An interactive Bayesian model for prediction of lymph node ratio and survival in pancreatic cancer patients

Abstract

Background: Regional lymph node status has long been used as a dichotomous predictor of clinical outcomes in cancer patients. More recently, interest has turned to the prognostic utility of lymph node ratio (LNR), quantified as the proportion of positive nodes examined. However, statistical tools for the joint modeling of LNR and its effect on cancer survival are lacking.

Methods: Data were obtained from the NCI SEER cancer registry on 6400 patients diagnosed with pancreatic ductal adenocarcinoma from 2004 to 2010 and who underwent radical oncologic resection. A novel Bayesian statistical approach was developed and applied to model simultaneously patients' true, but unobservable, LNR statuses and overall survival. New web development tools were then employed to create an interactive web application for individualized patient prediction.

Results: Histologic grade and T and M stages were important predictors of LNR status. Significant predictors of survival included age, gender, marital status, grade, histology, T and M stages, tumor size, and radiation therapy. LNR was found to have a highly significant, non-linear effect on survival. Furthermore, predictive performance of the survival model compared favorably to those from studies with more homogeneous patients and individualized predictors.

Conclusions: We provide a new approach and tool set for the prediction of LNR and survival that are generally applicable to a host of cancer types, including breast, colon, melanoma, and stomach. Our methods are illustrated with the development of a validated model and web applications for the prediction of survival in a large set of pancreatic cancer patients.

Keywords: Bayesian Prediction; Biostatistics; Medical Informatics; Pancreas Cancer; SEER; Survival Analysis.

Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.

Figures

Figure 1

Scatter plot of total lymph nodes examined (TLN) versus observed lymph node ratio (LNR). The colors and legend represent the number of subjects at each point, and the solid line a smoothing spline fit to the TLN and LNR data points. 6174 SEER subjects in the analysis dataset had at least one examined node and are included in the plot.

Figure 2

Mean (solid line) and 90% probability intervals (dashed lines) for the prior distribution induced on the baseline hazard function.

Figure 3

Interactive web application for posterior inference. (A) provides interactive widgets for the inputting of patient and disease characteristics, (B) displays the predicted survival curve and distribution for true lymph node ratio (LNR) status, and (C) gives corresponding estimates for median and time-specific survival, and for LNR and its probabilities of being >0.05, 0.10, 0.25, and 0.50.

Figure 4

Relationships between the final lymph node ratio and survival models and the data that inform on them.

Figure 5

Calibration of the hierarchical Bayesian lymph node ratio and survival model comparing 1-, 3-, and 5-year predicted overall survival to observed survival in the validation dataset.

Figure 6

Posterior means and 95% prediction intervals for numerical survival predictors (Monte Carlo SE (MCSE) ≤0.01).