A number of studies have dealt with determination of the age at onset of sperm emission (spermarche), based on observations of first occurrence of spermatozoa in urine. A major problem in this connection is the intermittent occurrence of sperm-negative urine samples after the achievement of spermarche. We have here considered an empirical Bayes approach for handling the probability of a sperm-positive urine sample after spermarche. The investigation was inspired by a concrete longitudinal study concerning 40 Scottish boys, which is used for illustration throughout. In this study, the urine was tested for spermatozoa from well before spermarche and every 3 months thereafter for at most 7 years. Some of the boys left the study earlier and techniques for handling such censoring were also developed.