Prediction of Colorectal Cancer Patient’s survival time by Fuzzy Logic Approach

Abstract

Introduction: Colorectal cancer is one of the most common cancers in the world. The incidence of this disease in Iran is increasing due to changes in lifestyle and diet so that its incidence is higher among Iranian youth compared to Western countries. Predicting survival time for cancer patients can be effective in the treatment process of patients. There are various statistical methods to investigate the effect of explanatory variables on survival. Commonly used models produce biased estimation in presense of highly censored data. Therefore, it is important to use a specific model in this situation. In this study, due to the limitations of standard statistical methods, a model based on the fuzzy product limit estimator was proposed that provides estimates with less bias and standard error. Method: Data from 173 patients referred to Imam Reza and Shahid Ghazi hospitals in Tabriz-Iran, were used. In this study utilized the fuzzy logic method to manage the censored data and model the possibility of survival after the moment of censorship. Given that similar patients have a similar survival trend regarding demographic characteristics and pathology, the data were clustered, and the fuzzy sets were formed in each cluster. The area under the fuzzy sets are used as an estimation of event time. Investigating the distribution of the estimated survival times, generalized linear model with Gamma distribution and log link was used to investigate the effect of covariates on survival time. The result are compared with Cox and Exponential regression models. Result: In this study, 56.1% of the 173 patients were male, and 75% were over 50 years old. In total, 71.9% of survival times were censored. The area under the fuzzy curves approximates the survival time for the censored data. Due to the structure of the fuzzy membership functions, this value was equal to the same survival time for the complete data (event time). The Kaplan-Meier method has estimated the mean and median of the survival times as 45.97(40.38-51.57) and 65(27.67-102.32) months, respectively, and also the fuzzy product limit method has estimated them as 82.69(61.29-103.58) and 43.90(36.08-59) months, respectively. Using the Kaplan-Meier method, the one, three, and five-year survival rates were estimated as 83, 57, and 52 percent, respectively. Moreover, using the fuzzy product limit, the one, three, five, ten, and twenty-year survival rates were estimated as 83, 58, 37, 21, and 9 percent, respectively. Also, to investigate the effect of variables on survival time according to the form of data distribution, a generalized linear model with the gamma distribution family (link=log) was used. According to the results of the fitted model, the variables of age, gender, having breakfast, and morphology had a significant effect on the survival of patients with colorectal cancer. The standard error of the coefficients in the generalized linear model with gamma distribution (link=Log) was less than the Cox and exponential models. Simulation studies showed that the proposed model has the least bias and standard error among the compared models: Cox and Exponential Regression. Conclusion: The proposed model based on fuzzy product limit estimator is a sutaible method for handling survival data with highly censoring