Application of the Parametric Regression Model with the Four-Parameter Log-Logistic Distribution for Determining of the Effecting Factors on the Survival Rate of Colorectal Cancer Patients in the Presence of Competi

Background In competing risks data, when a person experiences more than one event in the study, usually the probability of experiencing the event of interest is altered. Therefore, it is necessary to analyze the competing risk data. Objectives The current study aimed at analyzing the colorectal cancer (CRC) risk factors based on competing risks model. The log-logistic model was also fitted with 2-parameter to evaluate the prognostic factors that affect the survival of patients with CRC, and comparisons were made to find the best model. Methods The current retrospective study was conducted on 1054 patients with CRC registered in the Research Institute of gastroenterology and liver disease center (from 2004 to 2015), Taleghani hospital, Tehran, Iran. The demographic and clinical features including age at diagnosis, gender, family history of CRC, body mass index (BMI), tumor size, and tumor site were extracted from the hospital documents. Analysis was performed using competing risks model and was based on the 4-parameter log-logistic distribution and log-logistic distribution. The analysis was carried out using R software version 3.0.3. P value less than 0.05 was considered as significant. Results Overall, 1054 patients with CRC and complete data were included in the analysis. The mean ± standard deviation (SD) of survival time was 92 ± 6.62 months. Out of the 1054 patients, 379 (36%) subjects died of CRC and 49 (4.6%) subjects died of other causes such as myocardial infarction, stomach cancer, liver cancer, etc. Four-parameter log-logistic model and log-logistic model with competing risk analysis indicated age at diagnosis and BMI as the prognosis. Conclusions The current study indicated age and BMI as prognosis of CRC, using a 4-parameter log-logistic model with competing risk analysis. Although the odds ratio (OR) in 4-parameter log-logistic model and log-logistic model ones were approximately similar, according to Akaike information criterion, the 4-parameter log-logistic model was more appropriate for survival analysis.