I. Dvorcik, E.P. Popechitelev, J.W. Marsh, J.J. Fung, S. Iwatsuki

Санкт-Петербургский государственный электротехнический университет “ЛЭТИ”

Hepatic resection is the most effective treatment known for metastases from colorectal carcinoma. However, the outcomes of this procedure vary greatly among patients reflecting variability of the disease advancement. Ability to prognosticate preoperatively recurrence outcome of the resection procedure would yield enhancement in patient care by allowing to plan personalized follow-up and adjuvant treatment schedules. Such an ability can result from accessibility of staging or prognostic scoring system, which stratifies patients on homogeneous in terms of risk of recurrence categories. Although previous studies [1-5] identified various preoperative clinical and pathological risk factors for postoperative tumor recurrence, there has been no dependable staging or prognostic scoring system for metastatic hepatic tumors.

Sixteen clinical and pathological variables were examined in 305 consecutive patients who underwent primary hepatic resection for metastatic colorectal cancer between 1985 and 1996 at the University of Pittsburgh Medical Center. The available information initially was subjected to univariate analysis to identify the factors strongly associated with recurrence outcome. The Kaplan-Meier method with log-rank test [6] was used for comparison of survival distribution between various categories of the variables of interest. Each continuous variable was represented in a variety of categorical forms, each form was subjected to the log-rank test, and the one, which produced greater statistical significance level, was selected as a categorical representation of a continuous variable. The variables proved to be significant risk factors for postoperative tumor recurrence were further utilized for multivariate analysis and modeling.

The Cox proportional hazard (PH) regression model [7] was adapted for the task at hand. Two methods were used for variable selection strategy: purposeful variables selection based on heuristic procedure, and stepwise selection procedure. The heuristic procedure was based on the following rule: a model containing the selected set of variables has to prognosticate tumor-free survival within 10% of the Kaplan-Meier assessment for the given patient category at each year after resection starting from a second. The method of backward stepwise selection with the likelihood ratio test based on maximum partial likelihood estimates [8] was employed to determine independent predictors of tumor recurrence. Variables were considered eligible for removal from the model if the likelihood ratio test significance was ? 0.1.

The resulting model was employed to calculate an individual patient’s risk score and corresponding probability of having tumor recurrence at various time points after resection. Individual patient risk score (R) was calculated according to the formula: R = B₁X₁ +…+B_nX_n, where: X_i and B_i are the value of a patient’s risk factor and the coefficient of this risk factor calculated from the Cox PH model, respectively. Correspondingly, the probability that patient with risk score R will be recurrence-free t years after hepatic resection (S(t)) can be calculated as:

while R₀ is a risk score corresponding to the baseline survival function S₀(t). Since all of the 4 risk factors were presented as binary variables, S₀(t) was calculated for the patients with no significant risk factors (X_I) present.

Analysis revealed that presence of a certain risk factors (positive surgical margins or extrahepatic metastases including positive lymph nodes) assured extremely poor tumor-free survival, therefore, 62 patients with this factors were excluded from the further analysis. Six risk factors were found significantly affecting tumor-free survival (tumor size, number of tumors, lobar involvement, time from colorectal surgery to liver metastasis, Duke’s classification and extent of liver resection) by univariate analysis. The log-minus-log test confirmed that all of them, meet the assumption of proportionality of hazard, therefore justifying Cox PH regression as an appropriate modeling technique. The used heuristic approach found that four variables (number of tumors > 2, maximum tumor size of > 8 cm, interval between colorectal surgery and occurrence of liver metastasis ? 30 months, and lobar tumor involvement) is the most parsimonious set of variables which produces prediction of tumor-free survival within 10% of actuarial value (table 1). The stepwise model-building approach confirmed the set as independent predictors of tumor-free survival (table 2).

The obtained from the model patient-specific risk scores were stratified on the 5 non-overlapping groups: R₀ = 0 (no identified risk factors present), R_{0 ?} 0.6286 (1 risk factor present), 0.6286 < R_{0 ?} 1.101 (2 risk factors present), 1.101< R_{0 ?} 1.4904 (3 risk factors present), R₀ > 1.4904 (4 risk factors present).

To ensure appropriate fit of the developed model to various parts of the data set, two methods were employed. The Hosmer-Lemeshow test [9] produced a p-value of > 0.41, which indicates a good fit of the model. Also, predicted by the developed model and actuarial tumor-free survival were compared not only for all the patients included into the model (n=263), but for different subgroups of patients as well. In particular, figures 1 and 2 depict the actuarial and predicted tumor-free survival for the patient cohort stratified by the developed grades of risk. As can be seen from the figures, actuarial and model-predicted survival are within a few percent from each other starting from a second post-resection year. The larger difference during the first post-resection year is related to the used PH technique, in particular, to the choice of the baseline function, and can not be reduced without a sufficient loss of the prediction accuracy during subsequent years.

The proportional hazard regression technique allowed reasonably accurate prognostication of the probability and timing of recurrent liver metastasis of colorectal cancer after liver resection. The proposed risk grade, which is based on the developed model, enables physician to devise personalized follow-up and adjuvant therapy schedules for the patients suffering from the disease prior to liver resection. The comparative simplicity of the developed risk grade allows it’s effortless verification and implementation in various medical centers.