1. Adaptive experiments for comparative
trials. In general, sequential designs are stochastic
processes, where the dependence structure changes on the basis of
the information that will be used in the future assignments. In
this context we have analyzed the properties of sequential designs
(asymptotic optimality, speed of convergence, correct inferential
approach ...) both for response-adaptive and design-adaptive
procedures. Furthermore, we have introduced some new proposals of
restricted randomization mechanism, based on Polya urn models and
suitable Markov chains, for balancing the sequential allocation of
two treatments in clinical trials.
2. Dose-escalation
experiments. Traditionally, dose-escalation experiments are
binary clinical trials designed for the estimation of the dose with
a prefixed probability of toxicity. In this setting we have
proposed some extensions of the classical Up&Down procedures
(assuming that the dose-allocation process is random and subjects
are treated in groups), particularly useful even for
non-dichotomous responses.
3. Optimal design theory for
non-linear problems. Response-adaptive experiments represents a
natural solution for local optimality problems, which occur very
often in the so-called non-linear problems. The research activity
was focused on asymptotic inference and asymptotic optimality for
sequential procedures. Furthermore, the optimal design theory was
applied to random fields regression models, namely regressive
models with correlated observations, very popular in the analysis
of Computer Experiments.
4. Statistical applications to
clinical trials, jointly with the Neurological Unit of the
University of Bologna (Azienda Ospedaliera
di Bologna, Policlinico S. Orsola–Malpigli).
