Comparison of two treatments on a covariate variable.

In clinical trials, the efficacy of treatment might be dependent on the value of a covariate variable. Therefore, it might be possible to detect the region over the covariate variable where the two treatments under investigation do not have significantly different efficacy or the region of superiority of one treatment. The non-significant region can be verified to be a confidence interval for the abscissa of the intersection point of two regression lines, and each of the complementary regions of the confidence interval corresponds to a region of superiority. In this study, we develop a method of constructing the confidence interval based on the concept of a generalized pivotal quantity, so as to perform the task of detecting the possible three regions for a clinical trial. Two real-world examples are given to illustrate the application of our proposed method, and a simulation study is conducted to evaluate its performance.

A non-inferiority test for diagnostic accuracy based on the paired partial areas under ROC curves.

Non-inferiority is a reasonable approach to assessing the diagnostic accuracy of a new diagnostic test if it provides an easier administration or reduces the cost. The area under the receiver operating characteristic (ROC) curve is one of the common measures for the overall diagnostic accuracy. However, it may not differentiate the various shapes of the ROC curves with different diagnostic significances. The partial area under the ROC curve (PAUROC) may present an alternative that can provide additional and complimentary information for some diagnostic tests which require false-positive rate that does not exceed a certain level. Non-parametric and maximum likelihood methods can be used for the non-inferiority tests based on the difference in paired PAUROCs. However, their performance has not been investigated in finite samples. We propose to use the concept of generalized p-value to construct a non-inferiority test for diagnostic accuracy based on the difference in paired PAUROCs. Simulation results show that the proposed non-inferiority test not only adequately controls the size at the nominal level but also is uniformly more powerful than the non-parametric methods. The proposed method is illustrated with a numerical example using published data.

Statistical designs for two-color spotted microarray experiments.

Two-color cDNA or oligonucleotide-based spotted microarrays have been commonly used in measuring the expression levels of thousands of genes simultaneously. To realize the immense potential of this powerful new technology, budgeted within limited resources or other constraints, practical designs with high efficiencies are in demand. In this study, we address the design issue concerning the arrangement of the mRNA samples labeled with fluorescent dyes and hybridized on the slides. A normalization model is proposed to characterize major sources of systematic variation in a two-color microarray experiment. This normalization model establishes a connection between designs for two-color microarray experiments with a particular class of classical row-column designs. A heuristic algorithm for constructing A-optimal or highly efficient designs is provided. Statistical optimality results are found for some of the designs generated from the algorithm. It is believed that the constructed designs are the best or very close to the best possible for estimating the relative gene expression levels among the mRNA samples of interest.