In this paper a new P¶olya urn model is introduced and studied; in particular, a strong law of large
numbers and two central limit theorems are proven. This urn generalizes a model studied in Berti et
al. (2004), May et al. (2005) and in Crimaldi (2007) and it has natural applications in clinical trials.
Indeed, the model include both delayed and missing (or null) responses. Moreover, a connection with
the conditional identity in distribution of Berti et al. (2004) is given.