On power and sample size of the ANOVA-type rank test

When using nonparametric methods to analyze factorial designs with repeated measures, the ANOVA-type rank test has gained popularity due to its robustness and appropriate type I error control. This article proposes power and sample size calculation formulas under two scenarios where the nonparametric regression coefficients are known or they are unknown but a pilot study is available. When a pilot study is available, the formulas do not need any assumption on the underlying population distributions. Simulation results confirm the accuracy of the proposed methods. An STZ rat excisional wound study is used to demonstrate the application of the methods.     

Detection of change points using rank methods

In this paper, the detection and estimation of change points of local parameters are studied by means of localization procedures and rank statistics. These techniques are also applied to detection and estimation of the change points of scale parameters and that of location parameters of directional data.     

A signed rank test for censored paired lifetimes

A locally most powerful signed rank test is proposed for the comparison of two independent lifetimes under the accelerated failure time model.

The test is based on N independent pairs(X_i, Y_i), i = 1, …, N: it is supposed that the shortest lifetime in each pair is observed and the experiment is stopped after r(r≤N and fixed) such lifetimes are available (type II censoring).

Actual scores of the test statistic are computed for some specific source distributions of the observations. The asymptotic distribution of the test statistic, as well as the asymptotic power and efficiency are given. The values of these efficiencies are computed for the case where the X_i follow and exponential, Weibull Gamma or Rayleigh distribution.     

Sample size calculation for the one‐sample log‐rank test

In this paper, an exact variance of the one‐sample log‐rank test statistic is derived under the alternative hypothesis, and a sample size formula is proposed based on the derived exact variance. Simulation results showed that the proposed sample size formula provides adequate power to design a study to compare the survival of a single sample with that of a standard population. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust test for independence in high dimensions

This article develops a new test based on Spearman’s rank correlation coefficients for total independence in high dimensions. The test is robust to the non normality and heavy tails of the data, which is a merit that is not shared by the existing tests in literature. Simulation results suggest that the new test performs well under several typical null and alternative hypotheses. Besides, we employ a real data set to illustrate the use of the new test.     

A rank test for stochastically ordered alternatives

A rank test based on the number of ‘near-matches’ among within-block rankings is proposed for stochastically ordered alternatives in a randomized block design with t treatments and b blocks. The asymptotic relative efficiency of this test with respect to the Page test is computed as number of blocks increases to infinity. A sequential analog of the above test procedure is also considered. A repeated significance test procedure is developed and average sample number is computed asymptotically under the null hypothesis as well as under a sequence of contiguous alternatives.     

On small sample properties of the generalized signed rank and generalized sign tests

The generalized signed rank (GSR) and generalized sign (GS) tests were recently proposed for matched pair studies with censored observations (Woolson and Lechenbruch, 1980). The results provided in that paper were asymptotic, and no indicatin of small sample behavior was given. In this paper we report on simulation studied of these statistics for a variety of distributions. We find that the GSR is more powerful than the GS, and that censoring does not affect power greatly. In the original paper, we assumed each member of the pair has the same censoring time. We consider a variant of this in which each member of the pair has a censoring time chosen from a uniform distribution, and the minimum of these times is selected as the censoring time for the pair. It is found that the power of the test is slightly reduced because the number of doubly censored pairs is increased.     

A certain locally most powerful test for one-way random effects model: full distribution and power considerations

We investigate the properties of the locally most powerful nonparametric criterion against logistic alternatives developed by Govindarajulu (1975) for testing one-way random effects modcls. We deduce the appropriate computational forms for the test criterion T and tabulate the critical values of T for α = .01, .05 and 0.10, and various sample sizes. Certain features of the computational methods are discussed. In the tables we retain only those sample sizes beyond which the asymptotic theory is meaningful. We also study the power comparison of the test for two populations with the classical F-test under a range of normal alternatives.     

Local rank estimation and related test for varying-coefficient partially linear models

This paper develops a robust estimation procedure for the varying-coefficient partially linear model via local rank technique. The new procedure provides a highly efficient and robust alternative to the local linear least-squares method. In other words, the proposed method is highly efficient across a wide class of non-normal error distributions and it only loses a small amount of efficiency for normal error. Moreover, a test for the hypothesis of constancy for the nonparametric component is proposed. The test statistic is simple and thus the test procedure can be easily implemented. We conduct Monte Carlo simulation to examine the finite sample performance of the proposed procedures and apply them to analyse the environment data set. Both the theoretical and the numerical results demonstrate that the performance of our approach is at least comparable to those existing competitors.     

Order test for high-dimensional two-sample means

We propose a new method to test the order between two high-dimensional mean curves. The new statistic extends the approach of Follmann (1996) to high-dimensional data by adapting the strategy of Bai and Saranadasa (1996). The proposed procedure is an alternative to the non-negative basis matrix factorization (NBMF) based test of Lee et al. (2008) for the same hypothesis, but it is much easier to implement. We derive the asymptotic mean and variance of the proposed test statistic under the null hypothesis of equal mean curves. Based on theoretical results, we put forward a permutation procedure to approximate the null distribution of the new test statistic. We compare the power of the proposed test with that of the NBMF-based test via simulations. We illustrate the approach by an application to tidal volume traces.     

