Abstract: A model for selection bias in a large, single blind clinical trial is presented. The actual Type I error rate is evaluated, and this is used to quantify the degree of selection bias under random permuted block designs. The approach utilizes results from the theory of random walks to show rigorously that when the total number of patients is fixed and there is only one investigator, the least bias occurs when there is a single block (random allocation). Even under random allocation, however, the bias does not become negligible as the number of patients becomes large. It is also shown that if the total number of patients and blocks is fixed, the bias is maximized when the blocks are all the same size. On the other hand, if there are two or more investigators, each aware only of his own assignments and each attempting to bias the results, the bias appears to be minimized when the investigators enter the same number of patients.
Key words and phrases: Random allocation, random permuted blocks, returns to the origin of a constrained or unconstrained random walk, selection bias.