A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data

Nicholas A. Nechval; Gundars Berzins; Vadims Danovics

doi:doi:10.11648/j.ajtas.s.2016050201.13

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A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data

Nicholas A. Nechval, Gundars Berzins, Vadims Danovics

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 2-1)

Received: 2 November 2015 Accepted: 2 November 2015 Published: 30 November 2015

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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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 2-1) This article belongs to the Special Issue Novel Ideas for Efficient Optimization of Statistical Decisions and Predictive Inferences under Parametric Uncertainty of Underlying Models with Applications
DOI	10.11648/j.ajtas.s.2016050201.13
Page(s)	12-20
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Drug Development, Dose Estimation, Grouped Data, Likelihood Function, Maximization

References

[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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Nicholas A. Nechval, Gundars Berzins, Vadims Danovics. (2015). A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data. American Journal of Theoretical and Applied Statistics, 5(2-1), 12-20. https://doi.org/10.11648/j.ajtas.s.2016050201.13

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ACS Style

Nicholas A. Nechval; Gundars Berzins; Vadims Danovics. A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data. Am. J. Theor. Appl. Stat. 2015, 5(2-1), 12-20. doi: 10.11648/j.ajtas.s.2016050201.13

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AMA Style

Nicholas A. Nechval, Gundars Berzins, Vadims Danovics. A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data. Am J Theor Appl Stat. 2015;5(2-1):12-20. doi: 10.11648/j.ajtas.s.2016050201.13

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@article{10.11648/j.ajtas.s.2016050201.13,
  author = {Nicholas A. Nechval and Gundars Berzins and Vadims Danovics},
  title = {A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {2-1},
  pages = {12-20},
  doi = {10.11648/j.ajtas.s.2016050201.13},
  url = {https://doi.org/10.11648/j.ajtas.s.2016050201.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2016050201.13},
  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.},
 year = {2015}
}

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TY  - JOUR
T1  - A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data
AU  - Nicholas A. Nechval
AU  - Gundars Berzins
AU  - Vadims Danovics
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DO  - 10.11648/j.ajtas.s.2016050201.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
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AB  - 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.
VL  - 5
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Author Information

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

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APA Style

Nicholas A. Nechval, Gundars Berzins, Vadims Danovics. (2015). A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data. American Journal of Theoretical and Applied Statistics, 5(2-1), 12-20. https://doi.org/10.11648/j.ajtas.s.2016050201.13

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ACS Style

Nicholas A. Nechval; Gundars Berzins; Vadims Danovics. A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data. Am. J. Theor. Appl. Stat. 2015, 5(2-1), 12-20. doi: 10.11648/j.ajtas.s.2016050201.13

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AMA Style

Nicholas A. Nechval, Gundars Berzins, Vadims Danovics. A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data. Am J Theor Appl Stat. 2015;5(2-1):12-20. doi: 10.11648/j.ajtas.s.2016050201.13

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@article{10.11648/j.ajtas.s.2016050201.13,
  author = {Nicholas A. Nechval and Gundars Berzins and Vadims Danovics},
  title = {A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {2-1},
  pages = {12-20},
  doi = {10.11648/j.ajtas.s.2016050201.13},
  url = {https://doi.org/10.11648/j.ajtas.s.2016050201.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2016050201.13},
  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.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data
AU  - Nicholas A. Nechval
AU  - Gundars Berzins
AU  - Vadims Danovics
Y1  - 2015/11/30
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.s.2016050201.13
DO  - 10.11648/j.ajtas.s.2016050201.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 12
EP  - 20
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.s.2016050201.13
AB  - 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.
VL  - 5
IS  - 2-1
ER  -

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