Can a Bayesian Belief Network Be Used to Estimate 1-year Survival in Patients With Bone Sarcomas?

Abstract

Background: Extremity sarcoma has a preponderance to present late with advanced stage at diagnosis. It is important to know why these patients die early from sarcoma and to predict those at high risk. Currently we have mid- to long-term outcome data on which to counsel patients and support treatment decisions, but in contrast to other cancer groups, very little on short-term mortality. Bayesian belief network modeling has been used to develop decision-support tools in various oncologic diagnoses, but to our knowledge, this approach has not been applied to patients with extremity sarcoma.

Questions/purposes: We sought to (1) determine whether a Bayesian belief network could be used to estimate the likelihood of 1-year mortality using receiver operator characteristic analysis; (2) describe the hierarchal relationships between prognostic and outcome variables; and (3) determine whether the model was suitable for clinical use using decision curve analysis.

Methods: We considered all patients treated for primary bone sarcoma between 1970 and 2012, and excluded secondary metastasis, presentation with local recurrence, and benign tumors. The institution's database yielded 3499 patients, of which six (0.2%) were excluded. Data extracted for analysis focused on patient demographics (age, sex), tumor characteristics at diagnosis (size, metastasis, pathologic fracture), survival, and cause of death. A Bayesian belief network generated conditional probabilities of variables and survival outcome at 1 year. A lift analysis determined the hierarchal relationship of variables. Internal validation of 699 test patients (20% dataset) determined model accuracy. Decision curve analysis was performed comparing net benefit (capped at 85.5%) for all threshold probabilities (survival output from model).

Results: We successfully generated a Bayesian belief network with five first-degree associates and describe their conditional relationship with survival after the diagnosis of primary bone sarcoma. On internal validation, the resultant model showed good predictive accuracy (area under the curve [AUC] = 0.767; 95% CI, 0.72-0.83). The factors that predict the outcome of interest, 1-year mortality, in order of relative importance are synchronous metastasis (6.4), patient's age (3), tumor size (2.1), histologic grade (1.8), and presentation with a pathologic fracture (1). Patient's sex, tumor location, and inadvertent excision were second-degree associates and not directly related to the outcome of interest. Decision curve analysis shows that clinicians can accurately base treatment decisions on the 1-year model rather than assuming all patients, or no patients, will survive greater than 1 year. For threshold probabilities less than approximately 0.5, the model is no better or no worse than assuming all patients will survive.

Conclusions: We showed that a Bayesian belief network can be used to predict 1-year mortality in patients presenting with a primary malignancy of bone and quantified the primary factors responsible for an increased risk of death. Synchronous metastasis, patient's age, and the size of the tumor had the largest prognostic effect. We believe models such as these can be useful as clinical decision-support tools and, when properly externally validated, provide clinicians and patients with information germane to the treatment of bone sarcomas.

Clinical relevance: Bone sarcomas are difficult to treat requiring multidisciplinary input to strategize management. An evidence-based survival prediction can be a powerful adjunctive to clinicians in this scenario. We believe the short-term predictions can be used to evaluate services, with 1-year mortality already being a quality indicator. Mortality predictors also can be incorporated in clinical trials, for example, to identify patients who are least likely to experience the side effects of experimental toxic chemotherapeutic agents.

Fig. 1

The Bayesian belief network structure defines five first-degree associates that are directly related to the outcome (line); second-degree associations have an indirect relationship with the outcome (dotted line). Only 4.2% of patients underwent an inadvertent excision and the prevalence of synchronous metastasis or pathologic fracture was 13.98% and 13.57% respectively.

Fig. 2

Net benefit is plotted on this decision curve analysis graph against threshold probabilities and shows the benefit of intervention based on decision to treat from a model output. Threshold probability (p^t), is the probability of survival at which the surgeon would recommend treatment. Net benefit = ([true positive count/n] − [false positive count/n]) × (p^t / 1 − p^t).