Background
The medical history of a cancer patient is very complex and often includes different intermediate events, as for example the development of distant metastasis (DM) or local recurrence (LR) after surgery of the primary tumor, which plays a central role in influencing the survival prognosis. Standard survival analysis can analyze separately different endpoints but fails to give insight into what happens to a patient after a first event [
1]. Multi-state models are an extension of classical survival analysis which allows adjustment to the prediction of survival duration of the patient in the course of time by incorporating new information regarding the progression of the medical history and to better understand how prognostic factors influence the different phases of the disease/recovery process [
2]. A multi-state model (msm) is a model for time-to-event data in which all individuals start at one or possibly more starting states and eventually may end up in one (or more) absorbing or final state(s). In between, intermediate states can be visited, possibly more than once. Some individuals are censored before they reach an absorbing state [
2,
3]. For example, the starting state could represent the time of discovery of a disease, the final state usually is death, intermediate states reflect all relevant treatments or disease stages or generally clinical events between starting state and final state. These models are very helpful in clinical decision making because they allow the prognosis of the patient to be updated according to the progression of the disease.
The course of the events between diagnosis of cancer, the many possible intermediate events like a surgical intervention, the development of metastasis, the commencement of chemotherapy (CTx) and, in the worst case, the death of a patient as final event, can be described very well by a multi-state model. This relatively new method for analysis of survival data is still not well known in the medical world. The aim of this study was to implement a multi-state model on data of patients with rectal cancer to illustrate the advantages of multi-state analysis in comparison to standard survival analysis.
The prognosis of rectal cancer has been improved significantly over the past decades as reported by De Angelis et al.; in 2014 with an increase in the 5-year overall survival from 1999 to 2001 of 52.1% (51.6–52.6) to 2005–07 of 57.6% (57.1–58.1), respectively [
4]. This can be explained by the improvement of surgical techniques with the introduction of total mesorectal excision (TME) [
5‐
11] and of MRI as diagnostic instrument [
12] as well as multidisciplinary treatment with better neoadjuvant radiochemotherapy and adjuvant CTx [
13]. Regarding locally advanced rectal cancer (stage II and III) this multidisciplinary work increased the 5-year cause-specific survival rates from 53.4% for patients treated between 1981 and 1986 to 89.8% for patients treated between 2007 and 2011 [
13].
As the clinical history of rectal cancer patients can be well described with a msm, we analyzed the outcomes of patients from the multicentric FOGT-2 trial [
14] using a msm in order to assess the influence of certain prognostic factors like age, gender, body mass index (BMI), UICC tumor stage, tumor grade and type of operation on different phases of the disease/recovery process of the patient and to obtain more accurate predictions of long-term survival than with a standard survival model by adjusting the initial prediction in the course of time by incorporating new information regarding intermediate events [
2] like completion and duration of the adjuvant CTx or development of DM. So far, clinical applications of multi-state models have been limited because of the difficulties of the analysis [
2]. Putter et al. published in 2006 the first re-analysis of Breast cancer data by using a multi-state model, clearly showing the added value of this kind of analysis [
1]. We present the first application of a multi-state model to data from patients with locally advanced rectal cancer with the aim to introduce the advantages of this type of analysis in the research field of abdominal surgery.
Discussion
Multi-state models are an extension of standard survival analysis, where standard survival models measure the time span from some time origin until the occurrence of the event of interest but fail to give information when the analyzed process involves more than one type of event [
3].
So far most applications of multi-state models can be found in the field of hematological malignancies, in particular for the analysis of outcomes after hematopoietic stem cell transplantation, an intervention associated with many disease- and treatment-related events and therefore very suitable for multi-state modelling [
16‐
19]. In the field of solid tumors, less applications of multi-state models can be found. Putter et al. 2006 [
1] used a multi-state model to analyze survival data from women with breast cancer. Conlon et al. used a multi-state model with an incorporated cured fraction for recurrence to jointly model time to recurrence and time to death in colon cancer [
20,
21]. The authors considered a total of 13,938 subjects from 12 randomized phase III adjuvant trials of locally advanced colon cancer and used a Bayesian Markov-Chain-Monte-Carlo (MCMC) technique to estimate the parameters of the multi-state cure model, like those of the Weibull model for each of the hazard rates, covariate effects for each of the hazard models and covariate effects in the logistic model for the probability of cure [
20]. In a second publication, the same authors explore different ways in which the information about recurrence time and the assumptions in the multi-state model with an incorporated cured fraction for recurrence can lead to improved efficiency. Estimates of overall survival and disease-free survival can be derived directly from the model with efficiency gains obtained as compared to Kaplan-Meier estimates [
21]. Other applications are described by Andersen et al. [
22] who use a multi-state model for bleeding episodes and mortality in liver cirrhosis and by Mitchell et al. who show the application of a multi-state model for urinary tract infections [
23].
