zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Optimal Bayesian-feasible dose escalation for cancer phase I trials. (English) Zbl 0903.62064
Summary: We present an adaptive dose escalation scheme for cancer phase I clinical trials which is based on a parametric quantal response model. The dose escalation is Bayesian-feasible, Bayesian-optimal and consistent. It is designed to approach the maximum tolerated dose as fast as possible subject to the constraint that the predicted probability of assigning doses higher than the maximum tolerated dose is equal to a specified value.

62L05Sequential statistical designs
62P10Applications of statistics to biology and medical sciences
62F15Bayesian inference
Full Text: DOI
[1] Babb, J.; Rogatko, A.; Zacks, S.: Cancer phase I clinical trials: efficient dose escalation with overdose control. Statistics in medicine (1997)
[2] Eichhom, B. H.; Zacks, S.: Sequential search of an optimal dosage, I. Jour. amer. Statistic. assoc. 68, 594-598 (1973)
[3] Gastonis, C.; Greenhouse, J. B.: Bayesian methods for phase I clinical trials. Statist. med. 11, 1377-1389 (1992)
[4] O’quigley, J.; Pepe, M.; Fisher, L.: Continual reassessment method: a practical design for phase I clinical trials in cancer. Biometrics 46, 33-38 (1990) · Zbl 0715.62242
[5] O’quigley, J.; Chevret, S.: Methods for dose finding studies in cancer clinical trials: A review and result of Monte Carlo study. Statist. med. 10, 1047-1664 (1991)
[6] Shiryayev, A. N.: Probability. (1984)
[7] Storer, B. E.: Design and analysis of phase I clinical trials. Biometrics 45, 925-937 (1989) · Zbl 0715.62241
[8] Tsutakawa, R. K.: Selection of dose levels for estimating a percentage point of a logistic quantal response curve. J. roy. Statist. soc. Ser. C 29, 25-33 (1980) · Zbl 0429.62077
[9] Zacks, S.: Adaptive designs for parametric models. Handbook of statistics 13 (1996) · Zbl 0910.62075
[10] Zacks, S.; Eichhorn, B. H.: Sequential search of optimal dosages: the linear regression case. Statistical design and linear models (1975) · Zbl 0305.62056