Detecting a treatment-biomarker interaction, which is a task better suited for large sample sizes, in a phase II trial, which has a small sample size, is challenging. In this paper, we investigate how two plausibly available sources of historical data may contain partial information to help estimate the treatment-biomarker interaction parameter in a randomized phase II study. The parameter is n...

In statistical analysis, we usually use the observed sample values x1, . . . , xn to compute the values of several statistics v(x1, . . . , xn) – such as sample mean, sample variance, etc. The usual formulas for these statistics implicitly assume that we know the exact values x1, . . . , xn. In practice, the sample values x̃1, . . . , x̃n come from measurements and are, thus, only approximations ...

Although the distribution of frequencies of genes influencing quantitative traits is important to our understanding of their genetic basis and their evolution, direct information from laboratory experiments is very limited. In theory, different models of selection and mutation generate different predictions of frequency distributions. When a large population at mutation-selection balance passes...

Maturation of the striatum has been posited to play a primary role in observed increases in adolescent sensation-seeking. However, evidence of neurophysiological maturation in the human adolescent striatum is limited. We applied T2*-weighted imaging, reflecting indices of tissue-iron concentration, to provide direct in vivo evidence of neurophysiological development of the human adolescent stri...

Microarray technology allows a scientist to study genomewide patterns of gene expression. Thousands of individual genes are measured with a relatively small number of replications, which poses challenges to traditional statistical methods. In particular, the gene-specific estimators of variances are not reliable and gene-by-gene tests have low powers. In this article we propose a family of shri...

ABSTRACT. In paired randomized experiments units are grouped in pairs, often based on covariate information, with random assignment within the pairs. Average treatment effects are then estimated by averaging the within-pair differences in outcomes. Typically the variance of the average treatment effect estimator is estimated using the sample variance of the within-pair differences. However, con...

Some properties of the sample mean and sample variance of a long memory process are described. It is shown that for a particular class of long memory processes the asymptotic relative efficiency of the k -decimated sample mean xn (k) (formed by taking the mean of every k -th observation) with respect to the sample mean xn of all n observations is 1, but that the deficiency (as defined by Hodges...

The number of substitutions (of nucleotides, amino acids, etc.) that take place during the evolution of a sequence is a stochastic variable of fundamental importance in the field of molecular evolution. Although the mean number of substitutions during molecular evolution of a sequence can be estimated for a given substitution model, no simple solution exists for the variance of this random vari...