We present an adaptive dose-finding method, based on a joint model of repeated continuous activity measurements and a probit interval censored time-to-first DLT, with a shared random effect, using skewed normal distribution properties. Estimation relies on exact likelihood, that does not require distribution approximation, an important property in the context of small sample sizes. The objective is to identify the optimal dose (OD), which is defined as the lowest dose within a range of highly active doses. The MTD is associated to some cumulative risk of DLT over a predefined number of treatment cycles. In the design we consider the important case of missing at random data that stem from unacceptable toxicity, lack of activity and rapid deterioration of phase I patients. In a set of linear dose-activity models with constant activity beyond all possible dose levels, we select the one with minimum AIC. This allows increasing modeling flexibility, while still having exact likelihood formulation. Operating characteristics were explored via simulations in various scenarios. The percentage of correct OD selection was quite high and patients were not exposed to highly toxic doses.