A RANDOM-WALK RULE FOR PHASE-I CLINICAL-TRIALS

We describe a family of random walk rules for the sequential allocatio n of dose levels to patients in a dose-response study, or phase I clin ical trial. Patients are sequentially assigned the next higher, same, or next lower dose level according to some probability distribution, w hich may be determined by ethical considerations as well as the patien t's response. It is shown that one can choose these probabilities in o rder to center dose level assignments unimodally around any target qua ntile of interest. Estimation of the quantile is discussed; the maximu m likelihood estimator and its variance are derived under a two-parame ter logistic distribution, and the maximum likelihood estimator is com pared with other nonparametric estimators. Random walk rules have clea r advantages: they are simple to implement, and finite and asymptotic distribution theory is completely worked out. For a specific random wa lk rule, we compute finite and asymptotic properties and give examples of its use in planning studies. Having the finite distribution theory available and tractable obviates the need for elaborate simulation st udies to analyze the properties of the design. The small sample proper ties of our rule, as determined by exact theory, compare favorably to those of the continual reassessment method, determined by simulation.