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Recently, Rigon and Durante (2018) discussed a Bayesian nonparametric dependent mixture model, which is based on a predictor-dependent stick-breaking construction. They provided theoretical support and proposed a variety of algorithms for posterior inference, including a Gibbs sampler. Their results rely on a formal representation of the stick-breaking construction, which has an appealing interpretation in terms of continuation-ratio logistic regressions. In this paper we review the contribution of Rigon and Durante (2018), and we extend their proposal to the case of partial exchangeability with count data. As an illustration of this methodology, we analyze the number of epileptic seizures of a single patient in a clinical trial.