摘要:

A clinical trial setting is considered in which two treatments are available for a particular ailment. A two—stage trial is studied, in which patients are randomised equally in the first stage, and the better treatment at the end of this stage is used exclusively in the second stage. For exponential and Bernoulli responses, the exact bias and variance of the estimated treatment difference at the end of the trial are derived. Corresponding results for normal responses with unequal variances are also obtained, and the numerical accuracy of a normal approximation is investigated. The results indicate that the bias in estimation can be up to 25% when the size of the first stage is small, reducing to less than 7% for moderate first—stage sizes. For both exponential and Bernoulli responses, a normal approximation works well for moderate first—stage sizes, with the approximation for Bernoulli responses being slightly better.

ISSN:0747-4946    

DOI:10.1080/07474949208836262

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

Suppose two treatments with binary responses are available for patients with some disease. Sequential allocation rules based on the theory of Bayesian bandit processes are examined. The patient horizon is assumed to be random and the objective is to maximize the total expected number of successes. This problem is equivalent to the classical two—armed bandit problem if we assume that the only information acquired during the trial about the patient horizon is whether or not it has so far been reached. When one treatment has a known success rate, the optimal allocation rule may sometimes be expressed in terms of dynamic allocation indices. The calculation of the indices is discussed, and in particular error bounds for the accuracy of the calculation are given in terms of the starting point of the backward induction process. When both treatments have unknown success rates the use of dynamic allocation indices with geometric discounting is suggested. Simulation results indicate that this rule works well even when the distribution of the number of the patients is not geometrical, and that the choice of the discount factor is also not crucial.

ISSN:0747-4946    

DOI:10.1080/07474949208836263

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

Minimax optimal stopping times and minimax worst—case distributions are found for the problem of stopping a sequence of uniformly bounded i.i.d. random variables in a cost and a discount model when only the mean and/or the variance (and not the complete distribution) of the random variables is known

ISSN:0747-4946    

DOI:10.1080/07474949208836264

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

The use of sequential methods in clinical trials allows inferior treatments to be eliminated early. From an ethical point of view, the advantages are substantial. However, early stopping induces estimation bias and a deterioration in precision because of reduced sample sizes. This paper considers the problem of determining which of k ≥ 2 treatments with Bernoulli responses has the highest probability of success. Two sequential procedures are investigated and compared with a fixed—sample procedure. Various properties are derived and illustrated for the cases k =2,3 and 5. It is shown that the sequential procedures can achieve a pattern of error probabilities equivalent to the fixed—sample procedure for a much lower level of expected successes lost. Approximations for the bias and standard deviation of estimators of treatment differences are obtained by using results about the distribution of stopping times for a normal process.

ISSN:0747-4946    

DOI:10.1080/07474949208836265

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

The editors are grateful to the following persons for their diligent and invaluable work as referees during 1991-92. Thanks are also due to all members of the editorial board for their guidance in the reviewing process of numerous manuscripts.

ISSN:0747-4946    

DOI:10.1080/07474949208836266

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474949208836261

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor