An application of Pólya theory to cross-over designs with dropout
Abstract
Cross-over experiments in, for example, clinical and medical research often have subjects (patients) who fail to complete the sequence of treatments allocated to them in the planned design. Methodology has been developed for evaluating the robustness of a cross-over design to such dropouts. Implementing the methodology requires the assessment of a large number of designs and is computationally demanding, even for studies involving small numbers of subjects. This paper establishes an analogy between the design problem and enumeration problems encountered in combinatorial theory. It shows how the computations can be substantially reduced by applying results associated with Pólya theory making feasible an evaluation of the robustness of a design.
