Sequential Testing Procedure Research Articles

Sufficient cointegration and Wald tests of the monetary transmission mechanism

This letter re-examines the role of commercial loans versus demand deposits in the monetary transmission mechanism using short-run and long-run sequential causality testing procedures designed by Toda and Phillips. Empirical results support the credit view that bank loans are as good a predictor of income as demand deposits.

Optimization of testing times and critical values in sequential equivalence testing

In long-term clinical trials, interim analyses are planned to reduce the number of patients needed. To meet this issue in a practical way, group sequential designs are used. Most of these trials are conducted with the objective of demonstrating differences in efficacy of treatments, for example, to show superiority of a new drug or experimental treatment to a control. However, an increasing number of trials are designed to establish equivalence in efficacy or bioequivalence. This paper deals with group sequential test procedures in two-sided equivalence trials. Optimized designs with respect to sample size behaviour are constructed. Tables containing optimal testing times and corresponding optimal critical values or values to construct an underlying alpha-spending function, respectively, are provided. An example illustrates their use when planning interim analyses in equivalence trials.

Optimization of testing times and critical values in sequential equivalence testing

In long-term clinical trials, interim analyses are planned to reduce the number of patients needed. To meet this issue in a practical way, group sequential designs are used. Most of these trials are conducted with the objective of demonstrating differences in efficacy of treatments, for example, to show superiority of a new drug or experimental treatment to a control. However, an increasing number of trials are designed to establish equivalence in efficacy or bioequivalence. This paper deals with group sequential test procedures in two-sided equivalence trials. Optimized designs with respect to sample size behaviour are constructed. Tables containing optimal testing times and corresponding optimal critical values or values to construct an underlying α-spending function, respectively, are provided. An example illustrates their use when planning interim analyses in equivalence trials. Copyright © 1999 John Wiley & Sons, Ltd.

Sequential monitoring of low event rates: an application in environmental epidemiology

A sequential testing procedure for monitoring epidemiological data is considered. The approach is based on a discrete time process of interim analyses using the likelihood ratio as a test statistic. Sampling continues until either some predetermined practical time limit is reached or a decision can be made about the hazard rates characterizing the populations to be compared. The stopping boundaries of the sequential testing procedure are determined so as to control type I error at a given level during the whole study. Thus, the critical threshold is derived from the exact distribution of the maximum value of the test statistic which is observed across all the monitoring times. To this end, the appropriate quantiles in the probability distributions of interest are obtained empirically by Monte Carlo simulation, assuming both the null hypothesis and given experimental conditions. The method is illustrated by an example concerning the incidence of leukaemia in young people living in the vicinity of the French La Hague nuclear reprocessing plant. On the whole the previous analyses do not provide evidence for a spatial–temporal clustering of leukaemia, at least within the space–time window which was examined around the nuclear reprocessing plant (35 km radius, time period 1978–1992). Copyright © 1999 John Wiley & Sons, Ltd.

Group Sequential Monitoring with Arbitrary Inspection Times

The classical group sequential test procedures that were proposed by Pocock (1977) and O'Brien and Fleming (1979) rest on the assumption of equal sample sizes between the interim analyses. Regarding this it is well known that for most situations there is not a great amount of additional Type I error if monitoring is performed for unequal sample sizes between the stages. In some cases, however, problems can arise resulting in an unacceptable liberal behavior of the test procedure. In this article worst case scenarios in sample size imbalancements between the inspection times are considered. Exact critical values for the Pocock and the O'Brien and Fleming group sequential designs are derived for arbitrary and for varying but bounded sample sizes. The approach represents a reasonable alternative to the flexible method that is based on the Type I error rate spending function. The SAS syntax for performing the calculations is provided. Using these procedures, the inspection times or the sample sizes in the consecutive stages need to be chosen independently of the data observed so far.

On Testing for the Number of Components in a Mixed Poisson Model

Poisson mixtures are usually used to describe overdispersed data. Finite Poisson mixtures are used in many practical situations where often it is of interest to determine the number of components in the mixture. Identifying how many components comprise a mixture remains a difficult problem. The likelihood ratio test (LRT) is a general statistical procedure to use. Unfortunately, a number of specific problems arise and the classical theory fails to hold. In this paper a new procedure is proposed that is based on testing whether a new component can be added to a finite Poisson mixture which eventually leads to the number of components in the mixture. It is a sequential testing procedure based on the well known LRT that utilises a resampling technique to construct the distribution of the test statistic. The application of the procedure to real data reveals some interesting features of the distribution of the test statistic.

Policy regime changes and the long-run sustainability of fiscal policy: an application to Greece

This paper questions the widespread practice of assessing the hypothesis of long-run fiscal policy sustainability by means of conventional unit-root tests that do not allow for the possible impact of regime shifts. Using the Greek economy as a model case, the Zivot-Andrews sequential integratibility testing procedure which allows for the endogenous determination of possible regime changes is deployed to this end. The empirical evidence reached supports strongly the failure of the Greek government to satisfy intertemporal budget balance in the long-run and identifies as the cause of this failure a deterministic policy regime shift taking place in 1979.

