A Comparative Study of Cox Regression vs. Log-Logistic Regression (with and without its frailty) in Estimating Survival Time of Patients with Colorectal Cancer

Colorectal cancer is common and lethal disease with different incidence rate in different parts of the world which is taken into account as the third cause of cancer-related deaths. In the present study, using non-parametric Cox model and parametric Log-logistic model, factors influencing survival of patients with colorectal cancer were evaluated and the models efficiency were compared to provide the best model. This study is conducted on medical records of 1127 patients with colorectal cancer referred to Taleghani Medical and Training Center of Tehran between 2001 2007 and were definitely diagnosed with cancer, pathologically. Semi-parametric Cox model and parametric log-logistic model were fitted. Akaike's criterion of Cox Snell graph was used to compare the models. To take into account non-measured individual characteristics, frailty was added to Cox and log-logistic models. All calculations were carried out using STATA software version 12 and SPSS version 20.0, at the 0.05 level of significance. From a total of 1127 patients studied in this research, there were 690 men and 437 women. According to non-parametric Kaplan-Meier method, chances of surviving for 1, 3, 5 and 7 years were 91.16, 73.20, 61.00, and 54.94, respectively. Addition of frailty parameter did not change the model outcome. The results of fitting classified Cox and log-logistic models showed that body mass index (BMI), tumor grade, tumor size, and spread to lymph nodes, were the factors affecting survival time. Based on comparisons, and according to Cox Snell residuals, Cox and log-logistic models had almost identical results; however, because of the benefits of parametric models, in surveying survival time of patients with colorectal cancer, log-logistic can be replaced, as a parametric model, with Cox model.