Global Test Statistic Research Articles

New Treatments for Acute Ischemic Stroke

Two recently published studies have investigated new modalities for the treatment of acute ischemic stroke. The National Institute of Neurological Disorders and Stroke rt-PA Stroke Study Group1 recently reported the results of a randomized, double-blind trial of intravenous recombinant tissue plasminogen activator (TPA) for acute ischemic stroke. There were two parts to the overall study; a total of 624 patients were randomized in both parts. To qualify for inclusion in either of the two parts, patients had to (1) have had an ischemic stroke with a clearly defined time of onset; (2) have a deficit that was measurable according to the National Institutes of Health Stroke Scale (NIHSS), a 42-point serial measure of neurological deficit; and (3) have a baseline computed tomographic brain scan that showed no evidence of intracranial hemorrhage. Patients had to have treatment with study drug initiated within 3 hours of symptom onset. Exclusion criteria included another stroke or head trauma within the past 3 months, major surgery within …

One-sided multiple endpoint testing in two-sample comparisons

This article reviews several methods for comparing two treatments with multiple endpoints that take into account the dependence structure among the endpoints and that are sensitive to the multivariate one-sided alternative. The methods are classified into procedures that adjust sin-gle endpoint P-values separately, into bootstrap procedures that adjust single endpoint P-values through resampling from the whole data, and into procedures that summarize the data into a global test statistic. In this context, we describe step-down procedures leading to conclusions about the single endpoints. Applying the closed test principle, James (1991, Statistics in Medicine 10, 1123-1135)-based, O'Brien (1984, Biometries 40, 1079-1087)-based, Tang, Gnecco, and Geller (1989, Biometrika 76, 577-583)-based, and Westfall and Young 1989, Jour-nal of the American Statistical Association 84, 780-786)-based proce-dures are investigated and compared to standard techniques. Monte Carlo simulations for small to moderate sample size...

Incorporating Surrogate Endpoints into Group Sequential Trials

AbstractRecent developments proposed by Lin (1991) which allow for the sequential analysis of multivariate failure time data, are discussed in the context of clinical trials with marker process data. In particular, a marker based response observed as a univariate failure time variable is considered in a univariate manner and in combination with the primary failure time variable through global measures of treatment effect. A weighting scheme is introduced that is designed to make greater use of the marker process responses when they are consistent with the responses for the primary endpoint.Univariate analyses and analyses based on global test statistics are evaluated with respect to duration of study and type I and type II error rates for a variety of relative risk parameter configurations. The simulation study is designed to extend the work of Machado, Gail and Ellenberg (1990) to sequential trials and to assess the performance of the global test statistics in this context. The global measures are found to be preferable over the univariate primary endpoint analyses when the treatment affects all transition intensities in a consistent manner. Further, there are advantages over the univariate marker based analysis when the treatment effects on some transition intensities are in opposite directions. Such a scenario remains problematic however with the relative error rates determined to a large extent by the baseline weighting scheme.

Evaluation of Experiments with Adaptive Interim Analyses

A general method for statistical testing in experiments with an adaptive interim analysis is proposed. The method is based on the observed error probabilities from the disjoint subsamples before and after the interim analysis. Formally, an intersection of individual null hypotheses is tested by combining the two p-values into a global test statistic. Stopping rules for Fisher's product criterion in terms of critical limits for the p-value in the first subsample are introduced, including early stopping in the case of missing effects. The control of qualitative treatment-stage interactions is considered. A generalization to three stages is outlined. The loss of power when using the product criterion instead of the optimal classical test on the whole sample is calculated for the test of the mean of a normal distribution, depending on increasing proportions of the first subsample in relation to the total sample size. An upper bound on the loss of power due to early stopping is derived. A general example is presented and rules for assessing the sample size in the second stage of the trial are given. The problems of interpretation and precautions to be taken for applications are discussed. Finally, the sources of bias for estimation in such designs are described.

The weighted rank pairwise correlation statistic for linkage analysis: Simulation study and application to Alzheimer's disease

The weighted rank pairwise correlation (WRPC) statistic has been proposed as a robust test of genetic linkage, particularly adapted to the analysis of large and complex pedigrees and for age-dependent and heterogeneous diseases. In this paper a simulation study is presented. Validity and power of the WRPC test are studied and compared to the Haseman-Elston sibpair method for various types of problems. The power of the WRPC test is slightly lower than the Haseman-Elston method for analyzing a large number of small randomly chosen pedigrees. It is higher however in presence of genetic heterogeneity or for analyzing large individual pedigrees. Recently, evidence of linkage of Alzheimer's disease with a locus on chromosome 14, D14s43, has been obtained by the Lod-score method. We reanalyze these data using the WRPC test, essentially confirming the results of the Lod-score method. The WRPC test statistic is higher than the equivalent Lod-score statistic for the two pedigrees which show strong evidence of linkage with the two methods. The global WRPC test statistic is slightly lower than the Lod-score test statistic. The WRPC test, however, makes no hypothesis of a specific genetic transmission model and can be computed very quickly; in addition, an exact P-value can be computed by simulation for individual pedigrees.

