The modified Mann-Kendall test: on the performance of three variance correction approaches

The Mann-Kendall test has been used to detect climate trends in several parts of the Globe. Three variance correction approaches (MKD, MKDD and MKRD) have been proposed to remove the influence of serial correlation on this trend test. Thus, the main goal of this study was to evaluate the probability of occurrence of types I and II errors associated with these three approaches. The results obtained by means of Monte Carlo simulations and from a case of study allowed us to drawn the following conclusions: All approaches are capable of meeting the adopted significant level when they are applied to trend-free uncorrelated series. The approaches are as powerful as the original MK test when they are applied to uncorrelated series. Regarding serially correlated series it was verified that: (i) the performance of the MKDD and MKRD are comparable; (ii) both approaches may not be able to preserve the adopted significance level and (iii) although the MKD is capable of preserving the adopted significance level, it is less powerful than the MKDD and MKRD. Thus, there is a trade-off between the power of the three approaches and their capability of meeting the nominal significance level. Accordingly, we recommend the use of at least two approaches -MKD and MKDD(MKRD)- to evaluate the presence of trends in a given dataset.

Sample Size Reassessment in Non-inferiority Trials

SummaryObjectives: Analysis of covariance (ANCOVA) is widely applied in practice and its use is recommended by regulatory guidelines. However, the required sample size for ANCOVA depends on parameters that are usually uncertain in the planning phase of a study. Sample size recalculation within the internal pilot study design allows to cope with this problem. From a regulatory viewpoint it is preferable that the treatment group allocation remains masked and that the type I error is controlled at the specified significance level. The characteristics of blinded sample size reassessment for ANCOVA in non-inferiority studies have not been investigated yet. We propose an appropriate method and evaluate its performance.Methods: In a simulation study, the characteristics of the proposed method with respect to type I error rate, power and sample size are investigated. It is illustrated by a clinical trial example how strict control of the significance level can be achieved.Results: A slight excess of the type I error rate beyond the nominal significance level was observed. The extent of exceedance increases with increasing non-inferiority margin and increasing correlation between outcome and covariate. The procedure assures the desired power over a wide range of scenarios even if nuisance parameters affecting the sample size are initially mis-specified.Conclusions: The proposed blinded sample size recalculation procedure protects from insufficient sample sizes due to incorrect assumptions about nuisance parameters in the planning phase. The original procedure may lead to an elevated type I error rate, but methods are available to control the nominal significance level.