Journal ArticleDOI
Sequential Analysis with Delayed Observations
TLDR
In this article, the authors considered a special case of the situation in which after the decision to stop observation is made a fixed number of additional observations are available for the terminal decision, and the test is then based on the ratio of the likelihoods (at two simple hypotheses) of all the observations (whatever stopping rule is used).Abstract:
In testing one hypothesis against another, observations may be obtained sequentially. The special feature of the situation considered in this paper is that after the decision to stop observation is made a fixed number of additional observations are available for the terminal decision. The test is then based on the ratio of the likelihoods (at two simple hypotheses) of all the observations (whatever stopping rule is used). Numerical comparisons are made for various cases when the hypotheses concern the mean of a normal distribution with the variance known; these cases include a fixed-sample-size procedure as well as cases where several numbers of additional observations are available after the Wald sequential probability ratio test is used as a stopping rule.read more
Citations
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Journal ArticleDOI
Group sequential tests for delayed responses (with discussion)
TL;DR: In this article, the authors formulate a new form of group sequential test which gives a proper treatment of these pipeline subjects, which can be applied even when the continued accrual of data after the decision to stop the trial is unexpected.
Journal ArticleDOI
Sequential Linear Rank Tests for Two-Sample Censored Survival Data
TL;DR: In this article, under extremely general patterns of patient-arrival, allocation to treatment and loss to follow-up in (randomized) clinical trial settings, the sequentially computed logrank statistic (Mantel, 1966) is shown (under the null hypothesis of identically distributed lifetimes) to have exactly uncorrelated increments, and is shown via Rebolledo's (1980) martingale invariance principle to satisfy a functional central limit theorem, justifying sequential logrank tests of Jones and Whitehead (1979).
Journal ArticleDOI
The analysis of sequential clinical trials
John Whitehead,David R. Jones +1 more
TL;DR: In this article, the authors consider the comparison of two treatments using sequential tests based on straight line stopping boundaries and show that the results of traditional sequential analysis can be used only in the planning of the trial, but all the data, including the 'extra' observations, can be included in the analysis.
Book ChapterDOI
A Survey of Adaptive Sampling for Clinical Trials
TL;DR: This chapter reviews some work on a subject that treats the design of clinical trials in the light of ranking and selection theory and shows that a two-stage procedure requires only a small number of preliminary tests to benefit from the possibility of choosing between allocation methods.
Dissertation
Group sequential tests for delayed responses
TL;DR: It is shown how the benefits of lower expected sample size normally achieved by a group sequential test are reduced when there is a delay in response, by studying optimal versions of these new designs.
References
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Book
Testing statistical hypotheses
TL;DR: The general decision problem, the Probability Background, Uniformly Most Powerful Tests, Unbiasedness, Theory and First Applications, and UNbiasedness: Applications to Normal Distributions, Invariance, Linear Hypotheses as discussed by the authors.
Journal ArticleDOI
Optimum Character of the Sequential Probability Ratio Test
Abraham Wald,Jacob Wolfowitz +1 more
TL;DR: In this article, it was shown that the sequential probability ratio test for deciding between two simple alternatives (H_0 and H_1) requires on the average fewest observations.
Journal ArticleDOI
A modification of the sequential probability ratio test to reduce the sample size
TL;DR: In this article, the authors considered a special case of the sequential probability ratio test, where the distribution is normal with known variance and the parameter of interest is the mean, and showed that the expected sample size is relatively large for values of the parameter between the two specified ones; that is, in cases in which one does not care greatly which decision is taken, a large number of observations is expected.