A cohort of individuals exposed to some risk is followed up to a point of timeM, and observations on two random variables (Y, Δ) are recorded for each individual. The variable Δ refers to one of the four possible events that can occur for an individual in the period [0,M]: (i) dies of a specific disease, say cancer, (ii) dies of a natural cause, (iii) withdraws from the study, and (iv) is alive and still under study at timeM. The variableYrefers to the time at which an event occurs. Based on such data fornindividuals, we consider the problem of estimation of a specific occurrence/exposure rate (SOER), which is a risk ratio defined as the ratio of probability of death due to cancer in the interval [0,M]to the mean lifetime of all individuals up to the time pointM. The asymptotic distribution of a nonparametric estimator of SOER is shown to be normal, and the asymptotic variance involves unknown parameters. Various ways of bootstrapping are discussed for construction of confidence intervals for SOER and compared. Some numerical illustrations are provided.