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.

Continuous and group sequential conditional probability ratio tests for phase II clinical trials.

Abstract: We present continuous and group sequential designs for phase II clinical trials based on the sequential conditional probability ratio test (SCPRT). The SCPRT is derived from a conditional likelihood ratio, where the conditioning is on what the corresponding (reference) fixed sample size test (RFSST) would achieve. In other words, we obtain the sequential design by controlling the maximum probability that the SCPRT does not agree with the RFSST. We shall discuss the difference between SCPRT and stochastic curtailment which also uses the concept of conditional distribution. We show that the power function of the SCPRT is virtually the same as that of the RFSST and its average sample numbers (ASNs) are close to those of Wald's sequential probability ratio test (SPRT), whereas its maximum sample size is no greater than that of the RFSST. Thus the SCPRT has all the desirable properties, such as allowing the use of the RFSST at the last analysis, of the Fleming procedure for phase II trials. The SCPRT, however, preserves the power function of the RFSST better and gives us the option for continuous monitoring. Our recommendation, therefore, is to use a group SCPRT boundary (for interim analyses performed as scheduled) embedded in a continuous SCPRT boundary (for unplanned interim analyses and analyses at times based on data trends). We provide as well a bias-adjusted estimator of the success rate after sequential stopping. We illustrate the method with several examples. The method applies to any single-arm clinical trial with binary endpoints, such as the classic paired design.

Complete Classes for Sequential Tests of Hypotheses

Abstract: We consider problems of sequential testing when the loss function is the sum of a component due to an error in the terminal decision and a cost of observation component. In all cases we establish a characterization of a complete class or an essentially complete class. In order to obtain such results for testing a null hypothesis against an alternative hypothesis we establish complete class results for testing the closure of the null hypothesis against the closure of the alternative hypothesis. A complete class for testing closure of null against closure of alternative is an essentially complete class for testing null against alternative. Furthermore, a complete class for testing closure of null against closure of alternative is a complete class for testing null against alternative when the risks have certain continuity properties. Such continuity properties do hold in many cases. Three models are treated. The first is when the closure of the null space is compact and the cost of the first observation is positive. Under very unrestrictive conditions it is shown that the Bayes tests form a complete class. This result differs considerably from most fixed sample analogues that have been studied. The second model is when the closure of the null space is compact, the distributions are exponential family, and the cost of the first observation is zero. The third model is for the one dimensional exponential family case when the hypotheses are one sided.

An optimal property of the repeated significance test.

Abstract: We consider the problem of testing the sign of the drift θ of a Brownian motion. As in the preceding section we let the costs depend on the underlying parameter and choose it as “cθ2”, c>0. We show that a certain simple Bayes rule, which defines a repeated significance test, is optimal for the testing problem in a Bayes sense. The simple Bayes rules stop sampling when the posterior mass of the hypothesis or the alternative is too small.

SPRINT Multi-Objective Model Racing

Abstract: Multi-objective model selection, which is an important aspect of Machine Learning, refers to the problem of identifying a set of Pareto optimal models from a given ensemble of models. This paper proposes SPRINT-Race, a multi-objective racing algorithm based on the Sequential Probability Ratio Test with an Indifference Zone. In SPRINT-Race, a non-parametric ternary-decision sequential analogue of the sign test is adopted to identify pair-wise dominance and non-dominance relationship. In addition, a Bonferroni approach is employed to control the overall probability of any erroneous decisions. In the fixed confidence setting, SPRINT-Race tries to minimize the computational effort needed to achieve a predefined confidence about the quality of the returned models. The efficiency of SPRINT-Race is analyzed on artificially-constructed multi-objective model selection problems with known ground-truth. Moreover, SPRINT-Race is applied to identifying the Pareto optimal parameter settings of Ant Colony Optimization algorithms in the context of solving Traveling Salesman Problems. The experimental results confirm the advantages of SPRINT-Race for multi-objective model selection.