More Efficient Treatment Comparison in Cross-Over Design by Allocating Subject Based on Ranked Auxiliary Variables

In public health studies, there are many diseases hard to cure or health-risk factors hard to clearly eliminate from environment. But there are ways to moderating its effect to health. In such studies, the effect of treatments is primary interests of those experiments. The sequence in which the subjects receive treatments is not of interest. Experiments are designed in such a way that each subject, is given a number of treatments with the object of studying differences between these treatments. This experimental design, named cross-over design is widely used in clinical studies, behavioral interventions, environment experiments, epidemiology researches and animal studies. Many studies use Latin Square with cross-over design. It is used to eliminate two nuisance sources of variability. To allow inference from sampling results back to the population, simple random sample is widely used as a strategy of selection representative sample in cross-over studies. There are several desirable properties about simple random sample: easy to understand, easy to use, no selection bias, and it produces an unbiased estimator for the population mean. However, occasionally simple random sample cannot produce representative samples. Under some experimental setting, when nuisance factor is known and controllable, making an informal measurement on a unit is far cheaper than making a formal measurement, simple random sample may also become expensive. One solution to address these deficiencies in experiments is to construct an informative sampling design using available related information. Ranked set sampling is introduced to improve the efficiency of treatment comparison in cross-over design.