  Response-adaptive allocation designs refer to a class of designs where the
probability an observation is assigned to a treatment is changed throughout an
experiment based on the accrued responses. Such procedures result in random
treatment sample sizes. Most of the current literature considers unconditional
inference procedures in the analysis of response-adaptive allocation designs.
The focus of this work is inference conditional on the observed treatment
sample sizes. The inverse of information is a description of the large sample
variance of the parameter estimates. A simple form for the conditional
information relative to unconditional information is derived. It is found that
conditional information can be greater than unconditional information. It is
also shown that the variance of the conditional maximum likelihood estimate can
be less than the variance of the unconditional maximum likelihood estimate.
Finally, a conditional bootstrap procedure is developed that, in the majority
of cases examined, resulted in narrower confidence intervals than relevant
unconditional procedures.
