A comparison of several adaptive tests for paired data

In the last few years, two adaptive tests for paired data have been proposed. One test proposed by Freidlin et al. [On the use of the Shapiro–Wilk test in two-stage adaptive inference for paired data from moderate to very heavy tailed distributions, Biom. J. 45 (2003), pp. 887–900] is a two-stage procedure that uses a selection statistic to determine which of three rank scores to use in the computation of the test statistic. Another statistic, proposed by O'Gorman [Applied Adaptive Statistical Methods: Tests of Significance and Confidence Intervals, Society for Industrial and Applied Mathematics, Philadelphia, 2004], uses a weighted t-test with the weights determined by the data. These two methods, and an earlier rank-based adaptive test proposed by Randles and Hogg [Adaptive Distribution-free Tests, Commun. Stat. 2 (1973), pp. 337–356], are compared with the t-test and to Wilcoxon's signed-rank test. For sample sizes between 15 and 50, the results show that the adaptive test proposed by Freidlin et al. and the adaptive test proposed by O'Gorman have higher power than the other tests over a range of moderate to long-tailed symmetric distributions. The results also show that the test proposed by O'Gorman has greater power than the other tests for short-tailed distributions. For sample sizes greater than 50 and for small sample sizes the adaptive test proposed by O'Gorman has the highest power for most distributions.     

A comparative study of tests for paired lifetime data

In this paper, we investigate different procedures for testing the equality of two mean survival times in paired lifetime studies. We consider Owen’s M-test and Q-test, a likelihood ratio test, the paired t-test, the Wilcoxon signed rank test and a permutation test based on log-transformed survival times in the comparative study. We also consider the paired t-test, the Wilcoxon signed rank test and a permutation test based on original survival times for the sake of comparison. The size and power characteristics of these tests are studied by means of Monte Carlo simulations under a frailty Weibull model. For less skewed marginal distributions, the Wilcoxon signed rank test based on original survival times is found to be desirable. Otherwise, the M-test and the likelihood ratio test are the best choices in terms of power. In general, one can choose a test procedure based on information about the correlation between the two survival times and the skewness of the marginal survival distributions.     

The power of the modified Wilcoxon rank-sum test for the one-sided alternative

When testing hypotheses in two-sample problems, the Wilcoxon rank-sum test is often used to test the location parameter, and this test has been discussed by many authors over the years. One modification of the Wilcoxon rank-sum test was proposed by Tamura [On a modification of certain rank tests. Ann Math Stat. 1963;34:1101–1103]. Deriving the exact critical value of the statistic is difficult when the sample sizes are increased. The normal approximation, the Edgeworth expansion, the saddlepoint approximation, and the permutation test were used to evaluate the upper tail probability for the modified Wilcoxon rank-sum test given finite sample sizes. The accuracy of various approximations to the probability of the modified Wilcoxon statistic was investigated. Simulations were used to investigate the power of the modified Wilcoxon rank-sum test for the one-sided alternative with various population distributions for small sample sizes. The method was illustrated by the analysis of real data.     

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 new revised version of McNemar's test for paired binary data

By considering separately B and C, the frequencies of individuals who consistently gave positive or negative answers in before and after responses, a new revised version of McNemar's test is derived. It improves upon Lu's revised formula, which considers B and C together. When both B and C are 0, the new revised version produces the same results as McNemar's test. When one of B and C is 0, the new revised test produces the same results as Lu's version. Compared to Lu's version, the new revised test is a more complete revision of McNemar's test.     

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.     

Power and sample size calculation for paired right-censored data based on survival copula models

Sample size determination is essential during the planning phases of clinical trials. To calculate the required sample size for paired right-censored data, the structure of the within-paired correlations needs to be pre-specified. In this article, we consider using popular parametric copula models, including the Clayton, Gumbel, or Frank families, to model the distribution of joint survival times. Under each copula model, we derive a sample size formula based on the testing framework for rank-based tests and non-rank-based tests (i.e., logrank test and Kaplan–Meier statistic, respectively). We also investigate how the power or the sample size was affected by the choice of testing methods and copula model under different alternative hypotheses. In addition to this, we examine the impacts of paired-correlations, accrual times, follow-up times, and the loss to follow-up rates on sample size estimation. Finally, two real-world studies are used to illustrate our method and R code is available to the user.     

A new two-sample test for choosing between log-rank and Wilcoxon tests with right-censored data

When differences of survival functions are located in early time, a Wilcoxon test is the best test, but when differences of survival functions are located in late time, using a log-rank test is better. Therefore, a researcher needs a stable test in these situations. In this paper, a new two-sample test is proposed and considered. This test is distribution-free. This test is useful for choosing between log-rank and Wilcoxon tests. Its power is roughly the maximal power of the log-rank test and Wilcoxon test.     

An exact density-based empirical likelihood ratio test for paired data

The Wilcoxon rank-sum test and its variants are historically well-known to be very powerful nonparametric decision rules for testing no location difference between two groups given paired data versus a shift alternative. In this title, we propose a new alternative empirical likelihood (EL) ratio approach for testing the equality of marginal distributions given that sampling is from a continuous bivariate population. We show that in various shift alternative scenarios the proposed exact test is superior to the classic nonparametric procedures, which may break down completely or are frequently inferior to the density-based EL ratio test. This is particularly true in the cases where there is a nonconstant shift under the alternative or the data distributions are skewed. An extensive Monte Carlo study shows that the proposed test has excellent operating characteristics. We apply the density-based EL ratio test to analyze real data from two medical studies.     

