We describe a family of random walk rules for the sequential allocation of dose levels to patients in a dose-response study, or phase I clinical trial. Patients are sequentially assigned the next higher, same, or next lower dose level according to some probability distribution, which may be determined by ethical considerations as well as the patient's response. It is shown that one can choose these probabilities in order to center dose level assignments unimodally around any target quantile of interest. Estimation of the quantile is discussed; the maximum likelihood estimator and its variance are derived under a two-parameter logistic distribution, and the maximum likelihood estimator is compared with other nonparametric estimators. Random walk rules have clear advantages: they are simple to implement, and finite and asymptotic distribution theory is completely worked out. For a specific random walk rule, we compute finite and asymptotic properties and give examples of its use in planning studies. Having the finite distribution theory available and tractable obviates the need for elaborate simulation studies to analyze the properties of the design. The small sample properties of our rule, as determined by exact theory, compare favorably to those of the continual reassessment method, determined by simulation.

Stephen D. Durham

Nancy Flournoy

William F. Rosenberger

Biometrics

国际生物统计学会是一个促进统计和数学理论和方法在生物科学领域的发展和应用的国际协会，包括农业、生物医学科学和公共卫生、生态学、环境科学、林业和相关学科。协会欢迎统计学家、数学家、生物科学家和其他致力于跨学科努力推动生物科学信息收集和解释的人士成为会员。该协会赞助在世界各地举行的两年一度的国际生物识别会议；通过其国家团体和地区，它还赞助地区和地方会议。

The International Biometric Society is an international association dedicated to promoting the development and application of statistical and mathematical theories and methods in the field of biosciences. This includes areas such as agriculture, biomedical sciences, public health, ecology, environmental science, forestry, and related disciplines. The society welcomes statisticians, mathematicians, biologists, and other professionals committed to interdisciplinary efforts to advance the collection and interpretation of bioscience information. The society sponsors a biennial International Biometric Conference held worldwide, as well as regional and local meetings through its national and regional groups.

国际生物统计学会是一个致力于促进统计学和数学理论及方法在生物科学领域的应用与发展的国际性协会。该协会涵盖多个领域，包括农业、生物医学科学、公共卫生、生态学、环境科学、林业及相关学科。协会欢迎统计学家、数学家、生物科学家及其他致力于跨学科合作、推动生物科学信息收集与解释的专业人士加入。该协会每两年举办一次国际生物识别会议，并通过其国家和地区分支机构赞助地方和区域性会议。

Category	Quartile
数学	4
数学, 生物学	3
数学, 数学与计算生物学	3
数学, 统计学与概率论	3

A Random Walk Rule for Phase I Clinical Trials

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Journal Info

Category	Quartile
STATISTICS & PROBABILITY	2