After adjusting for confounders, regression analysis showed linear relationships between the AAPS (β = 0.605, p = 0.006), ATR (β = 70.76, p = 0.005), CR (β = −1.4451, p < 0.01), and age-standardized incidence rates (ASIRs) of prostate cancer, while no association was observed with APS (β = 0.030, p = 0.483) or AFS (β = 0.237, p = 0.405). This evidence concerns the gene ATR and autoimmune polyendocrinopathy.