Rank-sum test for two-sample location problem under order restricted randomized design.

摘要

There are many experimental settings, where experimental units have abundance of information. This information is usually available in two forms, either in formal measurements or in informal observations. While the formal measurements are successfully used in traditional analyses as covariates, the informal observations are usually ignored. The order restricted randomized design (ORRD) exploits the use of these informal observations (subjective information) to design an experiment. Sets of experimental units are recruited from a population along with subjective information that they may have. This subjective information is then used to create artificial covariates through judgment ranking of the experimental units. Artificial covariates, with restricted randomization of treatment regimes to experimental units, induce a positive correlation structure among within-set response measurements. This positive correlation structure then acts as a variance reduction technique in the inference of a contrast parameter in an ORRD. This dissertation develops statistical inference based on ORRD for the location shift between two populations.; Chapter 1 provides a review for existing designs in the literature that are closely connected to ORRD. Chapter 2 introduces a new nonparametric test based on the ORRD for the location shift between two populations. Sections 2.1 and 2.2 develop an asymptotic theory for the null distribution of the test statistic. Section 2.3 constructs an optimal design that maximizes the asymptotic Pitman efficacy of the proposed test. Section 2.4 shows that the size of the test is inflated if the design has some judgment ranking error. Section 2.5 develops point and interval estimates for the location shift parameter.; Chapter 3 develops an asymptotic theory under imperfect ranking and provides a calibration technique to reduce the impact of ranking error. It is shown that the test performs quite well even under imperfect ranking with this calibration. Chapter 4 provides simulation results for the empirical power of the test. Chapter 5 applies the proposed procedure to a clinical trial to draw inference on the difference between control and treatment regimes. Finally Chapter 6 provides some concluding remarks and discusses some open problems for future work.