Volume 5, Issue 2-1, March 2016, Page: 12-20
A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data
Nicholas A. Nechval, Department of Mathematics, Baltic International Academy, Riga, Latvia
Gundars Berzins, Department of Management, University of Latvia, Riga, Latvia
Vadims Danovics, Department of Marketing, University of Latvia, Riga, Latvia
Received: Nov. 2, 2015;       Accepted: Nov. 2, 2015;       Published: Nov. 30, 2015
DOI: 10.11648/j.ajtas.s.2016050201.13      View  3084      Downloads  67
Abstract
Identifying the ‘right’ dose is one of the most critical and difficult steps in the clinical development process of any medicinal drug. Its importance cannot be understated: selecting too high a dose can result in unacceptable toxicity and associated safety problems, while choosing too low a dose leads to smaller chances of showing sufficient efficacy in confirmatory trials, thus reducing the chance of approval for the drug. The optimal dose is the dose that gives the desired effect with minimum side effects. The dose of a drug is of course ‘optimal’ only for a given subject, but not necessarily for any other. In view of this the objective of a dose-finding trials is not to determine a single fixed dose for use in the early phases of clinical trials or in medical practice, but to determine an interval of doses within which there is a stated degree of confidence that the defined, acceptable therapeutic response and the frequency of adverse reactions will lie above and below, respectively, certain acceptable predetermined levels. If the subject samples used in the dose finding studies adequately represent the subject population for which the drug is intended, the interval of doses so defined can be applied to the subject population as a whole. In this paper, we propose the technique based on maximization of likelihood function in order to estimate the maximal tolerated dose (MTD) and minimal effective dose (MED) on the basis of l samples of subjects, which are grouped in a simplest way. The necessary and sufficient conditions for the existence and uniqueness of the maximum likelihood estimates are derived. The proposed approach to dose estimation in drug development is simple and suitable for medical practice. The numerical examples are given.
Keywords
Drug Development, Dose Estimation, Grouped Data, Likelihood Function, Maximization
To cite this article
Nicholas A. Nechval, Gundars Berzins, Vadims Danovics, A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data, American Journal of Theoretical and Applied Statistics. Special Issue: Novel Ideas for Efficient Optimization of Statistical Decisions and Predictive Inferences under Parametric Uncertainty of Underlying Models with Applications. Vol. 5, No. 2-1, 2016, pp. 12-20. doi: 10.11648/j.ajtas.s.2016050201.13
Reference
[1]
D.T. Greenwood and A. H. Todd, “From laboratory to clinical use,” in Clinical Trials, Johnson, F. N. and Johnson, S. (eds), Blackwell, London, 1977, pp. 50 –70.
[2]
J. R. Crout and M. J. Finkel, General Considerations for the Clinical Evaluation of 4 Drugs. U.S. Dept. of Health, Education and Welfare-Public Health Service F. D. A., 1977.
[3]
H. Robbins and S. Monro, “A stochastic approximation method,” Annals of Mathematical Statistics, vol. 22, pp. 400 – 407, 1951.
[4]
C.-F.J. Wu, “Efficient sequential designs with binary data,” J. Amer. Statist. Assoc., vol 80, pp. 974 – 984, 1985.
[5]
B. H. Eichhorn and S. Zacks, “Sequential search of an optimal dosage,” J. Amer. Statist. Assoc., vol. 68, pp. 594 –598, 1973.
[6]
B. H. Eichhorn and S. Zacks, “ Bayes sequential search of an optimal dosage: linear regression with both parameters unknown,” Communications in Statistics-Theory and Methods, vol. 10, pp. 931– 953, 1981.
[7]
J. Pinheiro, F. Bretz, and M. Branson, Dose Finding in Drug Development. New York: Springer, 2006.
[8]
B. Bornkamp, J. C. Pinheiro, and F. Bretz, “MCPMod: An R package for the design and analysis of dose-finding studies, ” Journal of Statistical Software, vol. 29, pp. 1–23, 2009.
[9]
M. Whitney and L. Ryan, “Quantifying dose-response uncertainty using Bayesian model averaging,” in Uncertainty Modeling in Dose Response: Bench Testing Environmental Toxicity. New York: Wiley, 2009, pp. 165–179.
[10]
M. Gasparini and J. Eisele, “A curve-free method for phase I clinical trials,” Biometrics, vol. 56, pp. 609 – 615, 2000.
[11]
I. J. Myung, “Tutorial on maximum likelihood estimation,” Journal of Mathematical Psychology, vol. 47, pp. 90–100, 2003.
[12]
F. Bretz and L. A. Hothorn, “Statistical analysis of monotone or non-monotone dose-response data from in vitro toxicological assays,” Alternatives to Lab Animals, vol. 31, pp.81– 96, 2003.
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