This paper describes results stemming from an in-depth analysis of Higgins' measure of heterogeneity for a meta-analysis applied in the context of meta-analysis for diagnostic problems. Higgins measure of heterogeneity I 2 has been criticized for being confounded by the study-specific sample size, in the sense that different I 2-values can be achieved for the same value of across-study variance if only the study-specific variance is varying enough. In particular, I 2 approaches one for any value of the heterogeneity variance (variance across studies) if the within-study variance becomes large. The paper proposes a measure which is unconfounded by sample size. It is essentially a philosophical question which heterogeneity measure is chosen. Nevertheless, a detailed simulation study has been launched and the results indicate that the newly suggest measure of heterogeneity has beneficial statistical properties. Both measures are also exemplified at hand of some meta-analytic case studies.
Optimal design ideas are increasingly used in different disciplines to rein in experimental costs. Given a nonlinear statistical model and a design criterion, optimal designs determine the number of experimental points to observe the responses, the design points and the number of replications at each design point. Currently, there are very few free and effective computing tools for finding different types of optimal designs for a general nonlinear model, especially when the criterion is not differentiable. We introduce an R package ICAOD to find various types of optimal designs and they include locally, minimax and Bayesian optimal designs for different nonlinear statistical models. Our main computational tool is a novel metaheuristic algorithm called imperialist competitive algorithm (ICA) and inspired by socio-political behavior of humans and colonialism. We demonstrate its capability and effectiveness using several applications. The package also includes several theory-based tools to assess optimality of a generated design when the criterion is a convex function of the design.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.