Unbalanced and Partial Group Sequential Methods for Normal Responses in Clinical Trials

Abstract

Group sequential methods for a two-treatment clinical trial with normal responses are discussed. First we consider the case where the sample sizes for two treatments are possibly unequal between the treatments due to an unequal randomization. Then we discuss group sequential design in the context of a historical control study, that is, under the partial sequential sampling scheme, in which the samples on one treatment, say control, are available at the outset, and the samples on the other treatment, say experimental, are obtained in the group sequential way. We discuss the cases of known and unknown variance for both unbalanced and partial group sequential setups. All of the procedures are discussed with numerical studies.     

U-Statistics in Sequential Tests and Change Detection

Abstract

Research on U-statistics within the general framework of sequential and change-point literature is surveyed. Some recent developments are discussed and extended. New sequential testing strategies based on Wiener process approximations are proposed, and empirical studies explore the finite sample performance of these tests. It allows users to choose one that is appropriate for their application.     

Sequential Detection of Change-Points in Linear Models

Abstract

A new method for sequential detection of change-points in multivariate linear models is proposed. The main performance characteristics of this method are analyzed theoretically for finite sample volumes. Comparison with other well known methods for sequential detection of structural changes in linear models is carried out via Monte Carlo tests. Practical applications for the analysis of stability of the German quarterly model of demand for money (1961–1995) and the Russian monthly model of inflation (1994–2005) are considered.     

Minimax Methods for Multihypothesis Sequential Testing and Change-Point Detection Problems

Abstract

In this paper a unified methodological approach to sequential testing of many composite hypotheses and multi-decision change-point detection for composite alternatives is proposed. New performance measures for methods of hypotheses testing and change-point detection are introduced. Theoretical lower bounds for these performance measures are proved that do not depend on methods of sequential testing and detection. Minimax tests are proposed for which these lower bounds are attained asympototically as decision thresholds tend to infinity. Results of Monte Carlo experiments are given.     

On locally most powerful sequential rank tests

Sequential ranks are defined as ranks of such observations, which have been observed so far in a sequential design. This article studies hypotheses tests based on sequential ranks for different situations. The locally most powerful sequential rank test is derived for the hypothesis of randomness against a general alternative, including the two-sample difference in location or regression in location as special cases for the alternative hypothesis. Further, the locally most powerful sequential rank tests are derived for the one-sample problem and for independence of two samples in an analogous spirit as the classical results of Hájek and ?idák (1967 Hájek, J. and ?idák, Z. (1967). Theory of Rank Tests, Prague: Academia. [Google Scholar]) for (classical) ranks. The locally most powerful tests are derived for a fixed sample size and the results bring arguments in favor of existing tests. In addition, we propose a sequential testing procedure based on these statistics of the locally most powerful tests. Principles of such sequential testing are explained on the two-sample Wilcoxon test based on sequential ranks.     

Optimal Sequential Tests for Two Simple Hypotheses

Abstract

A general problem of testing two simple hypotheses about the distribution of a discrete-time stochastic process is considered. The main goal is to minimize an average sample number over all sequential tests whose error probabilities do not exceed some prescribed levels. As a criterion of minimization, the average sample number under a third hypothesis is used (modified Kiefer–Weiss problem). For a class of sequential testing problems, the structure of optimal sequential tests is characterized. An application to the Kiefer–Weiss problem for discrete-time stochastic processes is proposed. As another application, the structure of Bayes sequential tests for two composite hypotheses, with a fixed cost per observation, is given. The results are also applied for finding optimal sequential tests for discrete-time Markov processes. In a particular case of testing two simple hypotheses about a location parameter of an autoregressive process of order 1, it is shown that the sequential probability ratio test has the Wald–Wolfowitz optimality property.     

