Odds ratio for a single 2 × 2 table with correlated binomials for two margins

While analyzing 2 × 2 contingency tables, the log odds ratio for measuring the strength of association is often approximated by a normal distribution with some variance. We show that the expression of that variance needs to be modified in the presence of correlation between two binomial distributions of the contingency table. In the present paper, we derive a correlation-adjusted variance of the limiting normal distribution of log odds ratio. We also propose a correlation adjusted test based on the standard odds ratio for analyzing matched-pair studies and any other study settings that induce correlated binary outcomes. We demonstrate that our proposed test outperforms the classical McNemar’s test. Simulation studies show the gains in power are especially manifest when sample size is small and strong correlation is present. Two examples of real data sets are used to demonstrate that the proposed method may lead to conclusions significantly different from those reached using McNemar’s test.     

Group sequential designs using both type I and type II error probability spending functions

We propose flexible group sequential designs using type I and type II error probability spending functions. The proposed designs preserve the overall significance level and power and allow the repeated testing to be perloimed at a flexible schedule. Computational methods are described. An example on a mega clinical trial is provided.     

Block Bootstrapping for Kernel Density Estimators under ψ-Weak Dependence

Block bootstrap methods are applied to kernel-type density estimator and its derivatives for ψ-weakly dependent processes. Nonparametric density estimation is discussed via moving block bootstrap (MBB) and disjoint block bootstrap (DBB). Asymptotic validity is proved for MBB and DBB. A Monte-Carlo experiment compares confidence intervals based on MBB and DBB with an existing method based on normal approximation (NA) in terms of serial correlation, dynamic asymmetry, and conditional heteroscedasticity. The experiment shows that, in cases of substantial serial correlation, MBB and DBB perform better than NA and, in the other cases, MBB and DBB perform as good as NA.     

The Diversity Imperative: The Effects of Local Economic Structure and Social Capital on Local Philanthropy

VOLUNTAS: International Journal of Voluntary and Nonprofit Organizations - Philanthropic endeavors are a form of institutionalized collective action that enhances a community’s capacity to...