Ullrich Munzel

The Nonparametric Behrens‐Fisher Problem: Asymptotic Theory and a Small‐Sample Approximation

A generalization of the Behrens-Fisher problem for two samples is examined in a nonparametric model. It is not assumed that the underlying distribution functions are continuous so that data with arbitrary ties can be handled. A rank test is considered where the asymptotic variance is estimated consistently by using the ranks over all observations as well as the ranks within each sample. The consistency of the estimator is derived in the appendix. For small samples (n 1 , n 2 > 10), a simple approximation by a central t-distribution is suggested where the degrees of freedom are taken from the Satterthwaite-Smith-Welch approximation in the parametric Behrens-Fisher problem. It is demonstrated by means of a simulation study that the Wilcoxon-Mann-Whitney-test may be conservative or liberal depending on the ratio of the sample sizes and the variances of the underlying distribution functions. For the suggested approximation, however, it turns out that the nominal level is maintained rather accurately. The suggested nonparametric procedure is applied to a data set from a clinical trial. Moreover, a confidence interval for the nonparametric treatment effect is given.

A unified approach to simultaneous rank test procedures in the unbalanced one-way layout

A general nonparametric approach to asymptotic multiple test procedures is proposed which is based on relative effects and which includes continuous as well as discontinuous distributions. The results can be applied to all relevant multiple testing problems in the one-way layout and include the well known Steel tests as special cases. Moreover, a general estimator for the asymptotic covariance matrix is considered that is consistent even under alternative. This estimator is used to derive simultaneous confidence intervals for the relative effects as well as a test procedure for the multiple nonparametric Behrens-Fisher problem.

The multivariate nonparametric Behrens–Fisher problem

Abstract In this paper, we consider the multivariate case of the so-called nonparametric Behrens–Fisher problem where two samples with independent multivariate observations are given and the equality of the marginal distribution functions under the hypothesis in the two groups is not assumed. Moreover, we do not require the continuity of the marginal distribution functions so that data with ties and, particularly, multivariate-ordered categorical data are covered by this model. A multivariate relative treatment effect is defined which can be estimated by using the mid-ranks of the observations within each component and we derive the asymptotic distribution of this estimator. Moreover, the unknown asymptotic covariance matrix of the centered vector of the estimated relative treatment effects is estimated and its L 2 -consistency is proved. To test the hypothesis of no treatment effect, we consider the rank version of the Wald-type statistic (as used in Puri and Sen, Nonparametric Methods in Multivariate Analysis, Wiley, New York, 1971) and the rank version of the ANOVA-type statistic which was suggested by Brunner et al. [J. Amer. Statist. Assoc. 92 (1997) 1494–1502] for univariate nonparametric models. Simulations show that the ANOVA-type statistic appears to maintain the pre-assigned level of the test quite accurately (even for rather small sample sizes) while the Wald-type statistic leads to more or less liberal decisions. Regarding the power, none of the two statistics is uniformly superior to the other.

Testing of individual blood donations for HCV RNA reduces the residual risk of transfusion-transmitted HCV infection.

BACKGROUND: To allow cost‐effective RNA testing with NAT techniques, the national authorities of several countries have planned or already introduced tests of mixed specimens, that is, plasma pools.

Linear rank score statistics when ties are present

The normalized versions of distribution functions are used to derive an asymptotic theory for rank statistics including ties. A mixed model which permits almost arbitrary dependencies is considered. Moreover, a Chernoff-Savage theorem in the presence of ties is proven.

Nonparametric methods in multivariate factorial designs

Abstract A nonparametric approach to the analysis of multivariate data is presented that is based on seperate rankings for different variables and extends the results of Akritas et al. (1997. J. Amer. Statist. Assoc. 89, 336–343.) to multivariate designs. Factorial designs are considered including degenerate distributions as well as discontinuous distributions. The asymptotic normality of a linear combination of dependent linear rank score statistics is shown under rather weak assumptions. Wald-type and ANOVA-type statistics are derived and their properties are compared in simulation studies. The theory is applied to a completely randomised two-way layout.

