An adaptive randomized design with application to estimation

Abstract

When allocating observations to two populations for estimation or testing, the optimal proportion of the data that should be allocated to the first population, if it exists, often depends on unknown parameters. Adaptive designs have thus been proposed, in which allocation of the next observation is based on an estimate of the optimal proportion computed from the data already gathered. The authors introduce a simple randomized adaptive design and give some of its properties. Applications are given to estimating the difference of two success probabilities, and the difference of two normal means.

Two-treatment covariate-dependent response adaptive allocation design for dichotomous response

“…Consequently, for both the choices of the estimates, we get ρ j+1 ≥ a G 4(j + 1) for any j. Hence the result follows from the Proposition 2 of Melfi, Page, and Geraldes (2001).…”

Inference for a RPW‐Type Clinical Trial with Repeated Monitoring for the Treatment of Rheumatoid Arthritis

“…Note that this likelihood is unaffected by the adaptive nature of the allocation design and can be used for making inference on the model parameters. See Melfi et al (2001) for an excellent discussion in this context (see also Ware, 1989;Berger and Wolpert, 1984). This likelihood is in very general terms and holds for any general model involving q T; j 's and q P; j 's, or for the joint distribution of the Z sj 's.…”

An urn model to construct an efficient test procedure for response adaptive designs

“…For this reason we can apply Proposition 3.1 of Aletti et al (2013) concerning the adaptive estimators M(n) and N (n) defined in (7), which is a consequence of Theorem 2 of Melfi et al (2001), i.e.…”

“…However, because of this asymptotic behavior, RRU models are not in the class of designs targeting a proportion in (0, 1), that usually is previously fixed or computed to optimize some suitable criteria. Hence, all the asymptotic properties concerning these procedures presented in literature [see for instance Melfi and Page (2000), Melfi et al (2001)], are not straightforwardly fulfilled by the RRU designs.…”

“…m R > m W . The asymptotic properties of MRRU studied in Aletti et al (2013) and Ghiglietti and Paganoni (2014), together with results about adaptive estimators proved in Melfi et al (2001), are crucial for the procedure presented in this paper.…”