In some clinical studies, treatment is a cumulative measure over time and, hence, different treatment levels refer to different treatment lengths. In the same studies, patients may be subject to a variety of competing events that interrupt treatment or otherwise cause the treatment process to halt. In randomized studies, the standard analysis is an intent-to-treat analysis of the assigned treatment length, ignoring all treatment interruptions. Alternatively, one can model the outcome as a function of observed treatment length and treatment interruption. The latter approach leads naturally to a potential outcome framework which may be extended to observational studies where the intent-to-treat analysis is not possible. We present this framework, some early work on this problem and its connections to dynamic treatment regimes. As time permits, we will also present some new results on semi-parametric efficient estimation. The methods are motivated from and illustrated in the ESPRT infusion trial. Other applications will also be discussed.