A prospective, randomized, sequential, crossover trial of large-volume versus normal-volume leukapheresis procedures: effect on progenitor cells and engraftment.

BACKGROUND: The influence of leukapheresis size on the number of harvested peripheral blood progenitor cells is still unclear. A prospective randomized crossover trial was thus performed, to evaluate the effect of large‐volume leukapheresis (LVL) versus normal‐volume leukapheresis (NVL) on progenitor cells and engraftment in 26 patients with breast cancer and 15 patients with non‐Hodgkin–s lymphoma who were eligible for peripheral blood progenitor cell transplantation.

A prospective, randomized, sequential crossover trial oflarge‐volume versus normal‐volume leukapheresis procedures:effects on serum electrolytes, platelet counts, and other coagulation measures

BACKGROUND: LVL procedures with the administration of heparin as an additional anticoagulant are increasingly performed because of the potentially higher yield of autologous peripheral blood HPCs. A prospective, randomized crossover trial was performed to evaluate the influence of leukapheresis volume—that is, large versus normal—on serum electrolytes, platelet count, and other coagulation measures in 25 patients with breast cancer and 14 patients with non‐Hodgkins lymphoma.

Nonparametric Tests in the Unbalanced Multivariate One-Way Design

A nonparametric model for the multivariate one-way design is discussed which entails continuous as well as discontinuous distributions and, therefore, allows for ordinal data. Nonparametric hypotheses are formulated by the normalized version of the marginal distribution functions as well as the common distribution functions. The differences between the distribution functions are described by means of the so-called relative treatment effects, for which unbiased and consistent estimators are derived. The asymptotic distribution of the vector of the effect estimators is derived and under the marignal hypothesis a consistent estimator for the asymptotic covariance matrix is given. Nonparametric versions of the Wald-type statistic, the ANOVA-type statistic and the Lawley-Hotelling statistic are considered and compared by means of a simulation study. Finally, these tests are applied to a psychiatric clinical trial.

Reciprocal translocations in patients with testicular seminoma before and after radiotherapy.

PURPOSE The evaluation of radiation-induced chromosomal translocations in peripheral lymphocytes using fluorescent in situ hybridization is a promising method for retrospective dosimetry after a radiation accident. We evaluated the genomic frequency of chromosomal translocations in patients with testicular seminoma who received adjuvant radiotherapy to the retroperitoneal lymph nodes, to evaluate the time-effect relationship of radiation-induced stable aberrations after partial body irradiation. METHODS In 13 patients, peripheral lymphocytes could be evaluated before radiotherapy and at several time points after radiotherapy. In 17 additional patients, lymphocyte samples were obtained after radiotherapy. Thirteen healthy men served as age-matched controls for the aberration frequency before radiotherapy. Fluorescent in situ hybridization was performed using whole chromosome probes against chromosomes No. 4, No. 6, and No. 7. RESULTS Nearly all patients displayed an increased spontaneous rate of genomic translocations (F(G)) before radiotherapy compared to age-matched, healthy men. The difference was significant in the paired ranks test (p < 0.0001). After adjuvant radiotherapy, the F(G) increased 2- to 8-fold in individual patients. Within 20 months after radiotherapy, the F(G) returned to pretherapeutic levels. CONCLUSIONS The frequency of genomic translocations after partial body irradiation is time dependent. A persistence of chromosomal aberrations, which is to be expected after total body irradiation, could not be observed. It is likely that the dose and the volume of the irradiated bone marrow are playing a role in the persistence of stable chromosomal aberrations. Patients with testicular seminoma displayed an increased frequency of spontaneous genomic translocations before the initiation of radiotherapy. This chromosomal instability might be related to the known increased rate of secondary cancers in this patient group.