A Linear Programming Approach to Sequential Hypothesis Testing

Abstract

Under some mild Markov assumptions it is shown that the problem of designing optimal sequential tests for two simple hypotheses can be formulated as a linear program. This result is derived by investigating the Lagrangian dual of the sequential testing problem, which is an unconstrained optimal stopping problem depending on two unknown Lagrangian multipliers. It is shown that the derivative of the optimal cost function, with respect to these multipliers, coincides with the error probabilities of the corresponding sequential test. This property is used to formulate an optimization problem that is jointly linear in the cost function and the Lagrangian multipliers and can be solved for both with off-the-shelf algorithms. To illustrate the procedure, optimal sequential tests for Gaussian random sequences with different dependency structures are derived, including the Gaussian AR(1) process.     

Asymptotically Optimal Methods of Early Change-Point Detection

Abstract

Based on the excellent review and numerical study presented by Professor T. N. Sriram and Professor R. Iaci, another sequential problem for autoregressive processes is discussed.     

Construction of an Optimal Sequential Plan for Testing a Treatment for an Adverse Effect

Abstract

Classical sequential procedures that collect a single observation at a time are often found impractical, expensive, and time consuming. Sequentially planned procedures, or simply sequential plans, extend and generalize the concepts of sequential analysis by allowing observations to be collected in groups of variable sizes. After every group, all of the previously collected data are used to determine the next course of action. An optimal (Bayes) sequential plan minimizes the (Bayes) risk function that combines the decision loss, observation (variable) cost, and group (fixed) cost. In general, determining the optimal sequential plan remains an open and challenging problem mainly because it requires risk optimization over a huge and rather unstructured set of all sequential plans. This article demonstrates how to obtain the optimal solution for a particular class of problems that may arise in testing a treatment for a rare but severe adverse effect. This solution is obtained by studying a number of properties of the Bayes sequential plan such as transitivity and monotonicity. This allows one to reduce the search to a small, manageable set of sequential plans within which the optimal plan can be calculated.     

Behaviour of environmentally degraded epoxy adhesives as a function of temperature

ABSTRACT

Structural adhesives are increasingly being used in the aerospace and automotive industries. They allow for light weight vehicles, fuel savings, and reduced emissions. However, the environmental degradation of adhesive joints is a major setback in its wide implementation. Moisture degradation of adhesive joints includes plasticization, attacking of the interface, swelling of the adhesive and consequent creation of residual stresses. This may lead to reversible and irreversible damage. The main factors affecting the strength of adhesive joints under high and low temperatures are the degradation of the adhesive mechanical properties and the creation of residual stresses induced by different coefficients of thermal expansion (between the adhesive and the adherends). The effect of the combined effect of moisture and temperature is not yet fully understood. The aim of this study is to shed light on this subject.

In this work bulk water absorption tests were conducted at different moisture conditions in order to assess the diffusion coefficient, maximum water uptake, and glass transition temperature. Aged and unaged small dogbone tensile specimens were tested under different temperature conditions. The glass transition temperature of the adhesives as a function of the water uptake was assessed. The aim is to determine the evolution of the properties of two epoxy adhesives as a function of two variables (environmental temperature and moisture).     

Design of Group Sequential Clinical Trials with Ordinal Categorical Data Based on the Mann–Whitney–Wilcoxon Test

Abstract

In this paper, methodology necessary do design group sequential trials based on ordinal categorical data based on the Mann–Whitney–Wilcoxon test is presented and illustrated in two practical examples. Curtailment for futility is an important component in improving the performance of the methods in terms of expected sample sizes under the null hypothesis. Simulation can also be employed to verify the asymptotic properties claimed by the method, and if necessary be used to tweak the design to better approximate the desired operating characteristics.     

Nonparametric Partial Sequential Tests for Patterned Alternatives in Multisample Problems

Abstract

In the present work we develop partial sequential nonparametric tests for multiple comparison. We provide tests for the identity of several unknown univariate continuous distribution functions against patterned alternatives. Our tests are based on Wilcoxon score. We conduct some Monte Carlo studies related to the proposed tests. We carry out a detailed comparison between the proposed procedures and the corresponding nonsequential procedures. We register significant gain in sample size through the proposed procedure, maintaining almost the same level and power for both the tests. We perform an analysis of life data arising out of a geological survey related to arsenic contamination. We also present some asymptotics in this context.     

