I am planning to conduct a study where we will be modelling waiting times for patients receiving radiotherapy based on the following - number of patients with a cancer, number of treatments given on a machine for each patient (known as fractions in radiotherapy parlance) and average number of patients on a machine. The waiting time will be captured in days and will be an estimate (rather than the actual waiting time). Based on literature review this may range between 15 - 120 days with most observations likely to fall around the 40 -50 day mark. Once this model is developed, validated (robust internal validation) and calibration checked we will be using this to predict the reduction in waiting time that can be achieved if the number of treatments can be reduced by use of hypofractionated radiotherapy. I had initially thought of using a linear regression for this problem but would like to take the opinion of the experts on alternatives.

That looks like an excellent reference @Jochen. In more general situations where there are competing risks and intervening events, and detailed patient-level data are available, consider state transition models. These are initially used to model the probability of changing states (e.g., of being indicated for a therapy and moving from a day in which the therapy is unavailable to a day at which it is available) and are converted to state occupancy probabilities and are used for computing the median or mean time in a state. So you could explicitly model, as a function of time, patient characteristics, and availability of a new treatment modality, the probability of getting the new treatment explicitly given that the patient is still alive and not disqualified for therapy because of too advanced new disease.

Many thanks for the reference @Jochen and @f2harrell for the guidance. I will go through the full text and revert back in case of queries.