In clinical trials, it is frequently of interest to estimate the time between the onset of two events (e.g. duration of response in oncology). Here, we consider the case where subjects are assessed at fixed visits but the initial event and the terminating event occur in between visits. This type of data, called doubly interval censored, is often analyzed with standard survival techniques, assuming either that the survival time (between initial and terminating event) is known exactly or is single interval censored. We introduce a motivating dataset in which the interest is to evaluate the impact of the treatment on the duration of response endpoint. We review the existing approaches and discuss their limitations with respect to the characteristics of our motivating dataset. Furthermore, we propose a stochastic EM algorithm that overcomes the problems in the existing approaches. We show by simulations the finite sample properties of our approach.