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Bias and loss: the two sides of a biased coin
Author(s) -
Atkinson Anthony C.
Publication year - 2012
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.5416
Subject(s) - randomness , covariate , computer science , econometrics , constant (computer programming) , statistics , transformation (genetics) , set (abstract data type) , mathematics , mathematical optimization , biochemistry , chemistry , gene , programming language
The paper assesses biased‐coin designs for sequential treatment allocation in clinical trials. Comparisons emphasise the importance of considering randomness, as well as treatment balance, which are calculated as bias and loss. In the numerical examples, the responses are assumed normally distributed, perhaps after transformation, and balance is required over a set of covariates. The effect of covariate distribution on the properties of five allocation rules is investigated, with an emphasis on methods of comparison, which also apply to other forms of response. The concept of admissibility shows that the widely used minimisation rule is outperformed by Atkinson's rule derived from the theory of optimum experimental design. We present a simplified form of this rule. For this rule, the ability to guess the next treatment allocation decreases with study size. For the other rules, it is constant. Copyright © 2012 John Wiley & Sons, Ltd.