Dose-response curve estimation: A semiparametric mixture approach

Biometrics

Volumn 67, Issue 4, 2011, Pages 1543-1554

  Yuan, Ying ^a   Yin, Guosheng ^b  

^a UNIVERSITY OF TEXAS MD ANDERSON CANCER CENTER   (United States)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Bootstrap; Dose response curve; Effective dose; Nonparametric method; Parametric model; Weighted average

Indexed keywords

STATISTICAL METHODS;

BOOTSTRAP; CURVE ESTIMATION; DOSE-RESPONSE CURVES; EFFECTIVE DOSE; MODEL MISSPECIFICATION; NONPARAMETRIC METHODS; NONPARAMETRICS; PARAMETRIC MODELS; SEMIPARAMETRIC; WEIGHTED AVERAGES;

PARAMETER ESTIMATION;

BOOTSTRAPPING; DOSE-RESPONSE RELATIONSHIP; ESTIMATION METHOD; NUMERICAL MODEL; PARAMETERIZATION;

EID: 83655201490     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2011.01620.x     Document Type: Article

References (30)

1. Agresti, A. (2002). Categorical Data Analysis, 2nd edition. New York: Wiley.
2. Barlow, R. E., Bartholomew, D. J., Bremner, J. M., and Brunk, H. D. (1972). Statistical Inference under Order Restrictions: The Theory and Application of Isotonic Regression. New York: Wiley.
3. Berkson, J. (1944). Application of the logistic function to bio-assay. Journal of the American Statistical Association 39, 357-365.
4. Bliss, C. I. (1934). The method of probits. Science 79, 38-39.
5. Bornkamp, B. and Ickstadt, K. (2009). Bayesian nonparametric estimation of continuous monotone functions with applications to dose-response analysis. Biometrics 65, 198-205.
6. Bretz, F., Pinheiro, J. C., and Branson, M. (2005). Combining multiple comparisons and modeling techniques in dose-response studies. Biometrics 61, 738-748.
7. Dette, H. and Scheder, R. (2010). A finite sample comparison of nonparametric estimates of the effective dose in quantal bioassay. Journal of Statistical Computation and Simulation 80, 527-544.
8. Dette, H., Neumeyer, N., and Pilz, K. F. (2005). A note on nonparametric estimation of the effective dose in quantal bioassay. Journal of the American Statistical Association 100, 503-510.
9. Einsporn, R. L. (1987). HATLINK: A link between least squares regression and nonparametric curve estimation. PhD Dissertation, Virginia Tech. Blacksburg, Virginia.
10. Fahrmeir, L. and Kaufmann, H. (1985). Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models. The Annals of Statistics 13, 342-368.
11. Gasser, T., Kneip, A., and Koehler, W. (1991). A flexible and fast method for automatic smoothing. Journal of the American Statistical Association 86, 643-652.
12. Ghouch, A. E. and Genton, M. G. (2009). Local polynomial quantile regression with parametric features. Journal of the American Statistical Association 104, 1416-1429.
13. Green, P. J. and Silverman, B. W. (1994). Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. London: Chapman & Hall.
14. Kelly, C. and Rice, J. (1990). Monotone smoothing with application to dose-response curves and the assessment of synergism. Biometrics 46, 1071-1085.
15. Kouassi, D. A. and Singh, J. (1997). A semiparametric approach to hazard estimation with randomly censored observations. Journal of the American Statistical Association 92, 1351-1355.
16. Lee, E. T. (1974). A computer program for linear logistic regression analysis. Computer Methods and Programs in Biomedicine 4, 80-92.
17. Mammen, E. (1991). Estimating a smooth monotone regression function. The Annals of Statistics 19, 724-740.
18. Mays, J. E., Birch, J. B., and Starnes, B. A. (2001). Model robust regression: Combining parametric, nonparametric, and semiparametric methods. Journal of Nonparametric Statistics 13, 245-277.
19. McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd edition. New York: Chapman and Hall.
20. Morgan, B. J. T. (1992). Analysis of Quantal Response Data. New York: Chapman and Hall.
21. Mukhopadhyay, S. (2000). Bayesian nonparametric inference on the dose level with specified response rate. Biometrics 56, 220-226.
22. Müller, H. G. and Schmitt, T. (1988). Kernel and probit estimates in quantal bioassay. Journal of the American Statistical Association 83, 750-759.
23. Nottingham Q. J. and Birch, J. B. (2000). A semiparametric approach to analysing dose-response data. Statistics in Medicine 19, 389-404.
24. Olkin, I. and Spiegelman, C. H. (1987). A semiparametric approach to density estimation. Journal of the American Statistical Association 82, 858-865.
25. Park, D. and Park, S. (2006). Parametric and nonparametric estimators of ED100α. Journal of Statistical Computation and Simulation 76, 661-672.
26. Pickle, M. G. S. M., Robinson, T. J., Birch, J. B., and Anderson-Cook, C. (2008). A semi-parametirc approach to robust parameter design. Journal of Statistical Planning and Inference 138, 114-131.
27. Robinson, T. J., Birch J. B., and Starnes, A. (2010). A semiparametric approach to dual modeling when no replication exists. Journal of Statistical Planning and Inference 140, 2860-2869.
28. Schmoyer, R. L. (1984). Sigmoidally constrained maximum likelihood estimation in quantal bioassay. Journal of the American Statistical Association 79, 448-453.
29. Wan, W. and Birch, J. B. (2011). A semiparametric technique for the multi-response optimization problem. Quality and Reliability Engineering International 27, 47-59.
30. Waterman, M. J., Birch, J. B., and Schabengerger, O. (2007). Linear mixed model robust regression. Technical Report #07-3, Virginia Tech Department of Statistics.