Mixed‐effects regression models for studying the natural history of prostate disease

Although prostate cancer and benign prostatic hyperplasia are major health problems in U.S. men, little is known about the early stages of the natural history of prostate disease. A molecular biomarker called prostate specific antigen (PSA), together with a unique longitudinal bank of frozen serum, now allows a historic prospective study of changes in PSA levels for decades prior to the diagnosis of prostate disease. Linear mixed-effects regression models were used to test whether rates of change in PSA were different in men with and without prostate disease. In addition, since the prostate cancer cases developed their tumours at different (and unknown) times during their periods of follow-up, a piece-wise non-linear mixed-effects regression model was used to estimate the time when rapid increases in PSA were first observable beyond the background level of PSA change. These methods have a wide range of applications in biomedical research utilizing repeated measures data such as pharmacokinetic studies, crossover trials, growth and development studies, aging studies, and disease detection.