Serial measurements of prostate-specific antigen (PSA) are used as a biomarker for men diagnosed with prostate cancer following an active monitoring programme. Distinguishing pathological changes from natural age-related changes is not straightforward. Here, we compare four approaches to modelling age-related change in PSA with the aim of developing reference ranges for repeated measures of PSA. A suitable model for PSA reference ranges must satisfy two criteria. First, it must offer an accurate description of the trend of PSA on average and in individuals. Second, it must be able to make accurate predictions about new PSA observations for an individual and about the entire PSA trajectory for a new individual.