Data driven smooth test for paired populations

In this paper we propose a smooth test of comparison of two distribution functions. This test adapts to the classical two-sample problem as well as that of paired populations, including discrete distributions. A simulation study and an application to real data show its good performances.     

An F-type small sample simultaneous test for nested linear regression models

A small sample simultaneous testing method is proposed for nested linear regression model. The methodology is based on the generalized likelihood ratio test which is the large sample simultaneous testing method for general nested models. The proposed test is also used for model identification.     

Small sample distribution for a nonparametric test for trend

The exact distribution of a nonparametric test statistic for ordered alternatives, the _rank ² statistic, is computed for small sample sizes. The exact distribution is compared to an approximation.     

One sample tests of location for nonnormal symmetric data

A score test of location is derived for data from a distorted normal distribution. A simulation study compares the performance of this test to the t-test and Wilcoxon test for symmetric data from such a distribution. For this type of data the score test can be considerably more powerful than both the t-test and Wilcoxon test. This suggests that such a score test may be useful in practice when variations from normality can be modeled by such a family of distributions.     

A new method for the comparison of survival distributions

The assessment of overall homogeneity of time‐to‐event curves is a key element in survival analysis in biomedical research. The currently commonly used testing methods, e.g. log‐rank test, Wilcoxon test, and Kolmogorov–Smirnov test, may have a significant loss of statistical testing power under certain circumstances. In this paper we propose a new testing method that is robust for the comparison of the overall homogeneity of survival curves based on the absolute difference of the area under the survival curves using normal approximation by Greenwood's formula. Monte Carlo simulations are conducted to investigate the performance of the new testing method compared against the log‐rank, Wilcoxon, and Kolmogorov–Smirnov tests under a variety of circumstances. The proposed new method has robust performance with greater power to detect the overall differences than the log‐rank, Wilcoxon, and Kolmogorov–Smirnov tests in many scenarios in the simulations. Furthermore, the applicability of the new testing approach is illustrated in a real data example from a kidney dialysis trial. Copyright © 2009 John Wiley & Sons, Ltd.     

A resampling‐based test for two crossing survival curves

The area between two survival curves is an intuitive test statistic for the classical two‐sample testing problem. We propose a bootstrap version of it for assessing the overall homogeneity of these curves. Our approach allows ties in the data as well as independent right censoring, which may differ between the groups. The asymptotic distribution of the test statistic as well as of its bootstrap counterpart are derived under the null hypothesis, and their consistency is proven for general alternatives. We demonstrate the finite sample superiority of the proposed test over some existing methods in a simulation study and illustrate its application by a real‐data example.     

A novel test to compare two treatments based on endpoints involving both nonfatal and fatal events

In a clinical trial comparing two treatment groups, one commonly‐used endpoint is time to death. Another is time until the first nonfatal event (if there is one) or until death (if not). Both endpoints have drawbacks. The wrong choice may adversely affect the value of the study by impairing power if deaths are too few (with the first endpoint) or by lessening the role of mortality if not (with the second endpoint). We propose a compromise that provides a simple test based on the time to death if the patient has died or time since randomization augmented by an increment otherwise. The test applies the ordinary two‐sample Wilcoxon statistic to these values. The formula for the increment (the same for experimental and control patients) must be specified before the trial starts. In the simplest (and perhaps most useful) case, the increment assumes only two values, according to whether or not the (surviving) patient had a nonfatal event. More generally, the increment depends on the time of the first nonfatal event, if any, and the time since randomization. The test has correct Type I error even though it does not handle censoring in a customary way. For conditions where investigators would face no easy (advance) choice between the two older tests, simulation results favor the new test. An example using a renal‐cancer trial is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

Distribution- free test for slope in linear regression model with replications

Some distribution-free methods are suggested in the paper for testing the hypothesis about the slope parameter in a one-sample linear regression model with multiple observations at each level of independent variable. Asymptotic relative efficiencies of these tests are discussed, and the tests are compared with their nonparametric competitors.     

A nonparametric test for interaction in two‐way layouts

The authors present a new nonparametric approach to test for interaction in two‐way layouts. Based on the concept of composite linear rank statistics, they combine the correlated row and column ranking information to construct the test statistic. They determine the limiting distributions of the proposed test statistic under the null hypothesis and Pitman alternatives. They also propose consistent estimators for the limiting covariance matrices associated with the test. They illustrate the application of their test in practical settings using a microarray data set.     

A test of the missing data mechanism for repeated measures data

The occurrence of missing data is an often unavoidable consequence of repeated measures studies. Fortunately, multivariate general linear models such as growth curve models and linear mixed models with random effects have been well developed to analyze incomplete normally-distributed repeated measures data. Most statistical methods have assumed that the missing data occur at random. This assumption may include two types of missing data mechanism: missing completely at random (MCAR) and missing at random (MAR) in the sense of Rubin (1976). In this paper, we develop a test procedure for distinguishing these two types of missing data mechanism for incomplete normally-distributed repeated measures data. The proposed test is similar in spiril to the test of Park and Davis (1992). We derive the test for incomplete normally-distribrlted repeated measures data using linear mixed models. while Park and Davis (1992) cleirved thr test for incomplete repeatctl categorical data in the framework of Grizzle Starmer. and Koch (1969). Thr proposed procedure can be applied easily to any other multivariate general linear model which allow for missing data. The test is illustrated using the hip-replacernent patient.data from Crowder and Hand (1990).