The impact of the character of natural organic matter in conventional treatment with alum

The objective of this study was to determine if the removal of NOM in reservoir waters in conventional treatment with alum is limited by the character of the NOM. A sequential jar test procedure, which included five treatment steps was employed to study the character of the NOM which could not be removed by flocculation/sedimentation. The NOM in the raw and treated waters was characterised by techniques including dissolved organic carbon (DOC), UV absorbance (UVA), high performance size exclusion chromatography (HPSEC), pyrolysis-gas chromatography-mass spectrometry (Py-GC-MS) and diffuse reflectance Fourier transform infrared spectroscopy (DRIFT). HPSEC analysis of the reservoir waters from three sources indicated that the organic fraction remaining after alum treatment was of lower molecular weight than that in the original raw waters. Pyrolysis of freeze dried material (FDM) from one raw water source (Hope Valley Reservoir) and following treatment with a high alum dose at pH 5 (coagulated and non coagulated material) gave by-products that indicated the presence of proteins, polyhydroxyaromatics and polysaccharides.

Multihypothesis sequential probability ratio tests .I. Asymptotic optimality

The problem of sequential testing of multiple hypotheses is considered, and two candidate sequential test procedures are studied. Both tests are multihypothesis versions of the binary sequential probability ratio test (SPRT), and are referred to as MSPRTs. The first test is motivated by Bayesian optimality arguments, while the second corresponds to a generalized likelihood ratio test. It is shown that both MSPRTs are asymptotically optimal relative not only to the expected sample size but also to any positive moment of the stopping time distribution, when the error probabilities or, more generally, risks associated with incorrect decisions are small. The results are first derived for the discrete-time case of independent and identically distributed (i.i.d.) observations and simple hypotheses. They are then extended to general, possibly continuous-time, statistical models that may include correlated and nonhomogeneous observation processes. It also demonstrated that the results can be extended to hypothesis testing problems with nuisance parameters, where the composite hypotheses, due to nuisance parameters, can be reduced to simple ones by using the principle of invariance. These results provide a complete generalization of the results given by Veeravalli and Baum (see ibid., vol.41, p.1994-97, 1995), where it was shown that the quasi-Bayesian MSPRT is asymptotically efficient with respect to the expected sample size for i.i.d. observations.

Local sequential testing procedures in a normal mixture model

For the simple normal mixture model with density function , either one of the following three null hypotheses: (i) and (iii) H 0: θ = 0 can be used to test for homogeneity. In this paper, the local sequential likelihood ratio tests are considered and their operating characteristics are investigated. The results show that the test developed under (iii) performs better. Concluding remarks on alternative sequential tests and one-sided case with 0 ≤ < ∞ are also made.

A discrete time sequential process for analyzing censored survival data using the likelihood ratio

A sequential testing procedure for comparing survival distributions with binary responses is considered. The data are monitored according to a discrete time process of reviewing the situation at regularly spaced intervals of time by using the likelihood ratio as a test statistic. Sampling continues until either a decision can be made about the hazard rates characterizing the survival distributions to be compared or a prespecified time limit is reached. Monte Carlo simulations are used to model and estimate the power of the process. More specifically, the critical threshold which allows one to control type-I error at a given level during the whole testing procedure is also determined empirically by simulation. Particular attention is paid to the gain of efficiency resulting from the sequential approach. The better understanding of the relative incidence of the parameters defining the experimental conditions on the power of the process is shown to be helpful in planning a proper experimental design for a wide range of comparative studies (e.g. clinical trials, environmental health studies). Two examples referring to survival data of couples trying to begin a pregnancy and patients with bladder cancer, including environmental or technical factors, are presented as an illustration.

Assessing Measurement Invariance in Cross‐National Consumer Research

Assessing the applicability of frameworks developed in one country to other countries is an important step in establishing the generalizability of consumer behavior theories. In order for such comparisons to be meaningful, however, the instruments used to measure the theoretical constructs of interest have to exhibit adequate cross-national equivalence. We review the various forms of measurement invariance that have been proposed in the literature, organize them into a coherent conceptual framework that ties different requirements of measure equivalence to the goals of the research, and propose a practical, sequential testing procedure for assessing measurement invariance in cross-national consumer research. The approach is based on multisample confirmatory factor analysis and clarifies under what conditions meaningful comparisons of construct conceptualizations, construct means, and relationships between constructs are possible. An empirical application dealing with the single-factor construct of consumer ethnocentrism in Belgium, Great Britain, and Greece is provided to illustrate the procedure.

A sequential testing procedure for outliers and structural change

In this paper a test for outliers based on externally studentized residuals is shown to be related to a test for predictive failure. The relationships between a test for outliers, a test for a correlated mean shift and a test for an intercept shift are developed. A sequential testing procedure for outliers and structural change is shown to be independent, so that the overall size of the joint test can be determined exactly. It is established that a joint test for outliers and constancy of variances cannot be performed.

