Application of Smoothing Methods for Determining of the Effecting Factors on the Survival Rate of Gastric Cancer Patients

Background: Smoothing methods are widely used to analyze epidemiologic data, particularly in the area of environmental health where non-linear relationships are not uncommon. This study focused on three different smoothing methods in Cox models: penalized splines, restricted cubic splines and fractional polynomials. Objectives: The aim of this study was to assess the effects of prognostic factors on survival of patients with gastric cancer using the smoothing methods in Cox model and Cox proportional hazards. Also, all models were compared to each other in order to find the best one. Materials and Methods: We retrospectively studied 216 patients with gastric cancer who were registered in one referral cancer registry center in Tehran, Iran. Age at diagnosis, sex, presence of metastasis, tumor size, histology type, lymph node metastasis, and pathologic stages were entered in to analysis using the Cox proportional hazards model and smoothing methods in Cox model. The SPSS version 18.0 and R version 2.14.1 were used for data analysis. These models compared with Akaike information criterion. Results: In this study, The 5 year survival rate was 30%. The Cox proportional hazards, penalized spline and fractional polynomial models let to similar results and Akaike information criterion showed a better performance for these three models comparing to the restricted cubic spline. Also, P-value and likelihood ratio test in restricted cubic spline was greater than other models. Note that the best model is indicated by the lowest Akaike information criterion. Conclusions: The use of smoothing methods helps us to eliminate non-linear effects but it is more appropriate to use Cox proportional hazards model in medical data because of its’ ease of interpretation and capability of modeling both continuous and discrete covariates. Also, Cox proportional hazards model and smoothing methods analysis identified that age at diagnosis and tumor size were independent prognostic factors for the survival of patients with gastric cancer (P < 0.05). According to these results the early detection of patients at younger age and in primary stages may be important to increase survival.