A Method for Computing State Probabilities under Competing Risks

Lawrence L. Wu, New York University (NYU)
Steven P. Martin, New York University (NYU)

This paper outlines a computationally intensive method for computing state probabilities in problems involving competing risks. Consider individuals who begin life in a single origin state and who are subsequently exposed to j=1,...,J competing risks. We discuss a computationally intensive method that provides, for any arbitrary time t, the J+1 quantities {p_{0}(t), p_{1}(t), ..., p_{J}(t)}, where p_{0}(t) denotes the probability of occupying the origin state at time t and p_{j}(t) denotes the probability of having experienced transition j by time t. The resulting state probabilities provide a more easily interpretable set of quantities that can be useful to those analyzing competing risks.