Do Japanese banks lead or follow international business? An empirical investigation

Although many precedent studies analyze the factors that promote the internationalization of banks, we have no empirical evidence answering the question as to whether banks follow or lead the manufacturing industries. In this paper, we investigate empirically whether Japanese banks are leaders or followers of the manufacturing industries in the process of internationalization. Using the Granger causality test based on Hsiao's (Hsiao, 1979, 1981) sequential test procedures, we find that Japanese banks have led Japanese manufacturing industries in the process of internationalization in Asia and Oceania and that banks have followed the manufacturing industries in the Near East. Furthermore, there is no clear causality in North America and Europe. The banks' leadership in Asia and Oceania seems to demonstrate that Japanese banks have comparative advantage against host-country competitors in these regions, while Japanese banks seem to enter US or European financial centers in order to avoid domestic regulations.

Estimating and reducing bias in group sequential designs with Gaussian independent increment structure

A concern in the use of sequential testing procedures is the bias associated with the estimates of treatment differences. Clinical trials that stop early because of evidence of therapeutic benefit are prone to exaggerate the magnitude of the treatment effect. We consider methods for estimating and reducing the bias of treatment differences estimators in group sequential designs with Gaussian independent increment structure. We derive an analytical expression for the bias and give an easy-to-calculate approximate bound for its variation. A simulation estimate of the bias, based on a Gaussian independent increment structure, is also described and a related bias reduced estimator is considered.

Transient detection with an application to a chemical process

We propose a sequential test procedure for transient detections in a stochastic process which can be expressed as an autoregressive moving average (ARMA) model. Preliminary analysis shows that if an ARMA( p, q) time series exhibits a transient behavior, then its residuals behave as an ARMA( Q, Q) process, where Q ≤ p + q. Based on this fact, we derive a new sequential test to determine when a transient behavior occurs in a given ARMA time series. Simulation experiments conducted in this study show that the proposed test can detect the occurrence of a transient in the ARMA model. We also apply the proposed method to detect transient changes in the pH of an erythromycin salt.

The remediation of clumsiness. I: An evaluation of Laszlo's kinaesthetic approach.

The effectiveness of a kinaesthetic training programme proposed by Laszlo for children with movement difficulties was evaluated by comparing two groups of 10 'clumsy' children matched pairwise on age, IQ and sex as well as degree of kinaesthetic and motor impairment. Tests of kinaesthetic ability, using the Parameter Estimation by Sequential Testing (PEST) procedure, and motor competence administered before and after treatment revealed an improvement in both groups on all measures but no differential effect of the training programme. Immediately after training, the changes we obtained in motor performance were confined to balance skills but, at follow up, 3 months later, changes in manual and ball skills were also evident. This unusual pattern of change requires replication. Our findings forced us to consider the possibility that any effect of Laszlo's recommended training programme had been obscured by our use of the PEST procedure, which had in itself facilitated motor learning.

The incidence of chrysanthemum stunt viroid and chrysanthemum B carlavirus, tomato aspermy cucumovirus and tomato spotted wilt tospovirus in Australian chrysanthemum crops

A sequential batch testing procedure was used in conjunction with ELISA or cDNA probes to estimate the incidence of chrysanthemum stunt viroid (CSVd), chrysanthemum carlavirus B (CVB), tomato aspermy cucumovirus (TAV) and tomato spotted wilt tospovirus (TSWV) in chrysanthemum (Dendranthema grandiflora) crops in Australia. A total of 2480 samples of potted, field-grown and greenhouse-grown chrysanthemums was tested from six Australian States. All four of these pathogens were detected. CVB (39.2%) and TAV (6.7%) were the most prevalent, CSVd (0.7%) was detected only in greenhouse chrysanthemums from Queensland, and TSWV (1.4%) was detected only in field-grown chrysanthemums from Western Australia.

Efficient allocations in group sequential tests

We derive asymptotically efficient data dependent allocation rules for three group sequential testing procedures: Pocock (1977), O'Brien and Fleming (1979) and Falissard and Lellouch (1992). Sampling costs are defined such that the costs of observing the next group are higher than the cumulative costs of the previous groups. This formulation is used in an attempt to favor procedures that stop early while allocating less patients to the inferior treatment, We use a simulation study to compare the performances of these procedures when the efficient and the pairwise allocations are used. An example of applications on data is presented.

A Class of Sequential Conditional Probability Ratio Tests

Abstract A new class of sequential testing procedures, sequential conditional probability ratio tests (SCPRT's), is proposed. These procedures have the property of having a maximum sample size no larger than a fixed-sample test with an almost identical power function. The efficiency of the SCPRT, in terms of expected sample size, is close to that of Wald's SPRT. Group sequential testing procedures derived from the SCPRT are not restricted to the choices of group sizes and number of groups. At the same time, the SCPRT, the group-SCPRT, and the reference fixed sample size test (RFSST) are agreeable in the sense of having very small probability of leading to different rejection/acceptance results. For the SCPRT or the group-SCPRT, stopping boundaries are decided by appropriate deflection factors determined by controlling absorption probabilities of a random bridge on the SCPRT boundaries. In this article the basic idea for the SCPRT is introduced in a general setup. But examples and technical discussions are restricted mainly to dichotomous distributions, in which the power functions and expected sample sizes for the sequential procedures can be easily computed by a method developed by Xiong.