An alternative procedure for performing a power analysis of Mantel's test

This study proposes a simple way to perform a power analysis of Mantel's test applied to squared Euclidean distance matrices. The general statistical aspects of the simple Mantel's test are reviewed. The Monte Carlo method is used to generate bivariate Gaussian variables in order to create squared Euclidean distance matrices. The power of the parametric correlation t-test applied to raw data is also evaluated and compared with that of Mantel's test. The standard procedure for calculating punctual power levels is used for validation. The proposed procedure allows one to draw the power curve by running the test only once, dispensing with the time demanding standard procedure of Monte Carlo simulations. Unlike the standard procedure, it does not depend on a knowledge of the distribution of the raw data. The simulated power function has all the properties of the power analysis theory and is in agreement with the results of the standard procedure.     

Comparison of ANOVA-F and ANOM tests with regard to type I error rate and test power

A Monte Carlo simulation was conducted to compare the type I error rate and test power of the analysis of means (ANOM) test to the one-way analysis of variance F-test (ANOVA-F). Simulation results showed that as long as the homogeneity of the variance assumption was satisfied, regardless of the shape of the distribution, number of group and the combination of observations, both ANOVA-F and ANOM test have displayed similar type I error rates. However, both tests have been negatively affected from the heterogeneity of the variances. This case became more obvious when the variance ratios increased. The test power values of both tests changed with respect to the effect size (Δ), variance ratio and sample size combinations. As long as the variances are homogeneous, ANOVA-F and ANOM test have similar powers except unbalanced cases. Under unbalanced conditions, the ANOVA-F was observed to be powerful than the ANOM-test. On the other hand, an increase in total number of observations caused the power values of ANOVA-F and ANOM test approach to each other. The relations between effect size (Δ) and the variance ratios affected the test power, especially when the sample sizes are not equal. As ANOVA-F has become to be superior in some of the experimental conditions being considered, ANOM is superior in the others. However, generally, when the populations with large mean have larger variances as well, ANOM test has been seen to be superior. On the other hand, when the populations with large mean have small variances, generally, ANOVA-F has observed to be superior. The situation became clearer when the number of the groups is 4 or 5.     

A goodness of fit test for multilevel survival data

No satisfactory goodness of fit test is available for multilevel survival data which occur when survival data are clustered or hierarchical in nature. Hence the aim of this research is to develop a new goodness of fit test for multilevel survival data and to examine the properties of the newly developed test. Simulation studies were carried out to evaluate the type ? error and the power. The results showed that the type I error holds for every combination tested and that the test is powerful against the alternative hypothesis of nonproportional hazards for all combinations tested.     

A new test for residual randomness in a class of dynamic autocorrelated econometric models

This paper presents a new test statistic for dynamic or stochastic mis-specification for the dynamic demand or dynamic adjustment class of economic models. The test statistic is based on residual autocorrelations, asymptotically X² and is suspected to be of low power. The test is illustrated with an example from recent econometric literature.     

A more powerful unconditional exact test of homogeneity for 2 × c contingency table analysis

The classical unconditional exact p-value test can be used to compare two multinomial distributions with small samples. This general hypothesis requires parameter estimation under the null which makes the test severely conservative. Similar property has been observed for Fisher's exact test with Barnard and Boschloo providing distinct adjustments that produce more powerful testing approaches. In this study, we develop a novel adjustment for the conservativeness of the unconditional multinomial exact p-value test that produces nominal type I error rate and increased power in comparison to all alternative approaches. We used a large simulation study to empirically estimate the 5th percentiles of the distributions of the p-values of the exact test over a range of scenarios and implemented a regression model to predict the values for two-sample multinomial settings. Our results show that the new test is uniformly more powerful than Fisher's, Barnard's, and Boschloo's tests with gains in power as large as several hundred percent in certain scenarios. Lastly, we provide a real-life data example where the unadjusted unconditional exact test wrongly fails to reject the null hypothesis and the corrected unconditional exact test rejects the null appropriately.     

Adaptive and repeated cumulative meta‐analyses of safety data during a new drug development process

During a new drug development process, it is desirable to timely detect potential safety signals. For this purpose, repeated meta‐analyses may be performed sequentially on accumulating safety data. Moreover, if the amount of safety data from the originally planned program is not enough to ensure adequate power to test a specific hypothesis (e.g., the noninferiority hypothesis of an event of interest), the total sample size may be increased by adding new studies to the program. Without appropriate adjustment, it is well known that the type I error rate will be inflated because of repeated analyses and sample size adjustment. In this paper, we discuss potential issues associated with adaptive and repeated cumulative meta‐analyses of safety data conducted during a drug development process. We consider both frequentist and Bayesian approaches. A new drug development example is used to demonstrate the application of the methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Assessing noninferiority: Evaluating efficacy of a new treatment without complete data

The FDA released the final guidance on noninferiority trials in November 2016. In noninferiority trials, validity of the assessment of the efficacy of the test treatment depends on the control treatment's efficacy. Therefore, it is critically important that there be a reliable estimate of the control treatment effect—which is generally obtained from historical trials, and often assumed to hold in the current setting (the assay constancy assumption). Validating the constancy assumption requires clinical data, which are typically lacking. The guidance acknowledges that “lack of constancy can occur for many reasons.” We clarify the objectives of noninferiority trials. We conclude that correction for bias, rather than assay constancy, is critical to conducting valid noninferiority trials. We propose that assay constancy not be assumed and discounting or thresholds be used to address concern about loss of historical efficacy. Examples are provided for illustration.     

