Two-dimensional toxic dose and multivariate logistic regression, with application to decompression sickness

Biostatistics

Volumn 12, Issue 1, 2011, Pages 143-155

  Li, Jialiang ^a   Wong, Weng Kee ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

2D toxic dose; Decompression sickness; Gumbel distribution; Maximum likelihood estimation; Multivariate logistic regression

Indexed keywords

ANIMAL; ARTICLE; DECOMPRESSION SICKNESS; DISEASE MODEL; MULTIVARIATE ANALYSIS; PRESSURE; SHEEP; STATISTICAL MODEL; TIME;

ANIMALS; DECOMPRESSION SICKNESS; DISEASE MODELS, ANIMAL; LOGISTIC MODELS; MODELS, STATISTICAL; MULTIVARIATE ANALYSIS; PRESSURE; SHEEP; TIME FACTORS;

ANIMALIA; OVIS ARIES;

EID: 78650642584     PISSN: 14654644     EISSN: 14684357     Source Type: Journal    
DOI: 10.1093/biostatistics/kxq044     Document Type: Article

References (30)

1. BROYDEN, C. G. (1970). The convergence of a class of double-rank minimization algorithms. Journal of the Institute of Mathematics and Its Applications 6, 76-90.
2. 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, 641-658.
3. CLAESKENS, G., AERTS, M., MOLENBERGHS, G. AND RYAN, L. (2002). Robust benchmark dose determination based on profle score methods. Environmental and Ecological Statistics 9, 357-377.
4. COLEMAN, T. F. AND LI, Y. (1994). On the convergence of refective newton methods for large-scale nonlinear minimization subject to bounds. Mathematical Programming 67, 189-224.
5. COLLETT, D. (2002). Modelling Binary Data, 2nd edition. London: Chapman & Hall/CRC.
6. COOK, R. D. AND JOHNSON, M. E. (1981). A family of distributions for modelling non-elliptically symmetric multivariate data. Journal of the Royal Statistical Society. Series B 43, 210-218.
7. COX, D. R. (1972). The analysis of multivariate binary data. Applied Statistics 21, 113-120.
8. DROMSKY, D. M., TONER, C. B., SURVANSHI, S., FAHLMAN, A., PARKER, E. AND WEATHERSBY, P. (2000). Natural history of severe decompression sickness after rapid ascent from air saturation in a porcine model. Journal of Applied Physiology 89, 791-798.
9. FINNEY, D. J. (1978). Statistical Method in Biological Assay. New York: Macmillan.
10. FITZMAURICE, G. M. AND LAIRD, N. M. (1993). A likelihood-based method for analyzing longitudinal binary patterns. Biometrika 80, 141-151.
11. GAUVREAU, K. AND PAGANO, M. (1997). The analysis of correlated binary outcome using multivariate logistic regression. Biometrical Journal 39, 309-325. (Pubitemid 127374032)
12. GLONEK, G. F. V. AND MCCULLAGH, P. (1995). Multivariate logistic models. Journal of the Royal Statistical Society. Series B 57, 533-546.
13. GUMBEL, E. J. (1961). Bivariate logistic distributions. Journal of American Statistical Association 56, 335-349.
14. HEAGERTY, P. J. AND ZEGER, S. L. (1996). Marginal regression models for clustered ordinal measurements. Journal of the American Statistical Association 91, 1024-1036.
15. HEISE, M. A. AND MYERS, R. H. (1996). Optimal designs for bivariate logistic regression. Biometrics 52, 612-624.
16. JOE, H. (1997). Multivariate Models and Dependence Concepts. London: Chapman & Hall.
17. 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.
18. LEHNER, C. E., DUELAND, R. T., WILSON, M. A., NORDHEIM, E. V., VAICEKAVICIUS, L., GENDRON-FITZPATRICK, A. P. AND CRUMP, P. M. (2000). Decompression risk in submarine escape with "drop-outs" after hyperbaric saturation: UW sheep model fndings. Undersea & Hyperbaric Medicine 27(Suppl), 41.
19. LIPSITZ, S. R., LAIRD, N. M. AND HARRINGTON, D. P. (1991). Generalized estimating equations for correlated binary data: using the odds ratio as a measure of association. Biometrika 78, 153-160.
20. MALIK, H. J. AND ABRAHAM, B. (1973). Multivariate logistic distributions. Annals of Statistics 1, 588-590.
21. MATHEW, T. AND ZHA, W. X. (1997). Multiple use confdence regions in multivariate calibration. Journal of the American Statistical Association 92, 1141-1150.
22. MEE, R. W. AND EBERHARDT, K. R. (1996). A comparison of uncertainty criteria for calibration. Technometrics 38, 221-229.
23. MEE, R. W., EBERHARDT, K. R. AND REEVE, C. P. (1991). Calibration and simultaneous tolerance intervals for regression. Technometrics 33, 211-220.
24. MOLENBERGHS, G. AND RITTER, L. L. (1996). Methods for analyzing multivariate binary data, with association between outcomes of interest. Biometrics 52, 1121-1133.
25. MOLENBERGHS, G. AND RYAN, L. (1999). An exponential family model for clustered multivariate binary data. Environmetrics 10, 279-300.
26. NIKOLOULOPOULOS, A. K. AND KARLIS, D. (2008). Multivariate logit copula model with an application to dental data. Statistics in Medicine 27, 6393-6406.
27. NOCEDAL, J. AND WRIGHT, S. J. (1999). Numerical Optimization, Springer Series in Operations Research. New York: Springer.
28. PLACKET, R. L. (1965). A class of bivariate distributions. Journal of the American Statistical Association 60, 516-522.
29. SAND, S., VICTORIN, K. AND FILIPSSON, A. F. (2008). The current state of knowledge on the use of the benchmark dose concept in risk assessment. Journal of Applied Toxicology 28, 405-421.
30. SATTERTHWAITE, S. P. AND HUTCHINSON, T. P. (1978). A generalisation of Gumbel's bivariate logistic distribution. Metrika 25, 163-170.