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Sequential probability ratio test

About: Sequential probability ratio test is a research topic. Over the lifetime, 1248 publications have been published within this topic receiving 22355 citations.


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Journal ArticleDOI
TL;DR: A new class of sequential generalized likelihood ratio tests for evaluating adverse event rates in two-armed pre-licensure clinical trials and single-armed post-licensing studies is proposed.
Abstract: The evaluation of vaccine safety involves pre-clinical animal studies, pre-licensure randomized clinical trials, and post-licensure safety studies. Sequential design and analysis are of particular interest because they allow early termination of the trial or quick detection that the vaccine exceeds a prescribed bound on the adverse event rate. After a review of the recent developments in this area, we propose a new class of sequential generalized likelihood ratio tests for evaluating adverse event rates in two-armed pre-licensure clinical trials and single-armed post-licensure studies. The proposed approach is illustrated using data from the Rotavirus Efficacy and Safety Trial. Simulation studies of the performance of the proposed approach and other methods are also given.

40 citations

Journal ArticleDOI
TL;DR: It was desired to see what could be expected if an estimate of the variance replaced the variance in this test, and so obtain an indication of what might result for a test in which the variance was replaced by an estimate.
Abstract: known, has been given by Wald (1945) It was desired to see what could be expected if an estimate of the variance replaced the variance in this test The performance characteristics of Wald's test are expressed in terms of certain inequalities It was therefore decided first to examine these by means of a large-scale sampling experiment, and so obtain an indication of what might result for a test in which the variance was replaced by an estimate This experiment was designed under the guidance of Dr H 0 Hartley, and the results are discussed in ? 3 The three points investigated are: (i) the accuracy of the first and second types of error, (ii) the distribution of the number of samples necessary to reach a decision and (iii) the effects of truncation The results obtained are described below and are consistent with Wald's theory Wald (1945) and Barnard (1946, 1950) give sequential tests for discriminating between means when o is unknown Armitage (1947) compares the first and second of these tests, giving the results of their application to sixty samples In a later paper it is hoped to give the results of further sampling experiments on all these tests, together with the results for a new test which is discussed in ? 4 The three tests referred to above for the case where o- is unknown are none of them altogether satisfactory, since they are unsymmetrical in Ito and atl Also they differentiate between means of #o and It1 = dto + &r, where o is unknown

39 citations

Journal ArticleDOI
TL;DR: In this paper, the rank-order sequential probability ratio test is examined and the stopping time has a finite moment generating function under a mild condition on the bivariate random variables which resembles the Stein-condition.
Abstract: We are motivated by Stein's proof (Stein (1946), Wald (1947), pages 157-158) of the termination of a sequential probability ratio test in the case of independent and identically distributed random variables. Extending his ideas to take certain "dependencies" into account we examine the rank-order sequential probability ratio test based on a Lehmann alternative studied in a paper with the above title by I. R. Savage and the author (1966) (referred to as SS I in the rest of this paper). We prove that this test terminates with probability one and that the stopping time has a finite moment generating function under a very mild condition on the bivariate random variables which resembles the Stein-condition, namely that a certain random variable $V(X_1, Y_1)$, defined in (32), is not identically equal to 0. Finally the asymptotic normality of the logarithm of the likelihood ratio of the rank order is established using the well-known Chernoff-Savage Theorem.

39 citations

Journal ArticleDOI
TL;DR: Specific early termination procedures have been developed to allow repeated statistical analyses to be performed on accumulating data and stop the trial as soon as the information is sufficient to conclude.
Abstract: Comparative clinical trials are performed to assess whether a new treatment has superior efficacy than a placebo or a standard treatment (one-sided formulation) or whether two active treatments have different efficacies (two-sided formulation) in a given population. The reference approach is the single-stage design and the statistical test is performed after inclusion and evaluation of a predetermined sample size. In practice, the single-stage design is sometimes difficult to implement because of ethical concerns and/or economic reasons. Thus, specific early termination procedures have been developed to allow repeated statistical analyses to be performed on accumulating data and stop the trial as soon as the information is sufficient to conclude. Two main different approaches can be used. The first one is derived from strictly sequential methods and includes the sequential probability ratio test and the triangular test. The second one is derived from group sequential designs and includes Peto, Pocock, and O'Brien and Fleming methods, alpha and beta spending functions, and one-parameter boundaries. We review all these methods and describe the bases on which they rely as well as their statistical properties. We also compare these methods and comment on their advantages and drawbacks. We present software packages which are available for the planning, monitoring and analysis of comparative clinical trials with these methods and discuss the practical problems encountered when using them. The latest versions of all these methods can offer substantial sample size reductions when compared with the single-stage design not only in the case of clear efficacy but also in the case of complete lack of efficacy of the new treatment. The software packages make their use quite simple. However, it has to be stressed that using these methods requires efficient logistics with real-time data monitoring and, apart from survival studies or long-term clinical trials with censored endpoints, is most appropriate when the endpoint is obtained quickly when compared with the recruitment rate.

39 citations

Journal ArticleDOI
01 Jan 1992
TL;DR: Bayesian analysis is used to show that Wald's sequential probability ratio test with varying thresholds is optimal for the nonstationary situation, where the observed samples are independent but not identically distributed.
Abstract: Bayesian analysis is used to show that Wald's sequential probability ratio test with varying thresholds is optimal for the nonstationary situation, where the observed samples are independent but not identically distributed. Some important properties useful for the design of the test thresholds are discussed. Wald's lower bound, generalized to the nonstationary situation, is also presented. The results have important applications in situations where the observed signal is time-varying. such as in radar signal processing, image processing, and spread spectrum communications. >

38 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20236
202223
202129
202023
201929
201832