Time-dependence of hazard ratios for prognostic factors in primary breast cancer

Some prognostic factors, such as steroid receptors, appear strongly related to outcome in early studies with short follow-up, but as follow-up matures the relationships appear to weaken. We investigated this phenomenon for several factors (tumor size, axillary lymph nodes, S-phase fraction, estrogen receptor (ER) status, and adjuvant therapy) in a large sample of breast cancer cases (N = 2,873) with up to 17 years of follow-up for disease-free survival (DFS). Subjects in the study were identified from patients who had hormone receptor assays performed in our laboratory. Analysis of DFS included fitting a multivariate Cox proportional hazards model, testing for nonproportionality, and examining diagnostic plots. The assumption of proportional hazards was violated for several factors including ER, tumor size, and S-phase fraction. For ER, the hazard ratio was initially less than 1.0, indicating a good effect on prognosis, but increased at later times to values greater than 1.0, indicating a bad effect on prognosis. In contrast, the hazard ratios for tumor size and S-phase were initially high and decreased asymptotically toward 1.0 over time. Analysis of p53 expression in a subset of cases yielded qualitatively similar results. We conclude that several standard prognostic factors (ER, tumor size, S-phase fraction) and possibly other investigational factors have important but nonproportional effects on hazard. It is likely that violation of proportional hazards is common and not limited to breast cancer. Failure to recognize violations of proportional hazards can lead to both over- and under-estimation of the effects of important prognostic factors.