The beta-binomial distribution is resulted when the probability of success per trial in the binomial distribution varies in successive trials and the mixing distribution is from the beta family. For experiments with binary outcomes, often it may happen that observations exhibit some extra binomial variation and occur in clusters. In such experiments the beta-binomial distribution can generally provide an adequate fit to the data. Here, we introduce an alternative when the mixing distribution is assumed to be from the log-Lindley family. The properties of this new model are explored and it is shown that similar to the beta-binomial distribution, the log-Lindley binomial distribution can also be applied in modeling clustered binary outcomes. An example with real experimental data from a developmental toxicity experiment is utilized to provide further illustration.

Risk ratio is usually the parameter of interest in epidemiologic and medical studies. Poisson regression model is an approach used to directly estimate risk ratio. When Poisson regression is applied to binomial data, the error for the estimated risk ratio will be overestimated. In other words, Poisson regression is likely to compute a confidence interval that is conservative. In this paper we aim at devising a modified Poisson regression method to rectify this problem.Methods: To illustrate modified Poisson regression, a simple 2-by-2 contingency table was used. Simple computation was performed to estimate variance. We compared ordinary and modified Poisson regression models by actual data from a study on predictors of coronary artery disease.Results: Application of ordinary and modified Poisson regression methods resulted in an estimated relative risk of 1.68 for hypercholesterolemia. The confidence intervals provided by these two methods were 1.005-2.82 and 1.05-2.68, respectively. The confidence interval provided by the modified Poisson regression was 10 percent narrower than that obtained by the ordinary method.Conclusion: Applying modified Poisson regression to cohort studies with binary data, compared with ordinary Poisson regression, reduces variance and increases precision of the estimated risk ratio. This method might result in different findings from ordinary Poisson regression for borderline statistical significance.

Sample size calculations are now mandatory for many research protocols and it is a main question before accomplishing a research. This paper outlines the ways of calculating sample sizes in clinical trial studies with two groups: binary, ordered categorical, and continuous outcomes. In each section a table for calculating sample size and working examples are given.

This paper presents an improved approach for handling stress constraints in minimum weight topological design. The Finite Element Method (FEM) and the material model of Solid Isotropic Material with Penalization (SIMP) are used to formulate the topology optimization problem. To evaluate the stress values in elements, the von Mises stresses are calculated at the so called super-convergent Gauss quadrature points. To reduce the time and computational cost, a clustering approach is here adopted and the P -norm integrated stress constraints are used. Doing this, a large number of local constraints are replaced with a few global ones and consequently the stress constraint sensitivities are calculated by using the adjoint method. The employed formulation as well as a complete explanation of the sensitivity analysis is provided. Due to the complexity of the topology optimization problem in the presence of stress constraints, the Method of Moving Asymptotes (MMA) is here employed. To demonstrate the performance and capability of the procedure, a couple of plane stress elasticity problems are taken into consideration. The resulted layouts indicate the superiority of the approach in generating acceptable and practical topological designs.