Models for cluster randomized designs using ranked set sampling.

Cluster randomized designs (CRD) provide a rigorous development for randomization principles for studies where treatments are allocated to cluster units rather than the individual subjects within clusters. It is known that CRDs are less efficient than completely randomized designs since the randomization of treatment allocation is applied to the cluster units. To mitigate this problem, we embed a ranked set sampling design from survey sampling studies into CRD for the selection of both cluster and subsampling units. We show that ranking groups in ranked set sampling act like a covariate, reduce the expected mean squared cluster error, and increase the precision of the sampling design. We provide an optimality result to determine the sample sizes at cluster and sub-sample level. We apply the proposed sampling design to a dental study on human tooth size, and to a longitudinal study from an education intervention program.

Design and analysis of two-phase experiments for gene expression microarrays-part I.

Gene expression microarray experiments are intrinsically two-phase experiments. Messenger RNA (mRNA), required for the microarray experiment, must first be derived from plants or animals that are exposed to a set of treatments in a previous experiment (Phase 1). The mRNA is then used in the subsequent laboratory-based microarray experiment (Phase 2) from which gene expression is measured and ultimately analyzed. We show that obtaining a valid test for the effects of treatments on gene expression depends on the design of both the Phase 1 and Phase 2 experiments. Examples show that the multiple dye-swap design at Phase 2 is more robust than the alternating loop design in the absence of prior knowledge of the relative size of variation in the Phase 1 and Phase 2 experiments.