Prostate-specific antigen (PSA) is a biomarker commonly used to screen for prostate cancer. Several studies have examined PSA growth rates prior to prostate cancer diagnosis. However, the resulting estimates are highly variable. In this article we propose a non-linear Bayesian hierarchical model to combine longitudinal data on PSA growth from three different studies. Our model enables novel investigations into patterns of PSA growth that were previously impossible due to sample size limitations. The goals of our analysis are twofold: first, to characterize growth rates of PSA accounting for differences when combining data from different studies; second, to investigate the impact of clinical covariates such as advanced disease and unfavorable histology on PSA growth rates.