A simple algorithm for the adaptation of scores and power behavior of the corresponding rank test

The purpose of this paper is twofold:On one hand we want to give a very simple algorithm for evaluating a special rank estimator of the type given in Behnen, Neuhaus, and Ruymgaart (1983) for the approximate optimal choice of the scores-generating function of a two-sample linear rank test for the general testing problem H_o:F=G versus H₁:F ≤ G, F ≠ G, in order to demonstrate that the corresponding adaptive rank statistic is simple enough for practical applications. On the other hand we prove the asymptotic normality of the adaptive rank statistic under H (leading to approximate critical values) and demonstrate the adaptive behavior of the corresponding rank test by a Monte Carlo power simulation for sample sizes as low as m=10, n=10.     

A modified test for testing exponentiality using transformed data

In this article, we present a test for testing uniformity. Based on the test, we provide a test for testing exponentiality. Empirical critical values for both the tests are computed. Both the tests are compared with the tests proposed by Noughabi and Arghami [H. Alizadeh Noughabi, and N.R. Arghami, Testing exponentiality using transformed data, J. Statist. Comput. Simul. 81 (4) (2011), pp. 511–516] using simulation experiments for a wide class of alternatives. The tests possess attractive power properties.     

A permutation test for multivariate data with grouped components

In this paper, we consider a nonparametric test procedure for multivariate data with grouped components under the two sample problem setting. For the construction of the test statistic, we use linear rank statistics which were derived by applying the likelihood ratio principle for each component. For the null distribution of the test statistic, we apply the permutation principle for small or moderate sample sizes and derive the limiting distribution for the large sample case. Also we illustrate our test procedure with an example and compare with other procedures through simulation study. Finally, we discuss some additional interesting features as concluding remarks.     

A modification of the kruskal-wallis statistic for the generalized behrens-fisher problem

The problem of testing the equality of the medians of several populations is considered. Standard distribution-free procedures for this problem require that the populations have the same shape in order to maintain their nominal significance level, ever asymptotically, under the null hypothesis of equal medians , A modification of the Kruskal-Wallis test statistic is proposed which is exactly distribution-free under the usual nonparanetric asswnption that the continuous populations are identical with any shape. It is asymptotically distribution-free when the Continuous populations are asswned to be syrmnetric with equal medians.     

A CLASS OF NONPARAMETRIC TESTS FOR THE ONE-SAMPLE LOCATION PROBLEM

A class of “optimal”U-statistics type nonparametric test statistics is proposed for the one-sample location problem by considering a kernel depending on a constant a and all possible (distinct) subsamples of size two from a sample of n independent and identically distributed observations. The “optimal” choice of a is determined by the underlying distribution. The proposed class includes the Sign and the modified Wilcoxon signed-rank statistics as special cases. It is shown that any “optimal” member of the class performs better in terms of Pitman efficiency relative to the Sign and Wilcoxon-signed rank statistics. The effect of deviation of chosen a from the “optimal” a on Pitman efficiency is also examined. A Hodges-Lehmann type point estimator of the location parameter corresponding to the proposed “optimal” test-statistics is also defined and studied in this paper.     

Adjusted Wilcoxon signed rank test tables for ratio of percentiles

The ordinary Wilcoxon signed rank test table provides confidence intervals for the median of one population. Adjusted Wilcoxon signed rank test tables which can provide confidence intervals for the median and the 10th percentile of one population are created in this paper. Base-(n + 1) number system and theorems about property of symmetry of the adjusted Wilcoxon signed rank test statistic are derived for programming. Theorem 1 states that the adjusted Wilcoxon signed rank test statistic are symmetric around n(n + 1)/4. Theorem 2 states that the adjusted Wilcoxon signed rank test statistic with the same number of negative ranks m are symmetric around m(n+1)/2. 87.5% and 85% confidence intervals of the median are given in the table for n = 12, 13,…, 29 to create approximated 95% confidence intervals of the ratio of medians for two independent populations. 95% and 92.5% confidence intervals of the 10th percentile are given in the table for n = 26, 27, 28, 29 to create approximated 95% confidence regions of the ratio of the 10th percentiles for two independent populations. Finally two large datasets from wood industry will be partitioned to verify the correctness of adjusted Wilcoxon signed rank test tables for small samples.     

Sample size determination for the weighted log‐rank test with the Fleming–Harrington class of weights in cancer vaccine studies

In recent years, immunological science has evolved, and cancer vaccines are available for treating existing cancers. Because cancer vaccines require time to elicit an immune response, a delayed treatment effect is expected. Accordingly, the use of weighted log‐rank tests with the Fleming–Harrington class of weights is proposed for evaluation of survival endpoints. We present a method for calculating the sample size under assumption of a piecewise exponential distribution for the cancer vaccine group and an exponential distribution for the placebo group as the survival model. The impact of delayed effect timing on both the choice of the Fleming–Harrington's weights and the increment in the required number of events is discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Weighted log‐rank test for time‐to‐event data in immunotherapy trials with random delayed treatment effect and cure rate

A cancer clinical trial with an immunotherapy often has 2 special features, which are patients being potentially cured from the cancer and the immunotherapy starting to take clinical effect after a certain delay time. Existing testing methods may be inadequate for immunotherapy clinical trials, because they do not appropriately take the 2 features into consideration at the same time, hence have low power to detect the true treatment effect. In this paper, we proposed a piece‐wise proportional hazards cure rate model with a random delay time to fit data, and a new weighted log‐rank test to detect the treatment effect of an immunotherapy over a chemotherapy control. We showed that the proposed weight was nearly optimal under mild conditions. Our simulation study showed a substantial gain of power in the proposed test over the existing tests and robustness of the test with misspecified weight. We also introduced a sample size calculation formula to design the immunotherapy clinical trials using the proposed weighted log‐rank test.