The Fifth International Workshop in Sequential Methodologies 2015

Consider multi-stream data and the problem of detecting sequentially that at an unknown time in the past, a small fraction of the data-streams has undergone a change in distribution. There have been a lot of detailed investigation on this, and influential works include Tartakovsky & Veeravalli (2008), Mei (2010) and Xie & Siegmund (2013). In particular Xie & Siegmund (2013) paid attention to designing tests that down-weight the contributions of data-streams that do not undergo change of distribution, so that the signal contributions are not drowned out by the noise. We consider score-based test statistics similar to that suggested in Xie & Siegmund (2013). However unlike in Xie & Siegmund (2013), our score is motivated by a limit of detectability argument rather than on supposed distribution changes. That is we first determine what strength (and fraction) of signals are not detectable, and then aim to do as well as possible on the boundary of the detectable region. We show that our tests achieve minimum detection delay under the usual average run length constraint, extending the optimality results of Moustakides (1986) to multi-stream data. We discuss various extensions of our score-based tests, for example the use of window-limited and geometric-sized windows, as suggested in Lai (1995), to reduce the computational burden. We consider the situations of non-normal data and signal strengths/frequencies that are not uniform across data-streams. We also consider how Mei’s sum of CUSUM test, which can work well when change of distributions do not occur simultaneously across data-stream, can be modified via an appropriate score function that down-weights the contributions from data-streams that did not go through change in distributions. Monday morning, June 22 [11:00 12:30] Tests and Estimation Organizer: Nitis Mukhopadhyay, University of Connecticut Chair: Seyed Yaser Samadi, Southern Illinois University Title: Empirical Likelihood Based Detection Procedure for Change Point in Mean Residual Life Functions under Random Censorship Speaker: Wei Ning, Bowling Green State University Abstract: Mean residual life function is an important function in survival analysis which describes the expected remaining lifetime given survival time up to a certain age. In this talk, I will propose a nonparametric method based on empirical likelihood to test the change point of mean residual life functions of independent random variables. Monte Carlo Simulations under different lifetime settings are carried out to show the power performance. Two real data examples are analyzed to illustrate the testing procedure. Mean residual life function is an important function in survival analysis which describes the expected remaining lifetime given survival time up to a certain age. In this talk, I will propose a nonparametric method based on empirical likelihood to test the change point of mean residual life functions of independent random variables. Monte Carlo Simulations under different lifetime settings are carried out to show the power performance. Two real data examples are analyzed to illustrate the testing procedure. Title: Confidence Interval Estimation Following SPRT in a Normal Distribution with Equal Mean and Variance Speaker: Debanjan Bhattacharjee, Utah Valley University Abstract: Confidence interval estimation following a sequential probability ratio test (SPRT) is an important and difficult problem (Siegmund 1978,1985). Considerable difficulties arise because following termination of SPRT, the customary estimator of an unknown parameter of interest, obtained from the randomly stopped sample (Anscombe 1952), is usually biased. As a result, the coverage probability of a naive confidence interval for the parameter based on the randomly stopped version of the customary estimator often falls below the target confidencecoefficient. In this article, we have addressed this problem for a normal distribution with equal mean and variance. Refer to Bhattacharjee and Mukhopadhyay (2011, 2012). This Confidence interval estimation following a sequential probability ratio test (SPRT) is an important and difficult problem (Siegmund 1978,1985). Considerable difficulties arise because following termination of SPRT, the customary estimator of an unknown parameter of interest, obtained from the randomly stopped sample (Anscombe 1952), is usually biased. As a result, the coverage probability of a naive confidence interval for the parameter based on the randomly stopped version of the customary estimator often falls below the target confidencecoefficient. In this article, we have addressed this problem for a normal distribution with equal mean and variance. Refer to Bhattacharjee and Mukhopadhyay (2011, 2012). This problem is different from the confidence interval estimation for mean in a normal distribution where the mean and the variance are not explicitly related to each other (Siegmund 1978). We propose a methodology essentially based on the random central limit theorem due to Anscombe (1952) which is remarkably easier to implement than Siegmund’s original methodology. We explore bias corrections and resulting more accurate variance estimation in order to come up with practically useful and easily implementable methodologies to deliver achieved coverage probability that is very close to the nominal goal. Title: Composite Sequential Monte Carlo Test for PostMarket Vaccine Safety Surveillance Speaker: Ivair Silva, Federal University of Ouro Preto Abstract: Group sequential hypothesis testing is now widely used to analyze prospective data. If Monte Carlo simulation is used to construct the signaling threshold, the challenge is how to manage the Type I error probability for each one of the multiple tests without losing control on the overall significance level. This paper introduces a valid method for a true management of the alpha spending at each one of a sequence of Monte Carlo tests. The method also enables the use of a sequential simulation strategy for each Monte Carlo test, which is useful for saving computational execution time. Thus, the proposed procedure allows for sequential Monte Carlo test in sequential analysis, and this is the reason why it is called composite sequential test. An upper bound for the potential power losses from the proposed method is deduced. The composite sequential design is illustrated through an application for post-market vaccine safety surveillance data. Group sequential hypothesis testing is now widely used to analyze prospective data. If Monte Carlo simulation is used to construct the signaling threshold, the challenge is how to manage the Type I error probability for each one of the multiple tests without losing control on the overall significance level. This paper introduces a valid method for a true management of the alpha spending at each one of a sequence of Monte Carlo tests. The method also enables the use of a sequential simulation strategy for each Monte Carlo test, which is useful for saving computational execution time. Thus, the proposed procedure allows for sequential Monte Carlo test in sequential analysis, and this is the reason why it is called composite sequential test. An upper bound for the potential power losses from the proposed method is deduced. The composite sequential design is illustrated through an application for post-market vaccine safety surveillance data. Acknowledgement: This research was funded by the National Institute of General Medical Sciences, grant #RO1GM108999, by Conselho Nacional de Desenvolvimento Cient́ıfico e Tecnológico(CNPq), Brazil, and by Fundação de Amparo á Pesquisa do Estado de Minas Gerais (FAPEMIG). Monday morning, June 22 [11:00 12:30] Sequential Designs in Drug Development Organizer: Vladimir Dragalin, Johnson & Johnson Chair: Vladimir Dragalin, Johnson & Johnson Title: Dose Expansion Cohorts in Phase I Trials Speaker: Alexia Iasonos, Memorial Sloan Kettering Cancer Center