To bring correlation between binomial random variables is an important statistical problem with a lot of theoretical and practical applications. In this paper we provide a new formulation of bivariate binomial distribution in the sense that marginally each of the two random variables has a...

In an adaptive clinical trial research, it is common to use certain data-dependent design weights to assign individuals to treatments so that more study subjects are assigned to the better treatment. These design weights must also be used for consistent estimation of the treatment effects as...

We consider experimental designs in a regression set-up where the unknown regression function belongs to a known family of nested linear models. The objective of our design is to select the correct model from the family of nested models as well as to estimate efficiently the parameters...

Optimal allocation designs for the allocation proportion are obtained in the present paper for a two-treatment situation, in a completely correlated setup where the sum of the responses no longer follows a binomial distribution. We consider treatment difference and odds ratio to find the optimal...

In this paper, we show the difference in the variance of the Mantel–Haenszel estimator and the profile maximum likelihood estimator of order O((kn)−3) or less, where the individual variances are of order O(n−1). Here n is the minimum number of samples available for any treatment in any...

In a two-sample clinical trial, a fixed proportion of true-and-surrogate and the remaining only-surrogate responses are observed. We quantify the increase in efficiency to compare the treatments as a linear function of the proportion of available true responses.