An exponential family model for clustered multivariate binary data

Environmetrics

Volumn 10, Issue 3, 1999, Pages 279-300

  Molenberghs, Geert ^a   Ryan, Louise M ^b  

^a HASSELT UNIVERSITY   (Belgium)

^b HARVARD SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

Developmental toxicity; Exponential family; Litter effect; Low birth weight; Malformation; Score test

Indexed keywords

EID: 0033020774     PISSN: 11804009     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-095X(199905/06)10:3<279::AID-ENV352>3.0.CO;2-X     Document Type: Article

References (49)

1. Aerts, M., Declerck, L. and Molenberghs, G. (1997). 'Likelihood misspecification and safe dose determination for clustered binary data'. Environmetrics 8, 613-627.
2. Agresti, A. (1990). Categorical Data Analysis. New York: John Wiley.
3. Ashford, J. R. and Sowden, R. R. (1970). 'Multivariate probit analysis'. Biometrics 26, 535-546.
4. Bahadur, R. R. (1961). 'A representation of the joint distribution of responses to n dichotomous items'. In Studies in Item Analysis and Prediction, ed. H. Solomon. Stanford Mathematical Studies in the Social Sciences VI. Stanford, California: Stanford University Press.
5. Breslow, N. E. and Clayton, D. G. (1993). 'Approximate inference in generalized linear mixed models'. Journal of the American Statistical Association 88, 9-25.
6. Carey, V. C., Zeger, S. L. and Diggle, P. J. (1993). 'Modelling multivariate binary data with alternating logistic regressions'. Biometrika 80, 517-526.
7. Catalano, P. J. and Ryan, L. M. (1992). 'Bivariate latent variable models for clustered discrete and continuous outcomes'. Journal of the American Statistical Association 87, 651-658.
8. Chen, J. J. and Kodell, R. L. (1989). 'Quantitative risk assessment for teratological effects'. Journal of the American Statistical Association 84, 966-971.
9. Chen, J. J., Kodell, R. L., Howe, R. B. and Gaylor, D. W. (1991). 'Analysis of trinomial responses from reproductive and developmental toxicity experiments'. Biometrics 47, 1049-1058.
10. Cox, D. R. (1972). 'The analysis of multivariate binary data'. Applied Statistics 21, 113-120.
11. Cox, D. R. and Hinkley, D. V. (ed.) (1974). Theoretical Statistics. London: Chapman and Hall.
12. Cox, D. R. and Wermuth, N. (1994). 'A note on the quadratic exponential binary distribution'. Biometrika 81, 403-408.
13. Crump, K. (1984). 'A new method for determining allowable daily intakes'. Fund. Appl. Toxicol. 4, 854-871.
14. Dale, J. R. (1986). 'Global cross-ratio models for bivariate, discrete, ordered responses'. Biometrics 42, 909-917.
15. Declerck, L., Aerts, M. and Molenberghs, G. (1998). 'Behaviour of the likelihood ratio test statistic under a Bahadur model for exchangeable binary data'. Journal of Statistical Computation and Simulation 61, 15-38.
16. Diggle, P. J., Liang, K.-Y and Zeger, S. L. (1994). Analysis of Longitudinal Data. Oxford: Clarendon Press.
17. Fitzmaurice, G. M. and Laird, N. M. (1993). 'A likelihood-based method for analysing longitudinal binary responses'. Biometrika 80, 141-151.
18. Fitzmaurice, G. M. and Laird, N. M. (1995). 'Regression models for bivariate discrete and continuous outcomes'. Journal of the American Statistical Association 90, 845-852.
19. Fitzmaurice, G. M., Laird, N. M. and Rotnitzky, A. (1993). 'Regression models for discrete longitudinal responses'. Statistical Science 8, 284-309.
20. Geys, H., Molenberghs, G. and Ryan, L. M. (1997a). 'Pseudo-likelihood inference for clustered binary data'. Communications in Statistics: Theory and Methods 26, 2743-2767.
21. Geys, H., Molenberghs, G. and Ryan, L. M. (1999). 'Pseudo-likelihood inference for exponential family models applied to toxicology data'. Journal of the American Statistical Association at press.
22. Geys, H., Molenberghs, G. and Williams, P. (1997b). 'Analysis of clustered binary data with covariates specific to each observation'. In Good Statistical Practice, Proceedings of the 12th International Workshop on Statistical Modelling, eds. C. E. Minder and H. Friedl. Schriftenreihe der Österreichischen Statistischen Gesellschaft, Band 5, Wien.
