Endpoints in clinical trials are often highly correlated. However, the commonly used multiple testing procedures in clinical trials either do not take into consideration the correlations among test statistics or can only exploit known correlations. Westfall and Young constructed a resampling-based stepdown method that implicitly utilizes the correlation structure of test statistics in situations with unknown correlations. However, their method requires a “subset pivotality” assumption. Romano and Wolf proposed a more general stepdown method, which does not require such an assumption. There is at present little experience with the application of such methods in analyzing clinical trial data. We advocate the application of resampling-based multiple testing procedures to clinical trials data when appropriate. We have conjectured that the resampling-based stepdown methods can be extended to a stepup procedure under appropriate assumptions and examined the performance of both stepdown and stepup methods under a variety of correlation structures and distribution types. Results from our simulation studies support the use of the resampling-based methods under various scenarios, including binary data and small samples, with strong control of Family wise type I error rate (FWER). Under positive dependence and for binary data even under independence, the resampling-based methods are more powerful than the Holm and Hochberg methods. Last, we illustrate the advantage of the resampling-based stepwise methods with two clinical trial data examples: a cardiovascular outcome trial and an oncology trial. 相似文献
To maximize the ecological services of urban forests, a better understanding of the effects of urbanization on urban forest characteristics, landscape metrics, and their associations is needed for landscape-related regulations in space-limited green infrastructure of metropolitan regions. In this study, Harbin, a typical fast-growing provincial-capital city in Northeast China, is used as a case study. Based on remote sensing images, field surveys, and correlation and variation partitioning analyses, we conclude that landscape characteristics and forest attributes have large variations among different urbanization intensity (UI) regions. Forest patch density (PD), landscape shape index, woody plants species richness, and the Shannon–Wiener index (H′) increased linearly, while stem section area and tree height decreased linearly with the increasing of UIs. UI had a greater influence on tree size and forest community attributes than the forest landscape pattern. Accordingly, any landscape regulation on forest attributes should be implemented according to UIs. In addition, Euclidean nearest neighbor distance(ENN-MN), mean perimeter-area ratio (PARA-MN), fractal dimension index(FRAC-MN), and PD could probably indicate forest attributes the most, e.g., the increase of PARA-MN may be accompanied with taller trees in low and heavy UI regions, but lower woody plants species evenness in low and medium UI regions. More diversified woody plants species, and afforested areas should be advocated in a low UI region, while in a heavy UI region, the conservation of large trees should be implemented. Our results highlight that the implementation of urban forest management should vary according to different urbanization regions to maximize ecological services.
AbstractThe problem of testing equality of two multivariate normal covariance matrices is considered. Assuming that the incomplete data are of monotone pattern, a quantity similar to the Likelihood Ratio Test Statistic is proposed. A satisfactory approximation to the distribution of the quantity is derived. Hypothesis testing based on the approximate distribution is outlined. The merits of the test are investigated using Monte Carlo simulation. Monte Carlo studies indicate that the test is very satisfactory even for moderately small samples. The proposed methods are illustrated using an example. 相似文献