  This paper presents the link between stochastic approximation and clinical
trials based on randomized urn models investigated in Bai and Hu (1999,2005)
and Bai, Hu and Shen (2002). We reformulate the dynamics of both the urn
composition and the assigned treatments as standard stochastic approximation
(SA) algorithms with remainder. Then, we derive the a.s. convergence and the
asymptotic normality (CLT) of the normalized procedure under less stringent
assumptions by calling upon the ODE and SDE methods. As a second step, we
investigate a more involved family of models, known as multi-arm clinical
trials, where the urn updating depends on the past performances of the
treatments. By increasing the dimension of the state vector, our SA approach
provides this time a new asymptotic normality result.
