Nonlinear associations between liver cancer and IGF-I and IGFBP-3 were observed (P=0.04 and P<0.01, respectively), strongest association at lowest levels (odds ratio (OR)=0.2, 95% confidence interval (CI)=0.1–0.7 for 80 vs 30 ng ml−1 of IGF-I; OR=0.2, 95% CI=0.1–0.6 for 1400 vs 700 ng ml−1 of IGFBP-3). This evidence concerns the gene IGFBP3 and liver cancer.