Cancer history is maybe the best domain for the application of multi-state models in the medical field. From diagnosis, the patient can experience different events, such as surgical treatment, CTx, LR, or DM, which alter the survival probability. By better knowing the probability of having a certain event (e.g. to develop DM or LR) after the primary event (e.g. surgery for rectal cancer) in the specific case of a patient with known baseline covariates and by knowing the time at which the prediction should be done, it is possible to adapt the follow-up examinations to the risk profile of that patient.
Multi-state models offer several advantages with respect to more commonly used methods in survival analysis. The models are more flexible than Cox models with time-dependent covariates since they allow different baseline hazards for different transitions. They are more comprehensive than landmark models since all prediction timepoints are included in a single model and since sequences of events can also be analyzed. A major advantage compared to both of these methods is that the model yields estimates of probabilities of being in both intermediate and absorbing states. In our model, e.g., we can consider the relevance of predictions starting from any of the states indicating treatment discontinuation by assessing the chance that a patient with certain characteristics really is in such a state at different moments after start.
We designed a msm with eight states with the aim to investigate the effect of the covariates on the different transitions from one state to the other and the role of intermediate events in affecting the survival probability of the patients. For applying standard formulas and software to estimate the quantities of interest, it had to be assumed that the model is Markovian, i.e., that the prognosis for a patient at a certain moment depends on the state where he/she is at that moment, and not on the states previously visited or the duration in the current state. By creating two CTx states instead of one and two discontinuation states, we managed to include information about the patients’ histories (length and possible discontinuation of CTx) and assessing the differential impact of risk factors on subsequent transitions, while still keeping the attractive statistical properties of the Markov model and the possibility to fit the model with the ‘mstate’ package. It must be noted, however, that the states 6 < CTx < 12 and CTx = 12 are not, like the other states, characterized by an event that makes the patient experience a transition, but only by the passing of time; they are thus more relevant for model fitting than for describing clinical histories. Other approaches exist in which time-dependent effects of the history of the patients can be modelled without categorizing time.
A weakness of the current study is that for some of the transitions the exact transition times were not available. For discontinuation of CTx, only the period was given in the data. This event should in principle have been treated as interval-censored and be analyzed by a method suitable for this kind of data. However, to remain within the semi-parametric framework of our model, we used a pragmatic approach by applying midpoint imputation. In addition, time-to-event data regarding the development of LR, DM or both LR and DM were recorded in the original study in only 3 categories: LR, DM or both LR and DM. For the patients in this last category only the date of the second of these two events (LR or DM) was recorded. According to the current literature which states that in case of simultaneous LR and DM the prognosis is defined by the DM [
24,
25], we decided to create one state named
´DM or both LR and DM
´. Of a total of 182 patients who entered this state, only 25 (13.7%) were categorized in the original study by the presence of both DM and LR. Time intervals between LR and DM or
viceversa were not available for these patients, implying the exact moment when they entered the LR or DM state is unknown. Since this only affects 25 patients and since this time interval will have been short for some of them, we assume that the impact of this missing data on the estimated probabilities is limited. In addition, information about a possible second operation to treat the LR and/or the DM, which could be represented as an additional state in our model since it may have affected the prognosis of the patients, was also not recorded in the original study.
In the current study, 40% of patients had to be excluded from the multi-state analysis. Also in other contexts, the lack of detailed data describing risk factors and the course of the disease for larger groups of patients is an impediment to the development of relevant and accurate multi-state models. Therefore, a major goal of the current study is to illustrate some of the features of multi-state models to advocate their use and to improve data collection to this end. For example, the multi-state model helps to zoom in on the differential impact of the three CTx regimens on different endpoints. This information cannot be retrieved by the primary analysis of the trial.
