Effect of design-adaptive allocation on inference for a regression parameter: Two-group, single-covariate and double-covariate cases

Assignment to treatment group by randomization has been advocated with great success in biomedical trials. Research on optimal experimental design suggests, however, that it should be possible to obtain efficiency gains over randomization by balancing treatment groups with regard to prognostic factors. The only practical way of doing this involves sequential allocation to treatment that evolves during the recruitment period, but any such method has been questioned on the grounds that statistical inference using the estimated treatment effect is suspect. Results reported here show by means of a regression simulation that the estimate obtained from a dynamically balanced trial is unbiased, and a new estimate of its standard deviation is similarly shown to be unbiased. If one does not adjust for the balancing factors in the analysis, then randomization is frequently unacceptably inefficient. If one does adjust, then the efficiency advantage of balancing is modest on average, but still important in an appreciable fraction of trials with small sample sizes.