Steady-state probabilities for regenerative semi-Markov processes with application to prevention and screening

There is a growing interest in planning and implementing broad-scale clinical trials with a focus on prevention and screening. Often, the data-generating mechanism for such experiments can be viewed as a semi-Markov process. In this communication, we develop general expressions for the steady-state probabilities for regenerative semi-Markov processes. Hence, the probability of being in a certain state at the time of recruitment to a clinical trial can be calculated. An application to breast cancer prevention is demonstrated.