New predictive models of heart failure mortality using time-series measurements and ensemble models

Morbidity and mortality rates associated with heart failure remain high. A wide variety of demographic and clinical factors as well as biomarkers are associated with increased mortality rates. Despite this, most multivariate predictive models for heart failure mortality have predictive accuracies characterized by a C-statistic (area under the receiver operating curve) of ≈0.74.

We analyzed data on 963 patients enrolled in the Vesnarinone Evaluation of Survival Trial (VEST), including circulating levels of 2 cytokines (tumor necrosis factor and interleukin-6) and their receptors sampled at baseline and at 8, 16, and 24 weeks. We built multivariate logistic regression models by using standard clinical variables and time-series of cytokine and cytokine receptor levels, using independent components analysis to handle collinearity among cytokine measurements, and L2-penalized stepwise regression for variable selection. We also built ensemble models with these data, using gentle boosting. Our multivariate logistic regression model using time-series cytokine measurements predicts 1-year mortality rates significantly better (P=0.001) than the baseline model, with a C-statistic of 0.81±0.03. Without the cytokines, the baseline model has a C-statistic of 0.73±0.03, and, with only baseline cytokine and cytokine receptor levels added, the model has a C-statistic of 0.74±0.04. An ensemble model of 100 decision stumps with serial cytokine measurements has a significantly better (P=0.04) C-statistic of 0.84±0.02. An ensemble model with baseline cytokine data and without the serial measurements has a C-statistic of 0.74±0.04.

Significant gains in accuracy of one year mortality prediction in chronic heart failure can be obtained by using logistic regression models that incorporate serial measurements of biomarkers such as cytokine and cytokine receptor levels. Ensemble models capture inherent variability in large patient populations, and boost predictive accuracy through the use of time-series measurements.