Long-term associations between animal-source food consumption and breast and prostate cancer incidence based on cointegration and ARIMAX models

Understanding whether and to what extent dietary habits influence the long-term incidence of hormone-sensitive cancers is undoubtedly a significant challenge. Conventional approaches, which are often limited to studies with short follow-up periods or methods that do not consider lag times, risk producing spurious associations and consequently lead to weak conclusions. In this study, we analyzed exceptionally long Italian national time series (1961-2020 for meat and dairy consumption; 1984-2020 for cancer incidence) to investigate the association between diet and the development of breast and prostate cancer. Initially, to avoid the risk of multicollinearity between variables, dairy and meat consumption data were summarized into a single index (PC1), obtained using principal components analysis (PCA). We then applied a rigorous econometric framework to investigate long-term dynamics. The first step consisted of testing for cointegration between PC1 and the cancer incidence series. The second step was ARIMAX modeling, with PC1 included as an exogenous variable at a lag that minimizes the AICc criterion. The study revealed evidence of cointegration between consumption and cancer incidence for both cancers, i.e., a long-term equilibrium. For breast cancer, the optimal ARIMAX model (0,0,1) identified a positive and highly significant association with PC1 at a lag of 18 years (beta = 0.108, p < 0.001). For prostate cancer, an identically structured model (0,0,1) showed an even stronger and highly significant association at 15 years (beta = 0.384, p < 0.001). Both models passed the diagnostic tests, confirming their validity and statistical robustness. These findings provide consistent quantitative evidence of long-term association between animal product consumption and hormone-sensitive cancers. More broadly, the study highlights the relevance of econometric methodologies in cancer epidemiology and emphasizes their potential to deepen our understanding of how cumulative dietary exposures influence population health.