For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These allow us to optimize parameters randomization schemes. We also suggest and numerically justify a procedure constructing designs with better separability properties than pure illustrate theoretical considerati...

This manuscript investigates sample sizes for interim analyses in group sequential designs. Traditional designs (GSD) rely on “information fraction” arguments to define the sizes. Then, maximum likelihood estimators (MLEs) are used decide whether stop early or continue data collection until next analysis. The possibility of stopping changes distribution and final MLEs: possible decisions trial ...

In this paper, deep holes of Reed-Solomon (RS) codes are studied. A new class of deep holes for generalized affine RS codes is given if the evaluation set satisfies certain combinatorial structure. Three classes of deep holes for projective Reed-Solomon (PRS) codes are constructed explicitly. In particular, deep holes of PRS codes with redundancy three are completely obtained when the character...

We consider the construction of efficient group sequential designs where the goal is a low expected sample size not only at the null hypothesis and the alternative (taken to be the minimal clinically meaningful effect size), but also at more optimistic anticipated effect sizes. Pre-specified Type I error rate and power requirements can be achieved both by standard group sequential tests and by ...