Numerical solution of optimal allocation problems in stratified sampling under box constraints

Modern sampling designs in survey statistics, in general, are constructed in order to optimize the accuracy of estimators such as totals, means and proportions. In stratified random sampling a variance minimal solution was introduced by Neyman and Tschuprov. However, practical constraints may lead to limitations of the domain of sampling fractions which have to be considered within the optimization process. Special attention on the complexity of numerical solutions has to be paid in cases with many strata or when the optimal allocation has to be applied repeatedly, such as in iterative solutions of stratification problems. The present article gives an overview of recent numerical algorithms which allow adequate inclusion of box constraints in the numerical optimization process. These box constraints may play an important role in statistical modeling. Furthermore, a new approach through a fixed point iteration with a finite termination property is presented.     

Conditionally unbiased estimation in the normal setting with unknown variances

To efficiently and completely correct for selection bias in adaptive two-stage trials, uniformly minimum variance conditionally unbiased estimators (UMVCUEs) have been derived for trial designs with normally distributed data. However, a common assumption is that the variances are known exactly, which is unlikely to be the case in practice. We extend the work of Cohen and Sackrowitz (Statistics & Probability Letters, 8(3):273-278, 1989), who proposed an UMVCUE for the best performing candidate in the normal setting with a common unknown variance. Our extension allows for multiple selected candidates, as well as unequal stage one and two sample sizes.     

An evaluation of methods for testing hypotheses relating to two endpoints in a single clinical trial

The issues and dangers involved in testing multiple hypotheses are well recognised within the pharmaceutical industry. In reporting clinical trials, strenuous efforts are taken to avoid the inflation of type I error, with procedures such as the Bonferroni adjustment and its many elaborations and refinements being widely employed. Typically, such methods are conservative. They tend to be accurate if the multiple test statistics involved are mutually independent and achieve less than the type I error rate specified if these statistics are positively correlated. An alternative approach is to estimate the correlations between the test statistics and to perform a test that is conditional on those estimates being the true correlations. In this paper, we begin by assuming that test statistics are normally distributed and that their correlations are known. Under these circumstances, we explore several approaches to multiple testing, adapt them so that type I error is preserved exactly and then compare their powers over a range of true parameter values. For simplicity, the explorations are confined to the bivariate case. Having described the relative strengths and weaknesses of the approaches under study, we use simulation to assess the accuracy of the approximate theory developed when the correlations are estimated from the study data rather than being known in advance and when data are binary so that test statistics are only approximately normally distributed.