Rank regression in order restricted randomised designs

This paper uses order restricted randomised design (ORRD) to create a judgment ranked blocking factor based on available subjective information in a small set of experimental units (EUs). The design then performs a carefully designed randomisation scheme with certain restriction to assign the treatment levels to EUs across these subjective judgment blocks. Such an assignment induces positive dependence among within-set units, and the restrictions on the randomisation translate this positive dependence into a variance reduction technique. We provide a unified theory to analyse the data sets collected from an ORRD. The analysis uses the general framework of rank regression methodology in linear models, with some modification to our randomisation scheme, to estimate regression parameter and to test general linear hypotheses. It is shown that the estimators and test statistics have limiting normal and chi-square distributions regardless the quality of ranking information. A simulation study shows that the asymptotic results remain valid even for relatively small sample sizes. The proposed tests are applied to a clinical trial data set.