Dynamic Functional Continuous Time Bayesian Networks for Prediction and Monitoring of the Impact of Patients' Modifiable Lifestyle Behaviors on the Emergence of Multiple Chronic Conditions

Abstract

More than a quarter of all Americans are estimated to have multiple chronic conditions (MCC). It is known that shared modifiable lifestyle behaviors account for many common MCC. What is not precisely known is the dynamic effect of changes in lifestyle behaviors on the trajectories of MCC emergence. This paper proposes dynamic functional continuous time Bayesian networks to effectively formulate the dynamic effect of patients' modifiable lifestyle behaviors and their interaction with non-modifiable demographics and preexisting conditions on the emergence of MCC. The proposed method considers the parameters of the conditional dependencies of MCC as a nonlinear state-space model and develops an extended Kalman filter to capture the dynamics of the modifiable risk factors on the MCC evolution. It also develops a tensor-based control chart based on the integration of multilinear principal component analysis and multivariate exponentially weighted moving average chart to monitor the effect of changes in the modifiable risk factors on the risk of new MCC. We validate the proposed method based on a combination of simulation and a real dataset of 385 patients from the Cameron County Hispanic Cohort. The dataset examines the emergence of 5 chronic conditions (Diabetes, Obesity, Cognitive Impairment, Hyperlipidemia, Hypertension) based on 4 modifiable lifestyle behaviors representing (Diet, Exercise, Smoking Habits, Drinking Habits) and 3 non-modifiable demographic risk factors (Age, Gender, Education). For the simulated study, the proposed algorithm shows a run-length of 4 samples (4 months) to identify behavioral changes with significant impacts on the risk of new MCC. For the real data study, the proposed algorithm shows a run-length of one sample (one year) to identify behavioral changes with significant impacts on the risk of new MCC. The results demonstrate the sensitivity of the proposed methodology for dynamic prediction and monitoring of the risk of MCC emergence in individual patients.

Keywords: Extended Kalman filter (EKF); functional continuous time bayesian network (FCTBN); multilinear principal component analysis (MPCA); multiple chronic conditions (MCC); multivariate exponentially weighted moving average (MEWMA) control chart.

FIGURE 1.

The overall scheme of the proposed approach for dynamic prediction and monitoring of the emergence and progression of MCC. The proposed scheme has three major components: (1) A Functional CTBN (FCTBN) to take into account the impact of the patients’ non-modifiable risk factors on the MCC emergence and progression, (2) a dynamic FCTBN (D-FCTB) for prediction of FCTBN parameters based on the changes in the modifiable lifestyle behavioral risk factors using Extended Kalman Filter, and (3) A tensor-based control chart for monitoring the changes in the D-FCTBN parameters.

FIGURE 2.

Illustration of the impact of lifestyle behavioral risk factors dynamics on the conditional intensities/dependencies and risk trajectory of developing new MCC conditions, i.e. Diabetes, at three time points, including baseline, 5-year follow up, and 10-year follow up, using extended Kalman filter; The nodes with thick outlines represent the preexisting or developed conditions over time. (The nodes, OB: Obesity, HP: High Blood Pressure, DI: Diabetes, HL: Hyperlipidemia, and CI: Cognitive Impairment).

FIGURE 3.

Visual illustration of multilinear projection; projection in the 1-mode vector space.

FIGURE 4.

Flow diagram of sample selection and the final number of patients included in the analysis.

FIGURE 5.

The estimated parameters of FCTBN based on the optimal value of tuning parameters. The matrix contains all the possible combinations of parent and child interaction. For example, the first row set (first 32 rows) of the matrix represents the parameters learned child node 1 while considering the parents’ node are 2, 3, 4, and 5. The right side of the Figure shows all the possible condition possible (1 for the presence of a condition and 0 for no presence of no condition).

FIGURE 6.

A visualization of the estimated parameters of the proposed D-FCTBN using EKF for 5 patients over 11 consecutive periods. The illustration shows the changes in learned parameters/coefficients with respect to base year (t = 0) as estimated using D-FCTBN Algorithm (The block of coefficients in Figure 5).

FIGURE 7.

The stability check of the D-FCTBN model for estimating the model parameters in the presence of new data. The Figure shows the MSE of predictions for two patients. The time axis shows the parameters estimated at each time step, and the iteration axis shows the steps to minimize the error at each time step.

FIGURE 8.

MEWMA Control chart of the reconstruction error obtained from the proposed model. (a) In-control control chart (simulation case) (b-c) shows case 1 where only one of the lifestyle behavioral risk factors are modified (simulation case), (d) shows case 2 where we randomly change more than one lifestyle behavioral risk factor (simulation case), and (e) shows (uncontrolled) changes in more than one lifestyle behavioral risk factor (real case)).