Survival of Patients with Primary Brain Tumors: Comparison of Two Statistical Approaches

Purpose: We reviewed the survival time for patients with primary brain tumors undergoing treatment with stereotactic radiation methods at the Masaryk Memorial Cancer Institute Brno. We also identified risk factors and characteristics, and described their influence on survival time. Methods: In summarizing survival data, there are two functions of principal interest, namely, the survival function and the hazard function. In practice, both of them can depend on some characteristics. We focused on nonparametric methods, propose a method based on kernel smoothing, and compared our estimates with the results of the Cox regression model. The hazard function is conditional to age and gross tumor volume and visualized as a color-coded surface. A multivariate Cox model was also designed. Results: There were 88 patients with primary brain cancer, treated with stereotactic radiation. The median survival of our patient cohort was 47.8 months. The estimate of the hazard function has two peaks (about 10 months and about 40 months). The survival time of patients was significantly different for various diagnoses (p≪0.001), KI (p = 0.047) and stereotactic methods (p = 0.033). Patients with a greater GTV had higher risk of death. The suitable threshold for GTV is 20 cm3. Younger patients with a survival time of about 50 months had a higher risk of death. In the multivariate Cox regression model, the selected variables were age, GTV, sex, diagnosis, KI, location, and some of their interactions. Conclusion: Kernel methods give us the possibility to evaluate continuous risk variables and based on the results offer risk-prone patients a different treatment, and can be useful for verifying assumptions of the Cox model or for finding thresholds of continuous variables.