICITY TESTING;

EID: 0034063490     PISSN: 0006341X     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0006-341X.2000.00125.x     Document Type: Article

References (27)

1. Ahn, H. and Chen, J. J. (1995). Generation of over-dispersed and under-dispersed binomial variates. Journal of Computational and Graphical Statistics 4, 55-64.
2. Boos, D. D. (1993). Analysis of dose-response data in the presence of extrabinomial variation. Applied Statistics 42, 173-184.
3. Bowman, D. and George, E. O. (1995). A saturated model for analyzing exchangeable binary data: Applications to clinical and developmental toxicity studies. Journal of the American Statistical Association 90, 871-879.
4. Carr, G. J. and Portier, C. J. (1993). An evaluation of some methods for fitting dose-response models to quantal response developmental toxicology data. Biometrics 49, 779-792.
5. Catalano, P. J. and Ryan, L. M. (1994). Statistical methods in developmental toxicology. In Handbook of Statistics, Volume 12, Environmental Statistics, G. P. Patil and C. R. Rao (eds), 507-534. New York: North-Holland/Elsevier.
6. Gaylor, D. W. (1994). Dose response modelling. In Developmental Toxicology, C. Kimmel and J. Buelke-Sam (eds), 363-375. New York: Raven.
7. Haseman, J. K. and Piegorsch, W. W. (1994). Statistical analysis of developmental toxicity data. In Developmental Toxicology. C. Kimmel and J. Buelke-Sam (eds), 349-361. New York: Raven.
8. Heckman, J. J. and Willis, R. J. (1977). A beta-logistic model for the analysis of sequential labor force participation by married women. Journal of Political Economy 85, 27-58.
9. Heindel, J. J., Price, C. J., Field, E. A., Marr, M. C., Myers, C. B., Morrissey, R. E., and Schwetz, B. A. (1992). Developmental toxicity of boric acid in mice and rats. Fundamental and Applied Toxicology 18, 266-277.
10. Hertzberg, V. S., Lemasters, G. K., Hansen, K., and Zenick, H. M. (1991). Statistical issues in risk assessment of reproductive outcomes with chemical mixtures. Environmental Health Perspectives 90, 171-175.
11. Jennings, D. E. (1986). Judging inference adequacy in logistic regression. Journal of the American Statistical Association 81, 471-476.
12. Krewski, D. and Zhu, Y. (1994). Applications of multinomial dose response models in developmental toxicity risk assessment. Risk Analysis 14, 613-628.
13. Kupper, L. L., Portier, C. J., Hogan, M. D., and Yamamoto, E. (1986). The impact of litter effects on dose-response modeling in teratology. Biometrics 42, 85-98.
14. Liang, K.-Y. and Hanfelt, J. (1994). On the use of the quasi-likelihood method in teratology experiments. Biometrics 50, 872-880.
15. Lipsitz, S. R., Laird, N. M., and Harrington, S. P. (1991). Generalized estimating equations for correlated binary data: Using the odds ratio as a measure of association. Biometrika 78, 153-160.
16. Lockhart, A.-M., Piegorsch, W. W., and Bishop, J. B. (1992). Assessing overdispersion and dose response in the male dominant lethal assay. Mutation Research 272, 35-58.
17. Moore, D. F. (1987). Modelling the extraneous variance in the presence of extra-binomial variation. Applied Statistics 36, 8-14.
18. National Toxicology Program. (1989). Developmental toxicity of boric acid (CAS No. 10043-35-3) administered to CD-1 Swiss mice. Technical Report NTP-89-250, U.S. National Toxicology Program, Research Triangle Park, North Carolina.
19. Paul, S. R. (1982). Analysis of proportions of affected foetuses in teratological experiments. Biometrics 38, 361-370.
20. Paul, S. R. and Islam, A. S. (1995). Analysis of proportions in the presence of over-/under-dispersion. Biometrics 51, 1400-1410.
21. Piegorsch, W. W. (1993). Biometrical methods for testing dose effects of environmental stimuli in laboratory studies. Environmetrics 4, 483-505.
22. Prentice, R. L. (1986). Binary regression using an extended beta-binomial distribution, with discussion of correlation induced by covariate measurement errors. Journal of the American Statistical Association 81, 321-327.
23. Ryan, L. M. (1992). The use of generalized estimating equations for risk assessment in developmental toxicology. Risk Analysis 12, 439-447.
24. Skellam, J. G. (1948). A probability distribution derived from the binomial distribution by regarding the probability of success as variable between the sets of trials. Journal of the Royal Statistical Society, Series B 10, 257-261.
25. Tarone, R. E. (1979). Testing the goodness of fit of the binomial distribution. Biometrika 66, 585-590.
26. Williams, D. A. (1975). The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity. Biometrics 31, 949-952.
27. Williams, D. A. (1996). Overdispersion in logistic-linear models. In Statistics in Toxicology, B. J. T. Morgan (ed), 75-84. Oxford: Clarendon.