Gross error detection when variance‐covariance matrices are unknown

AbstractEquations introduced here identify measurement biases and process leaks, when gross errors exist in measured process variables and the variance‐covariance matrix of the measurements, Σ, is unknown. Σ is estimated by the sample variance, S, using process data.For an unknown Σ, the global test statistic is the well‐known Hotelling T2 statistic. Its power function has a noncentral F‐distribution. For component tests used for specific identification of measurement biases and nodal leaks, two tests are presented with Σ unknown. The first test is independent of the number of component tests, k, and is given by a statistic with an F‐distribution. The second test depends on k and has a student t‐distribution. The power functions for both component tests are provided. Process examples and a Monte Carlo simulation study presented demonstrate the use and performance of these statistical equations in identifying biases and process leaks.

A Goodness-of-Fit Test for Binary Regression Models, Based on Smoothing Methods

A new global test statistic for models with continuous covariates and binary response is introduced. The test statistic is based on nonparametric kernel methods. Explicit expressions are given for the mean and variance of the test statistic. Asymptotic properties are considered and approximate corrections due to parameter estimation are presented. Properties of the test statistic are studied by simulation. The goodness-of-fit method is illustrated on data from a Dutch follow-up study on preterm infants. Recommendations for practitioners are given.

Risk Analysis in Cohort Studies with Heterogeneous Strata. A Global χ2-Test for Dose-Response Relationship, Generalizing the Mantel-Haenszel Procedure

In cohort studies the Mantel-Haenszel estimator ORMH is computed from sample data and is used as a point estimator of relative risk. Test-based confidence intervals are estimated with the help of the asymptotic chi-squared distributed MH-statistic chi 2MHS. The Mantel-extension-chi-squared is used as a test statistic for a dose-response relationship. Both test statistics--the Mantel-Haenszel-chi as well as the Mantel-extension-chi--assume homogeneity of risk across strata, which is rarely present. Also an extended nonparametric statistic, proposed by Terpstra, which is based on the Mann-Whitney-statistics assumes homogeneity of risk across strata. We have earlier defined four risk measures RRkj (k = 1,2,...,4) in the population and considered their estimates and the corresponding asymptotic distributions. In order to overcome the homogeneity assumption we use the delta-method to get "test-based" confidence intervals. Because the four risk measures RRkj are presented as functions of four weights gik we give, consequently, the asymptotic variances of these risk estimators also as functions of the weights gik in a closed form. Approximations to these variances are given. For testing a dose-response relationship we propose a new class of chi 2(1)-distributed global measures Gk and the corresponding global chi 2-test. In contrast to the Mantel-extension-chi homogeneity of risk across strata must not be assumed. These global test statistics are of the Wald type for composite hypotheses.(ABSTRACT TRUNCATED AT 250 WORDS)

Combining Outcome Measures: Statistical Power Is Irrelevant

In a paper in this journal, Pocock, Geller, and Tsiatis (Biometrics 43, 487-498, September 1987) discuss a global test statistic for comparing treatment groups for which k correlated endpoints have been measured, which uses the correlation structure of the measures to produce suitable weights for their combination into a unified measure. This procedure is clearly superior to the regrettably common approach of carrying out separate significance tests on each and every measure and selectively reporting those which are significant-a procedure which, of course, totally fails to control size. Pocock et al. dismiss the usual multivariate statistic, Hotelling's TV, because "it is intended to detect any departure from the null hypothesis and hence lacks power to detect any specific types of departure that are considered a priori to be biologically plausible." Instead, they develop an approach due to O'Brien (1984) which they recommend in terms of its power.

A Test of Missing Completely at Random for Multivariate Data with Missing Values

Abstract A common concern when faced with multivariate data with missing values is whether the missing data are missing completely at random (MCAR); that is, whether missingness depends on the variables in the data set. One way of assessing this is to compare the means of recorded values of each variable between groups defined by whether other variables in the data set are missing or not. Although informative, this procedure yields potentially many correlated statistics for testing MCAR, resulting in multiple-comparison problems. This article proposes a single global test statistic for MCAR that uses all of the available data. The asymptotic null distribution is given, and the small-sample null distribution is derived for multivariate normal data with a monotone pattern of missing data. The test reduces to a standard t test when the data are bivariate with missing data confined to a single variable. A limited simulation study of empirical sizes for the test applied to normal and nonnormal data suggests th...

The Analysis of Multiple Endpoints in Clinical Trials

Treatment comparisons in randomized clinical trials usually involve several endpoints such that conventional significance testing can seriously inflate the overall Type I error rate. One option is to select a single primary endpoint for formal statistical inference, but this is not always feasible. Another approach is to apply Bonferroni correction (i.e., multiply each P-value by the total number of endpoints). Its conservatism for correlated endpoints is examined for multivariate normal data. A third approach is to derive an appropriate global test statistic and this paper explores one such test applicable to any set of asymptotically normal test statistics. Quantitative, binary, and survival endpoints are all considered within this general framework. Two examples are presented and the relative merits of the proposed strategies are discussed.