In the present study, a multi-state Markov model was used to joint modeling of recurrence and death in colorectal cancer (CRC) with an incorporated cured fraction, in order to study the factors that influence the transition intensities between different states. The structure of this multi-state cure model was motivated by the disease process of CRC. This model was first introduced by Conlon et al in 2014 to analyze colon cancer data (34) and Lauren et al in 2018 extended an EM algorithm to estimate the parameters of this model and applied their model on head and neck cancer data (35). As we were awarded, there were no studies that have applied this model on CRC data and assessed the effects of variables on recurrence and death events jointly in the presence of the cured fraction of patients.
It has been reported that 30% to 50% of CRC patients who underwent resection will experience the recurrence (9, 14). Although, our results revealed that the tumor of a significant proportion of patients was eliminated by the treatment so that they will never experience a recurrence of CRC. Moreover, as there were a sufficient follow-up period and a number of patients who were censored for recurrence after the last observed time (the Kaplan–Meier survival plot for recurrence event in Figure2 shows a clear level plateau), it was justifiable to use a mixture cure model for the recurrence event (32). On the other hand, as the recurrence and death events were correlated, joint modeling of recurrence and death events could diminish the bias which might occur in separated model.
The joint modeling of the recurrence and survival time could also aid in identifiability of the cure part of the model because subjects with survival greater than the last observed recurrence time (which was approximately 50 months) were considered to be apparently cured of the recurrence. The probability of being cured for subjects with survival times lower than 50 months did not experience the recurrence have been estimated by logistic model and according to this model the subjects were appointed to apparently cured/not cured latent states. About 70% of our CRC patients were classified in cured group based on the model.
According to the findings, there was a significant association between sex, stage and receiving radiotherapy with the probability of being cured. The result suggested that females were less likely to be cured of CRC (the odds of being cured in males was 2.747 times of females). Based on our results, patients who diagnosed at stage IV were at about twofold higher odds of not being cured of CRC compared to patients at the stage II. In addition, patients who underwent radiotherapy were about 2.841 times more likely to be cured. However, the effect of the variables on the recurrence of CRC have been assessed in other studies (37-39), we have not found any study that have investigated its effect on the probability of being cured.
Generally, in patients with CRC, death can occur with or without a prior recurrence. The deaths following a recurrence may be due to the cancer, whereas the deaths without a prior recurrence are known not to be directly due to the regrowth of the tumor (34). However, the cause of death was not considered in this study, and we have not followed this issue as a competing risk event.
The results showed that the survival time of patients after resection was affected by age at diagnosis (among patients who their cancer was completely eliminated by resection), and stage of the disease and receiving radiotherapy (among patients who may experience the recurrence lately). It can be concluded from the findings, as the age of patients increased, the hazard of death in apparently cured patients increased. The effect of age on the survival of CRC patients had been assessed in different studies which are controversy. Some of them indicated that older patients are at higher risk of death (25, 43, 44), while the results of some others did not show a significant association between age and the risk of death in CRC patients (45-48). However, none of these studies assessed the effect of age separately on the survival rate of apparently cured and not cured CRC patients. Moreover, it has been shown that the risk of death was substantially higher in patients diagnosed with more advanced stages (patients at stage IV and III were at higher risk of death compared those at stage II). It should be noted that stage of the disease at diagnosis were just significantly effective on the survival time of patients whose disease was not cured by resection and the tumor of more than 50% of these patients, was regrowth. Other studies also showed a significant association between the stage of the CRC at diagnosis and the survival time (40, 46, 49, 50).
Based on our results, the risk of death and recurrence of CRC was lower among patients who underwent radiation therapy. Different clinical trials also have shown that the adjuvant radiotherapy can decrease the rate of death and recurrence among patients with CRC after surgery and improve their survival time. However, its effect was dependent on dose regimen (53, 54).
On the other hand, two competing risks (recurrence/death) were encountered by the patients after resection. Among 30% (85 of 283) of patients who were not cured by resection, 51.8% (44 of 85) experienced the recurrence. In this study we have founded that males were at higher risk of recurrence after resection by HR=2.614. Tartter (38) and Kobayashi et al (51) have showed that the risk of recurrence is significantly different in both males and females patients with colon and rectal cancer while based on the survival analysis there were no association between sex and recurrence time or disease-free survival. Dancourt et al (25) by joint modeling of recurrence and death in CRC data using a multi-state model showed that the time of recurrence is affected by sex and males were more likely to be recurred, which was aligned with our finding.
The results also showed that the risk of death after recurrence among patients who were diagnosed at stages III and IV, were 2.965 and 4.169 times of the patients who were at the stage II, respectively. Other clinical study also had showed that the patients who underwent resection and diagnosed at the stage III had a greater probability of death after experiencing the recurrence than the patients at the stage I&II (25). The coefficient of sojourn time in recurrent state, which had been included as a covariate in transition from state 3 to state 4, indicated that the Markov assumption was satisfied for our CRC data.
The results also revealed that BMI did not have a substantial effect on any transition intensities. Vrieling and Kampman conducted a review to investigate the role of BMI, diet, and physical activity in CRC recurrence and survival rate. They revealed that there was a high association between BMI before or at the time of diagnosis and mortality or recurrence of CRC. In this review, they just found one study that assessed the effect of BMI on CRC survival rate, so there was a need to more studies to examine the effect of this variable on progression or survival time of the CRC (52).
As most of our patients underwent chemotherapy, assessing the effect of this variable were not possible in two transitions. Chemotherapy schedule was different. Most of the studies have assessed the effect of chemotherapy on the rate and time of (local) recurrence after resection (9, 55-58). Collaborative Group showed that the relative risk of recurrence and death were higher in patients underwent chemotherapy. However, according to their findings there was no significant difference in efficacy of treatment by chemotherapy schedule (57).
This study has some limitations. First, for survival analysis, reliable data based on prospective cohort studies are required. However, our data were based on a retrospective study, and information was based on the data recorded by registry centers. Therefore, we were unable to assess the accuracy of the data. This issue may introduce information bias. Moreover, according to this limitation some important variables such as period /exposition to chemotherapy /radiotherapy and clinical state of the patients were not included in the collected data. Second, although patients were followed about 25 years, the number of all available patients who underwent resection was limited. On the other hand, as in the multi-state cure model, there were many parameters to be estimated and their number increased by the number of variables in each transition, our sample size was relatively small. Due to this limitation, the confidence interval of some HR was relatively wide. It is clear that bigger sample sizes will provide much more precise estimates.
Despite these limitations, the main purpose of the present study was to use powerful statistical methods (here multi-state cure model) which take all aspects of the data into account. In the future clinical studies, it is suggested that if there were different states of disease, multi-state or multi-state cure model would be used instead of separated models to analyze the data. Moreover, in this study, the used model was based on the semi-parametric Cox model. Although, based on the Schoenfeld residuals, the PH assumption was reasonable, it is suggested to use log-linear models and to develop R codes for this extended model in future studies.