Inference for sequential experiments with an adaptive treatment allocation and/or an adaptive stopping rule

The main purpose of this paper is to provide a critical approach to asymptotic inference on treatment effects for response-adaptive experiments. Some recently obtained results of Baldi Antognini and Giovagnoli (2004) on the asymptotic optimality (in Kiefer's sense) of suitable sequential randomized experiments are compared with the existing literature and some examples are provided. Since inverse sampling schemes may be regarded as special cases of response-adaptive designs, the same results can then be applied to this type of sampling too. Furthermore, adaptive stopping rules can be combined with adaptive allocation rules, thereby also extending the adaptive design methodology to include random sample size. In this paper we draw attention to the still relatively little-known literature and indicate some inferential problems which the very nature of the sequential procedures gives rise to.