Bias induced by adaptive dose-finding designs

There is a long literature on bias in maximum likelihood estimators. Here we demonstrate that adaptive dose-finding procedures (such as Continual Reassessment Methods, Up-and-Down and Interval Designs) themselves induce bias. In particular, with Bernoulli responses and dose assignments that depend on prior responses, we provide an explicit formula for the bias of observed response rates. We illustrate the patterns of bias for designs that aim to concentrate dose allocations around a target dose, which represents a specific quantile of a cumulative response-threshold distribution. For such designs, bias tends to be positive above the target dose and negative below it. To our knowledge, this property of dose-finding designs has not previously been recognized by design developers. We discuss the implications of this bias and suggest a simple shrinkage mitigation formula that improves estimation at doses away from the target.