This study aimed to utilize the Bayesian framework of semi-competing risks to model the effect of background and clinical characteristics on recurrence and postoperative death in patients with CRC. Therefore, the effect of these variables on the nonterminal event (recurrence), the probability of the terminal event (death), and the conditional probability of the terminal event on the nonterminal event. The illness-death model is utilized because of its association with common methods for survival analysis and also its software is available. Due to the nature of the studied data, there is a strong association between the terminal and non-terminal events. Therefore, the simple utilization of a univariate survival model for the non-terminal event, leads to an overestimation of the terminal event rates, because the analysis considers the terminal event as an independent censoring mechanism (Haneuse and Lee, 2016). Utilizing semi-competing risk analysis, the terminal event is considered a competing event, and the dependence between the two events is assumed to be part of the model specifications.
The Bayesian approach is a scientific and effective alternative to the frequent approaches. Bayesian design and analysis are possible due to computational advances and available software In considering the analysis of semi-competing risks data, the proposed Accelerated failure time illness-death model supply as a beneficial complement to the more traditional hazard-based approach of, say, Xu et al (2010) and Lee et al. (2015). We choose the best model using DIC and present the results of just the optimal model.
Wioletta Grzenda used a similar model to analyze the duration of her first job among young people. For this purpose, four Weibull, Gamma, Log-normal, and Log-Logistic models were proposed. Wioletta Grzenda used a similar model to analyze the duration of the first job among young people. For this purpose, four Weibull, Gamma, Log-normal, and Log-Logistic models with the Bayesian approach were proposed. Based on the comparison of the models using the DIC index, the gamma model was a good fit for the data [18] Kyu Ha Lee outlined a new Bayesian framework for an AFT illness-death model.DIC and LMPL indices were used to compare the models [19]. M. Ganjali conducted a study to evaluate the duration of unemployment in conditions where the pH was not assumed. For this purpose Bayesian log-logistic, log-normal, and Weibull AFT models were used [20]. Marcus Abiso Arango utilized three common Bayesian joint models with AFT Weibull, log-normal, and log-logistics probability distributions. For comparison between models using DIC, AIC, and BIC indices, according to the results of analysis and comparisons, the common Bayesian logistics model was considered the final model.[21]
The results of the study in the AFT model with log-Normal based showed, that men compared with women and the Grade (differentiation level), PN Stage at N2 level, PT Stage in T3 stage, and Tumor size were associated with a decrease in recurrence survival time. Also, older age was associated with decreased survival time in all three outcomes but more chemotherapy sessions were associated with increased survival time in all three outcomes. In addition, metastasis to other sites, Grade (differentiation level) at a Moderate level, Tumor size, and PT Stage in T4 T3 stage were associated with decreased time ratio of death without recurrence.
Recurrence affects survival and death in the first 5 years after recurrence in patients with curative resection, as reported in some studies [22][23][24]. In some studies, The 5-year cumulative recurrence rates were 4.9%, 11.0%, and 23.5% for stage I, stage II, and stage III tumors (P < 0.001), respectively. [4]. In patients with colon cancer, local recurrence was less than in patients with rectal cancer [25].
In this study, the postoperative survival rate was decreased in older ages, in the line of this study, Ahmad Reza Baghestani showed that age at diagnosis was significantly related to patients’ survival time. [26], some studies reported similar results [27][28]. Also, in some studies, age was significantly associated with local recurrence and distance [29][30][31]. Also, according to the results of several studies, age is significantly associated with the survival of patients with colorectal cancer. In these studies, it has been reported that increasing the age of patients is associated with a decrease in patient survival. [32][33][34], But in some other studies, no significant association was reported [35][36][37][38]. In addition, several studies showed an effective and significant association between age and 5-year survival [39][31]. For that reason, early screening in adults to diagnose cases can increase the survival time ratio in patients with colorectal cancer. In line with the result, the ratio of recurrence survival time was lower in men than women. In some studies, sex was not significantly associated with survival time [40][27]. One possible explanation is due to socioeconomic factors. In the Artes and Müller study, men had lower survival than women [41]. in Heidarnia's study, 5-year survival in the second step was higher in women than men [31]. So appropriate screening strategies should be considered.
Metastasis to other sites was another factor that showed a significant association with nonterminal and terminal events. Other studies showed similar results [29][30]. According to Doğan Yazılıtaş studies, The rate of Grade I tumors was significantly upper in the group that had late metastasis (35.1% vs. 64.9%, P = 0.001)[42]. In this study metastasis to other sites was associated with decreased survival time of death without experiencing recurrence. Ryuk JP showed that the liver and lung were the first and second well-known sites of recurrence, respectively[25]. As a result, patients should be under intensive care in this regard.
According to This study Grade (differentiation level) and Tumor size were associated with a decrease in recurrence survival time. Grade (differentiation level) at a Moderate level, Tumor size was associated with decreased time ratio of death without recurrence. in some studies, patients with Stage III tumors had low recurrence rates [43][44].
As a complementary treatment after surgery, the number of chemotherapies was significantly related to greater survival of non-terminal and terminal events and non-terminal event condition of the terminal event. Several studies have reported that postoperative adjuvant therapy with fluorouracil and levamisole (as standard adjuvant chemotherapy) reduces mortality in patients with colorectal cancer.[45][46]. Additionally, in the study of Vassiliki L Tsikitis and Newland, chemotherapy effectively reduced the recurrence [47][48]. Therefore, chemotherapy can be suggested to decline the hazard of recurrence and death. In the present study, lower disease stages were generally connected with higher survival of recurrence, death without recurrence, and death after recurrence.
Depending on the stage of cancer, Cancer extent in the body is determined and appropriate treatment can be assigned according to the stage of cancer. In the present study, PT Stages in T4, and T3 stages were associated with decreased time ratio of death without recurrence, and PN Stages at the N2 level, and PT Stages in the T3 stage were associated with a decrease in recurrence survival time. Biyuan Wang reported that factors T3 to T4 were significantly and effectively associated with stage II CRC [49]. In Yuan-Tzu Lan's study, PT-stage( T4)and PN-stage(N2) were significantly related to early recurrence [50]. Also in the studies by Aquina et al., and Jalaeikhoo et al, the mortality rate was higher in patients with higher stages of colon cancer [51][52]. According to a study by A. Belot et al, In the higher stages of CRC, the rate of local recurrence and metastasis is higher [53]. Miyoshi et al discovered that the PN-Stage was effective on recurrence [54].
Limitation of the study:
The limitation was the difficulty in fitting Bayesian models, which was minimized by using appropriate approaches in modeling, selecting the appropriate initial values in the models, and selecting the appropriate amount of memory for the systems running the program. In particular, more cases are needed to achieve higher statistical power to find out significant differences that have been expressed as suggested or fundamental. Another limitation of the present study was its generalizability because the participants in this study were specific in terms of environmental, cultural, social, and geographical conditions, which should be generalized to other individuals and communities with caution. Data mining methods such as neural networks, classification algorithms, and regression trees automatically consider linear and nonlinear interaction relationships and possibly provide more accurate results. For our upcoming project, we intend to follow machine learning methods.