### Abstract

Background:

Recently, mobile devices, such as smartphones, have been introduced into healthcare research to substitute paper diaries as data-collection tools in the home environment. Such devices support collecting patient data at different time points over a long period, resulting in clinical time-series data with high temporal complexity, such as time irregularities. Analysis of such time series poses new challenges for machine-learning techniques. The clinical context for the research discussed in this paper is home monitoring in chronic obstructive pulmonary disease (COPD).

Objective:

The goal of the present research is to find out which properties of temporal Bayesian network models allow to cope best with irregularly spaced multivariate clinical time-series data.

Methods:

Two mainstream temporal Bayesian network models of multivariate clinical time series are studied: dynamic Bayesian networks, where the system is described as a snapshot at discrete time points, and continuous time Bayesian networks, where transitions between states are modeled in continuous time. Their capability of learning from clinical time series that vary in nature are extensively studied. In order to compare the two temporal Bayesian network types for regularly and irregularly spaced time-series data, three typical ways of observing time-series data were investigated: (1) regularly spaced in time with a fixed rate; (2) irregularly spaced and missing completely at random at discrete time points; (3) irregularly spaced and missing at random at discrete time points. In addition, similar experiments were carried out using real-world COPD patient data where observations are unevenly spaced.

Results:

For regularly spaced time series, the dynamic Bayesian network models outperform the continuous time Bayesian networks. Similarly, if the data is missing completely at random, discrete-time models outperform continuous time models in most situations. For more realistic settings where data is not missing completely at random, the situation is more complicated. In simulation experiments, both models perform similarly if there is strong prior knowledge available about the missing data distribution. Otherwise, continuous time Bayesian networks perform better. In experiments with unevenly spaced real-world data, we surprisingly found that a dynamic Bayesian network where time is ignored performs similar to a continuous time Bayesian network.

Conclusion:

The results confirm conventional wisdom that discrete-time Bayesian networks are appropriate when learning from regularly spaced clinical time series. Similarly, we found that time series where the missingness occurs completely at random, dynamic Bayesian networks are an appropriate choice. However, for complex clinical time-series data that motivated this research, the continuous-time models are at least competitive and sometimes better than their discrete-time counterparts. Furthermore, continuous-time models provide additional benefits of being able to provide more fine-grained predictions than discrete-time models, which will be of practical relevance in clinical applications.

Recently, mobile devices, such as smartphones, have been introduced into healthcare research to substitute paper diaries as data-collection tools in the home environment. Such devices support collecting patient data at different time points over a long period, resulting in clinical time-series data with high temporal complexity, such as time irregularities. Analysis of such time series poses new challenges for machine-learning techniques. The clinical context for the research discussed in this paper is home monitoring in chronic obstructive pulmonary disease (COPD).

Objective:

The goal of the present research is to find out which properties of temporal Bayesian network models allow to cope best with irregularly spaced multivariate clinical time-series data.

Methods:

Two mainstream temporal Bayesian network models of multivariate clinical time series are studied: dynamic Bayesian networks, where the system is described as a snapshot at discrete time points, and continuous time Bayesian networks, where transitions between states are modeled in continuous time. Their capability of learning from clinical time series that vary in nature are extensively studied. In order to compare the two temporal Bayesian network types for regularly and irregularly spaced time-series data, three typical ways of observing time-series data were investigated: (1) regularly spaced in time with a fixed rate; (2) irregularly spaced and missing completely at random at discrete time points; (3) irregularly spaced and missing at random at discrete time points. In addition, similar experiments were carried out using real-world COPD patient data where observations are unevenly spaced.

Results:

For regularly spaced time series, the dynamic Bayesian network models outperform the continuous time Bayesian networks. Similarly, if the data is missing completely at random, discrete-time models outperform continuous time models in most situations. For more realistic settings where data is not missing completely at random, the situation is more complicated. In simulation experiments, both models perform similarly if there is strong prior knowledge available about the missing data distribution. Otherwise, continuous time Bayesian networks perform better. In experiments with unevenly spaced real-world data, we surprisingly found that a dynamic Bayesian network where time is ignored performs similar to a continuous time Bayesian network.

Conclusion:

The results confirm conventional wisdom that discrete-time Bayesian networks are appropriate when learning from regularly spaced clinical time series. Similarly, we found that time series where the missingness occurs completely at random, dynamic Bayesian networks are an appropriate choice. However, for complex clinical time-series data that motivated this research, the continuous-time models are at least competitive and sometimes better than their discrete-time counterparts. Furthermore, continuous-time models provide additional benefits of being able to provide more fine-grained predictions than discrete-time models, which will be of practical relevance in clinical applications.

Original language | English |
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Pages (from-to) | 104-117 |

Number of pages | 14 |

Journal | Artificial Intelligence in Medicine |

Volume | 95 |

DOIs | |

Publication status | Published - Apr 2019 |

### Keywords

- Dynamic Bayesian networks
- Continuous-time Bayesian networks
- Point evidence
- Interval evidence
- Irregular time-series data
- COPD

## Cite this

Liu, M., Stella, F., Hommersom, A., Lucas, P. J. F., Boer, L., & Bischoff, E. (2019). A comparison between discrete and continuous time Bayesian networks in learning from clinical time series data with irregularity.

*Artificial Intelligence in Medicine*,*95*, 104-117. https://doi.org/10.1016/j.artmed.2018.10.002