On a goodness-of-fit test for normality with unknown parameters and type-II censored data

We propose a new goodness-of-fit test for normal and lognormal distributions with unknown parameters and type-II censored data. This test is a generalization of Michael's test for censored samples, which is based on the empirical distribution and a variance stabilizing transformation. We estimate the parameters of the model by using maximum likelihood and Gupta's methods. The quantiles of the distribution of the test statistic under the null hypothesis are obtained through Monte Carlo simulations. The power of the proposed test is estimated and compared to that of the Kolmogorov–Smirnov test also using simulations. The new test is more powerful than the Kolmogorov–Smirnov test in most of the studied cases. Acceptance regions for the PP, QQ and Michael's stabilized probability plots are derived, making it possible to visualize which data contribute to the decision of rejecting the null hypothesis. Finally, an illustrative example is presented.     

Inferences on a linear combination of K multivariate normal mean vectors

In this paper, the hypothesis testing and confidence region construction for a linear combination of mean vectors for K independent multivariate normal populations are considered. A new generalized pivotal quantity and a new generalized test variable are derived based on the concepts of generalized p-values and generalized confidence regions. When only two populations are considered, our results are equivalent to those proposed by Gamage et al. [Generalized p-values and confidence regions for the multivariate Behrens–Fisher problem and MANOVA, J. Multivariate Aanal. 88 (2004), pp. 117–189] in the bivariate case, which is also known as the bivariate Behrens–Fisher problem. However, in some higher dimension cases, these two results are quite different. The generalized confidence region is illustrated with two numerical examples and the merits of the proposed method are numerically compared with those of the existing methods with respect to their expected areas, coverage probabilities under different scenarios.     

On some test statistics for testing homogeneity of variances: a comparative study

In this paper, we have reviewed 25 test procedures that are widely reported in the literature for testing the hypothesis of homogeneity of variances under various experimental conditions. Since a theoretical comparison was not possible, a simulation study has been conducted to compare the performance of the test statistics in terms of robustness and empirical power. Monte Carlo simulation was performed for various symmetric and skewed distributions, number of groups, sample size per group, degree of group size inequalities, and degree of variance heterogeneity. Using simulation results and based on the robustness and power of the tests, some promising test statistics are recommended for practitioners.     

Sensitivity analysis of longitudinal count responses: a local influence approach and application to medical data

Longitudinal count responses are often analyzed with a Poisson mixed model. However, under overdispersion, these responses are better described by a negative binomial mixed model. Estimators of the corresponding parameters are usually obtained by the maximum likelihood method. To investigate the stability of these maximum likelihood estimators, we propose a methodology of sensitivity analysis using local influence. As count responses are discrete, we are unable to perturb them with the standard scheme used in local influence. Then, we consider an appropriate perturbation for the means of these responses. The proposed methodology is useful in different applications, but particularly when medical data are analyzed, because the removal of influential cases can change the statistical results and then the medical decision. We study the performance of the methodology by using Monte Carlo simulation and applied it to real medical data related to epilepsy and headache. All of these numerical studies show the good performance and potential of the proposed methodology.     

Identification of longitudinal biomarkers for survival by a score test derived from a joint model of longitudinal and competing risks data

In this paper, we consider joint modelling of repeated measurements and competing risks failure time data. For competing risks time data, a semiparametric mixture model in which proportional hazards model are specified for failure time models conditional on cause and a multinomial model for the marginal distribution of cause conditional on covariates. We also derive a score test based on joint modelling of repeated measurements and competing risks failure time data to identify longitudinal biomarkers or surrogates for a time to event outcome in competing risks data.     

Comparing diagnostic tests: test of hypothesis for likelihood ratios

Likelihood ratios (LRs) are used to characterize the efficiency of diagnostic tests. In this paper, we use the classical weighted least squares (CWLS) test procedure, which was originally used for testing the homogeneity of relative risks, for comparing the LRs of two or more binary diagnostic tests. We compare the performance of this method with the relative diagnostic likelihood ratio (rDLR) method and the diagnostic likelihood ratio regression (DLRReg) approach in terms of size and power, and we observe that the performances of CWLS and rDLR are the same when used to compare two diagnostic tests, while DLRReg method has higher type I error rates and powers. We also examine the performances of the CWLS and DLRReg methods for comparing three diagnostic tests in various sample size and prevalence combinations. On the basis of Monte Carlo simulations, we conclude that all of the tests are generally conservative and have low power, especially in settings of small sample size and low prevalence.     

Comparing the overlapping of two independent confidence intervals with a single confidence interval for two normal population parameters

Two overlapping confidence intervals have been used in the past to conduct statistical inferences about two population means and proportions. Several authors have examined the shortcomings of Overlap procedure and have determined that such a method distorts the significance level of testing the null hypothesis of two population means and reduces the statistical power of the test. Nearly all results for small samples in Overlap literature have been obtained either by simulation or by formulas that may need refinement for small sample sizes, but accurate large sample information exists. Nevertheless, there are aspects of Overlap that have not been presented and compared against the standard statistical procedure. This article will present exact formulas for the maximum % overlap of two independent confidence intervals below which the null hypothesis of equality of two normal population means or variances must still be rejected for any sample sizes. Further, the impact of Overlap on the power of testing the null hypothesis of equality of two normal variances will be assessed. Finally, the noncentral t-distribution is used to assess the Overlap impact on type II error probability when testing equality of means for sample sizes larger than 1.