23. Hauck, W. W. and Donner, A. (1997). 'Wald's test as applied to hypotheses in logic analysis'. Journal of the American Statistical Association 72, 851-853.
24. Hosmer, D. W. and Lemeshow, S. (1980). 'A goodness-of-fit test of the multiple logistic regression model'. Communications in Statistics A10, 1043-1069.
25. Hosmer, D. W. and Lemeshow, S. (1989). Applied Logistic Regression. New York: Wiley.
26. Kleinman, J. C. (1973). 'Proportions with extraneous variance: single and independent samples'. Journal of the American Statistical Association 68, 46-54.
27. Lefkopoulou, M., Moore, D. and Ryan, L. (1989). 'The analysis of multiple correlated binary outcomes: application to rodent teratology experiments'. Journal of the American Statistical Association 84, 810-815.
28. Lefkopoulou, M., Rotnitzky, A. and Ryan, L. M. (1995). Trend tests for clustered data'. In Statistics in Toxicology, ed. B. T. Morgan. Oxford: Oxford University Press.
29. Lefkopoulou, M. and Ryan, L. M. (1993). 'Global tests for multiple binary outcomes'. Biometrics 49, 974-988.
30. Legler, J. M., Lefkopoulou, M. and Ryan, L. M. (1995). 'Efficiency and power of tests for multiple binary outcomes'. Journal of the American Statistical Association 90, 680-693.
31. Liang, K.-Y and Zeger, S. L. (1986). 'Longitudinal data analysis using generalized linear models'. Biometrika 73, 13-22.
32. Liang, K.-Y and Zeger, S. L. (1989). 'A class of logistic regression models for multivariate binary time series'. Journal of the American Statistical Association 84, 447-451.
33. Molenberghs, G., Declerck, L. and Aerts, M. (1997). 'Misspecifying the likelihood for clustered binary data'. Computational Statistics and Data Analysis 26, 327-349.
34. Molenberghs, G. and Lesaffre, E. (1994). 'Marginal modelling of correlated ordinal data using a multivariate Plackett distribution'. Journal of the American Statistical Association 89, 633-644.
35. Pendergast, J. F., Gange, S. J., Newton, M. A., Lindstrom, M. J., Palta, M. and Fisher, M. R. (1996). 'A survey of methods for analyzing clustered binary response data'. International Statistical Review 64, 89-118.
36. Prentice, R. L. (1988). 'Correlated binary regression with covariates specific to each binary observation'. Biometrics 44, 1033-1048.
37. Price, C. J., Kimmel, C. A., George, J. D. and Marr, M. C. (1987). The developmental toxicity of diethylene glycol dimethyl ether in mice'. Fundamental and Applied Toxicology 8, 115-126.
38. Rai, K. and Van Ryzin, J. (1985). 'A dose-response model for teratological experiments involving quantal responses'. Biometrics 47, 825-839.
39. Rosner, B. (1984). 'Multivariate methods in ophtamology with applications to other paired-data situations'. Biometrics 40, 1025-1035.
40. Rotnitzky, A. and Jewel, N. P. (1990). 'Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster correlated data'. Biometrika 77, 485-497.
41. Ryan, L. (1992). 'Quantitative risk assessment for developmental toxicity'. Biometrics 48, 163-174.
42. Stiratelli, R., Laird, N. and Ware, J. H. (1984). 'Random-effects models for serial observations with binary response'. Biometrics 40, 961-971.
43. Thélot, C. (1985). 'Lois Logistiques à deux dimensions'. Annales de l'Insée 58, 123-149.
44. Tyl, R. W., Price, M. C., Marr, M. C. and Kimmel, C. A. (1988). 'Developmental toxicity evaluation of dietary di(2-ethylhexyl)phthalate in Fisher 344 rats and CD-1 mice'. Fundamental and Applied Toxicology 10, 395-412.
45. White, H. (1982). 'Maximum likelihood estimation of misspecified models'. Econometrica 50, 1-25.
46. Williams, D. A. (1975). 'The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity'. Biometrics 31, 949-952.
47. Wolfinger, R. and O'Connell, M. (1993). 'Generalized linear mixed models: a pseudo-likelihood approach'. Journal of Statistical Computation and Simulation 48, 233-243.
48. Zeger, S. L., Liang, K.-Y and Albert, P. S. (1988). 'Models for longitudinal data: a generalized estimating equation approach'. Biometrics 44, 1049-1060.
49. Zhao, L. P. and Prentice, R. L. (1990). 'Correlated binary regression using a quadratic exponential model'. Biometrika 77, 642-648.