In accordance with current literature we found that patients with higher tumor stage and/or grade have a higher risk to develop DM both after early and late discontinuation of CTx and after completion of 12 months of CTx [
26]. Interesting is the result regarding the worse survival prognosis of women after the development of LR compared to that of men. However, this finding may be partly due to chance because of the low number of events in this transition (
n = 26). For this reason we considered both the poor and good risk reference patient to be male. No specific literature exists regarding how gender affects survival after the development of LR or DM. One publication dealing with gender [
27] aimed to investigate the association of gender and age with acute toxicity after radio-chemotherapy for UICC II/III rectal cancer. Although women showed higher hematologic (
p < 0.001) and acute organ toxicity (
p < 0.001) in comparison to men, the authors found a trend toward higher 10-year overall survival in women (62.7% vs. 58.4%,
p = 0.066). By analyzing our data stratified for gender (by the Kaplan-Meier method), we found similar survival in women and men (log-rank test,
p = 0.85).
Patients that underwent an abdominoperineal amputation have a higher risk to develop DM or both DM and LR. It is known and has been shown in several studies that a higher incidence of LR after abdominoperineal resection occurs compared to low anterior resection [
28]. In fact, patients who need this type of surgery have a tumor which is locally advanced and most likely muscle infiltrating, which makes the accomplishment of a radical resection difficult, increasing the possibility of the development of LR due to remaining tumor tissue or cells after the operation [
28]. Kornmann et al. reported in 2010 a 5-year recurrence-free survival rate for locally advanced rectal cancer of 60.4% (95% CI [55%–65.4%]) after anterior resection vs. 46.2% (95% CI [38.6%–53.5%]) after abdominoperineal amputation (
p = 0.005) [
29]. We could not demonstrate a higher risk to develop LR with this type of operation in our data. However, as previously described, we have not enough sample size in the transitions into the state LR. Finally, none of the risk factors included in the models was significantly associated with discontinuation of CTx.
Based on the results of the msm analysis and on current literature [
14,
24‐
26,
30] we defined a high and low risk reference patient based on the baseline covariate profile, representing well the patients in the dataset.
The graphical illustrations of the 5-year predicted probabilities answer immediately the question about the relevance, in term of survival probabilities, of each event in the clinical history of the patient allowing the adjustment of the survival probabilities in the course of time. In fact, dynamic prediction allows the estimation of survival probabilities of a patient at each point in time taking into consideration all new events which take place. Additionally we showed how different combinations of covariates (high and low risk patient) define from the beginning the survival probability. Generally the prognosis got worse for all patients when they experienced DM, even if the 5-year-survival probability of survival for the low risk patient was higher than that of the high risk one, 21% vs. 11% at 1 year and 33% vs. 20% at 2 year after start of CTx, respectively.
The question about a possible correlation between duration of CTx, risk factor profile and survival probability in locally advanced rectal cancer remains open and more studies are needed. In fact, regarding the low risk patient we observed that the survival curves representing 5-year survival probability with late discontinuation vs. CTx = 12 are too close to each other to conclude that 6–12 months CTx is better than 12 months. The actual guidelines for locally advanced rectal cancer (UICC II and III) in absence of any neoadjuvant treatment, as was the case for the patients included in the FOGT-2 study, suggest a 6 months long adjuvant radio-chemotherapy with 5FU or Capecitabine [
21,
22].
. We defined consequently in our multi-state model the three groups: CTx duration < 6 months, CTx duration between six and 12 months according to the recommendations of the S3 guidelines, CTx duration of 1 year according to the study protocol.
One promising field which is gaining more and more interest regarding response prediction to CTx is gene expression profiling [
31,
32]. In a recent study published in 2015 [
33], a gene expression profile was developed which was able to predict treatment response in CRC patients treated with standard CTx regimens. Indeed, patients with a favourable gene expression profile had a higher response rate (58% vs. 13%,
p = 0.024), progression-free survival (61% vs. 13% at 1 year, HR = 0.32,
p = 0.009) and overall survival (32 vs. 16 months, HR = 0.21,
p = 0.003) than patients with an unfavourable predictive signature. Future studies should consider also this variable as important prognostic factor.
One partial limitation regarding the routine use of msm in surgical research is the complexity of the computer program needed for such an analysis. However very good tutorials are freely available online and explain the procedure in detail [
2,
3]. Our aim was to illustrate an intuitive application of a multi-state model in the medical field with an immediate and concrete answer to the question about survival probability given a particular medical history of a patient. We think it is important to introduce multi-state models in the medical field in a way which is understandable for clinicians.