DLT is an urn-based method where treatment assignment is determined by a simulated urn. By removing balls when the treatment fails and by adding balls uniformly so that no type runs out, we can balance the trial allocation in a sensible way.
The actual algorithm, for a two treatment study:
Consider an urn containing three types of balls. Balls of types 1 and 2 represent treatments. Balls of type 0 are termed immigration balls. When a subject arrives, one ball is drawn at random. If a treatment ball of type k (1 or 2) is selected, the k-th treatment is given to the subject and the response is observed. If it is a failure, the ball is not replaced. If the treatment is a success, the ball is replaced and consequently, the urn composition remains unchanged. If an immigration ball (type 0) is selected, no subject is treated, and the ball is returned to the urn together with two additional treatment balls, one of each treatment type. This procedure is repeated until a treatment ball is drawn and the subject treated accordingly. The function of the immigration ball is to avoid the extinction of a type of treatment ball.
Extending DLT to multi-treatment settings is as simple as adding additional ball types.
Simulation studies show that DTL performs very well as a way to maximise statistical power. I’ve read that this is because it (1) approaches the correct ratio asymptotically and (2) has lower variance than other proposed methods, although I don’t have an intuitive understanding of why this is.
I’ve had a look around and this paper has a nice summary of the method (and proposes how it should handle delayed responses).
Can you briefly explain how DTL works?
DLT is an urn-based method where treatment assignment is determined by a simulated urn. By removing balls when the treatment fails and by adding balls uniformly so that no type runs out, we can balance the trial allocation in a sensible way.
The actual algorithm, for a two treatment study:
(Source)
Extending DLT to multi-treatment settings is as simple as adding additional ball types.
Simulation studies show that DTL performs very well as a way to maximise statistical power. I’ve read that this is because it (1) approaches the correct ratio asymptotically and (2) has lower variance than other proposed methods, although I don’t have an intuitive understanding of why this is.
I’ve had a look around and this paper has a nice summary of the method (and proposes how it should handle delayed responses).