Study of Optimal Adaptive Rule in Testing Composite Hypothesis

Abstract

In this article on sequential adaptive testing, we have studied the optimal allocation between two populations for testing a composite hypothesis involving the parameters, with the goal of decreasing allocation of one of the treatments to the order of the logarithm of the sample size while decreasing the probability of incorrect selection to zero. We have proved the result for large sample sizes both mathematically and by simulation studies.     

The Contributions of Robert A. Wijsman to Sequential Analysis

Abstract

Robert A. Wijsman made fundamental contributions to the field of sequential analysis, especially in the area of invariant sequential tests and exponential boundedness of stopping times. This article provides an overview of the main themes and ideas of this impressive body of work, along with some personal remembrances from family members and colleagues.     

Test methods for bond strength of glass fiber posts to dentin: A review

ABSTRACT

In this paper, a review of the test methods for bond strength of glass fiber posts to dentin is presented. The main variables that influence the bond strength tests are related to substrate, to specimen properties, specimen preparation, and test methodology. The impact of these variables on the test outcome is analyzed. The search was performed on studies published between 2007 and 2015. Most of the tests carried out, in the literature, were the push-out (75%), pull-out (13%), and microtensile (11.9%) tests, showing an inversion compared to the results found in studies published between 2005 and 2010, when push-out test was used in a proportion of 2% and microtensile test in a proportion of 67%. The push-out test emerged as a practical tool for evaluating the interfacial shear strength between fiber post and root canal walls.     

Sequential Change-Point Detection and Estimation

Abstract

Two groups of sequential testing procedures are proposed to detect an abrupt change in the distribution of a sequence of observations: truncated and open ended. They are based on large sample strong approximations of the efficient score vector under the null hypothesis of no change and under the alternative hypothesis. An estimator of the time of change is proposed and its approximate bias is analyzed. The estimation of the new parameters that describe the changed distribution naturally follows.     

Bootstrapping Sequential Change-Point Tests

Abstract

In this article we propose some bootstrapping methods to obtain critical values for sequential change-point tests. We consider a change in the mean with i.i.d. errors. Theoretical results show the asymptotic validity of the proposed bootstrap procedures. A simulation study compares the bootstrap and the asymptotic tests and shows that the studentized bootstrap test behave generally better than asymptotic tests if measured by α- resp. β-errors and its run length.     

Distribution theory of group sequential t,χ2and F-tests for general linear models

We derive the joint distribution of the sequence of estimates of the parameter vector θ in a normal general linear model when data accumulate over a series of analyses. This seclllerlce of estimates has a remarkably simple covariance structure, even when observations are correlated, allowing standard group sequential tests to be applied in very general settings. If observations variaices and covariances depend on an unknown scale factor σ², the joint distribution of the sequence of estimates of θ σ² has a simple form. again even in the case of correlated observations. From these results, we establish a general treatment of group sequential t,χ²and F-tests.     

A Sequential and Iterative Testing Procedure to Identify the Nature of a Time Series Generating Process

Abstract

An inferential approach is proposed to identify the nature of the generating process corresponding to a real time series. This new sequential and iterative testing procedure goes beyond the Box and Jenkins methodology for the identification, estimation, and validation of linear data generating processes by investigating the probabilistic structure of non-Gaussian estimated residuals {? _t } for the possible presence of nonlinear serial dependence. The testing procedure aims at indicating the right type of dependence present in a series by means of specific inferential tests on the moments of the generating structure probability distribution. The test statistics adopted are very popular and powerful and encompass a wide range of stochastic nonlinearity alternatives. The U.S. Industrial Production Index series is used to illustrate the iterative testing procedure proposed.     

Authors' Response

Abstract

This article contains our responses to the eight discussion pieces written by experts, commenting on the results presented in Sriram and Iaci (2014). The majority of the discussants described complementary sequential problems arising in time series and other models involving dependent data, while two of the discussants provided thoughtful views on the phenomenon of negative regret investigated in our article. Prompted by an excellent observation made in one of the discussion pieces, we have attempted to shed further light on the phenomenon of negative regret in the context of sequential estimation of the autoregressive parameter.