Estimating survival in patients with operable skeletal metastases: an application of a bayesian belief network

Abstract

Background: Accurate estimations of life expectancy are important in the management of patients with metastatic cancer affecting the extremities, and help set patient, family, and physician expectations. Clinically, the decision whether to operate on patients with skeletal metastases, as well as the choice of surgical procedure, are predicated on an individual patient's estimated survival. Currently, there are no reliable methods for estimating survival in this patient population. Bayesian classification, which includes bayesian belief network (BBN) modeling, is a statistical method that explores conditional, probabilistic relationships between variables to estimate the likelihood of an outcome using observed data. Thus, BBN models are being used with increasing frequency in a variety of diagnoses to codify complex clinical data into prognostic models. The purpose of this study was to determine the feasibility of developing bayesian classifiers to estimate survival in patients undergoing surgery for metastases of the axial and appendicular skeleton.

Methods: We searched an institution-owned patient management database for all patients who underwent surgery for skeletal metastases between 1999 and 2003. We then developed and trained a machine-learned BBN model to estimate survival in months using candidate features based on historical data. Ten-fold cross-validation and receiver operating characteristic (ROC) curve analysis were performed to evaluate the BNN model's accuracy and robustness.

Results: A total of 189 consecutive patients were included. First-degree predictors of survival differed between the 3-month and 12-month models. Following cross validation, the area under the ROC curve was 0.85 (95% CI: 0.80-0.93) for 3-month probability of survival and 0.83 (95% CI: 0.77-0.90) for 12-month probability of survival.

Conclusions: A robust, accurate, probabilistic naïve BBN model was successfully developed using observed clinical data to estimate individualized survival in patients with operable skeletal metastases. This method warrants further development and must be externally validated in other patient populations.

Figure 1. Kaplan-Meier curves showing overall survival for patients by diagnosis group.

The overall survival of patients in Group 1 was significantly lower than that of patients in Groups 2 and 3 at the 3-month time point^∞ (p<0.0001, log-rank test). Overall survival was significantly different between all groups at the 12-month time point* (p<0.0001, log-rank test).

Figure 2. Three-month BBN model with posterior distributions depicted as proportions (%) of the training population.

As shown, there are five first-degree predictors of 3-month survival: the surgeon's estimate of survival (“surgeon_estimate_of_survival”), preoperative hemoglobin concentration (“hemoglobin”), preoperative absolute lymphocyte count (“absolute_lymphocyte_count”), ECOG performance status (“ECOG”), and the presence of a completed pathologic fracture (“completed_path_fx”). The network structure indicates that the primary oncologic diagnosis (“dx_grouping”) and the presence of visceral metastases (“visceral_mets”) are both first-degree associates of the surgeon's estimate node.

Figure 3. Twelve-month BBN model.

As shown, there are four first-degree predictors of 12-month survival: the surgeon's estimate of survival (“surgeon_estimate_of_survival”), preoperative hemoglobin concentration (“hemoglobin”), the number of bone metastases (“bone_mets”), and the primary oncologic diagnosis (“dx_grouping”). In contrast to the 3-month model, the network structure of the 12-month model indicates that the ECOG performance status (“ECOG”) and the presence of visceral metastases (visceral_mets) are both first-degree associates of the surgeon's estimate node.