How large must a dose-optimization trial be?

Recently promulgated Draft Guidance from the US Food and Drug Administration Oncology Center of Excellence (OCE) recommends randomized, parallel dose-response trials for "dose optimization," but with vaguely stated aims that engage none of the statistical principles which typically attend randomization. Here, I advance a criterion for reasonable precision of such trials, and examine its implications for minimum enrollment, within a utility-based framework that acknowledges interindividual heterogeneity simultaneously in pharmacokinetics/pharmacodynamics and in the subjective evaluation of efficacy-toxicity trade-offs. Even when designed and conducted under ideal circumstances, reasonably sized trials of the kind advocated by OCE may need to enroll many hundreds of participants.