Utilization of run lengths in bonus play-the-winner rules for clinical trials

We consider play-the-winner(PW)schemes which use memory of results on previous patients, as embodied in length of success runs, to allocate treatments for future patients. A computer-aided Markov chain approach is used to obtain exact results for the probability of correct selection, ASN, and expected number of patients on the inferior treatment. Excluding the case of small treatment success probabilities, our plans seem to perform somewhat better than an improved PW plan suggested by Hsi and Louis(1975)and far better than the randomized PW plan suggested by Wei and Durham(1978). Our results also suggest the interesting observation that for our plans the use of even more extensive memory led to a slight deterioration of performance.