Some large trial properties of minimum likelihood allocation

The method of minimum likelihood allocation (MLA) for allocating subjects to treatments in a clinical trial amounts to checking at each stage which allocation would lead an outside observer to find the least evidence of a relationship between treatment and factors of prognostic significance, assuming that the observer would use a linear exponential model. One advantage of MLA is that results from game theory and likelihood theory can be used to prove it has desirable long run properties. Two of these demonstrated here are (1) ‘consistency’, in the sense that the average likelihood ratio which measures design imbalance tends to zero, and (2) ‘efficiency’ in the sense that the variance estimates of treatment effects will tend to be minimized in the long run.