Understanding the progression of labor in women has long been a challenge for obstetricians, especially the association between various stages of labor. The first stage of labor during which the woman dilates to 10 cm and the second stage of labor during which she pushes to expel the fetus are of primary interest. Consequently, assessing the joint distributions of the durations of these two stages is of considerable interest. Given that women are only observed after they get admitted to hospital when they are already dilated to a certain level, the data on the first stage duration is length biased. Also, the duration of second stage of labor is competing risks type of data, as her delivery mode can be either spontaneous or due to medical interventions. We propose a shared parameter joint model for the durations of the two stages which take into account the unknown truncation time of the first stage duration as well as the competing risks in the second stage. The proposed approach also allows for prediction of second stage duration based on the first stage characteristics and the fitted joint model. The proposed methods are illustrated on Consortium of Safe Labor Study.