Axillary Lymph Node Involvement in Breast Cancer: A Random Walk Model of Tumor Burden

We reinvestigate the relationship between axillary lymph node involvement in breast cancer and the overall risk of death. Patients were women from the Surveillance, Epidemiology, and End Results (SEER) program, aged between 50 and 65 years, presenting a first primary T1-T2 (tumor size ≤5 cm), node-positive, non-metastasized unilateral breast carcinoma, diagnosed from 1988 to 1997, treated with mastectomy without radiotherapy. Hazard ratios (HRs) were computed at each percentage of involved nodes using the proportional hazards model, adjusting for the patient's demographic and tumor characteristics. The pattern of the hazard ratios was examined using serial correlations. Significance testing used the "portmanteau" test. Based on 4,387 records available for analysis, the relation between adjusted mortality and axillary lymph node involvement was modeled as H_t - H_{t- 1} = μ + a_t, where t is the percentage of involved nodes, H_t is the mortality hazard ratio at the percentage t, μ is a constant, and a_t is white noise. The constant μ was estimated at 0.020, corresponding to a 2% increment in the mortality hazard ratio per 1% increase in the percentage of positive nodes. The model was considered acceptable by the "portmanteau" test (P=0.205). We conclude that the effect of the tumor burden might be expressed as a random walk difference model, relating the mortality hazard ratio with the percentage of involved nodes. We will use the model to explore how treatments affect the course of the disease.