Urn Models for Response-Adaptive Designs

The essential feature of controlled clinical trials is the random assignment of subjects to two or more treatment groups under investigation. The principle of randomization provides a protection against hidden biases and thus increases the validity of the trial’s findings.

In recent years, there has been an increasing interest, in the context of clinical trials research, in response-adaptive designs. This is because response-adaptive designs are sequential procedures that can skew, along the experiment, the allocation probabilities of statistical units on the base of previous allocations and responses. In a clinical trial to compare two or more treatments, the experimenter faces two simultaneous goals: collecting evidence to determine the superior treatment, and skewing the allocations toward the superior treatment in order to reduce the proportion of patients that receive the worst treatment. The first is an inferential goal and concerns future patients’ interest; the second is an ethical responsibility and concerns the current study patients’ interest.

A large class of response-adaptive randomized designs is based on urn models, since they represent a classical tool to guarantee a randomized device for the allocation of the treatments to the subjects. Some of these models generates designs whose proportion of subjects assigned to treatments converge to specific unknown values. Other urn models allows the design to asymptotically assign all subjects to the superior treatment.

In particular the group is involved in the study of:

  • response-adaptive urn models targeting the best treatment;
  • response-adaptive urn models targeting a desired unknown allocation proportion;
  • asymptotic and inferential properties of the reinforced urn models.