Deep learning for clustering of multivariate clinical patient trajectories with missing values

Abstract

Background: Precision medicine requires a stratification of patients by disease presentation that is sufficiently informative to allow for selecting treatments on a per-patient basis. For many diseases, such as neurological disorders, this stratification problem translates into a complex problem of clustering multivariate and relatively short time series because (i) these diseases are multifactorial and not well described by single clinical outcome variables and (ii) disease progression needs to be monitored over time. Additionally, clinical data often additionally are hindered by the presence of many missing values, further complicating any clustering attempts.

Findings: The problem of clustering multivariate short time series with many missing values is generally not well addressed in the literature. In this work, we propose a deep learning-based method to address this issue, variational deep embedding with recurrence (VaDER). VaDER relies on a Gaussian mixture variational autoencoder framework, which is further extended to (i) model multivariate time series and (ii) directly deal with missing values. We validated VaDER by accurately recovering clusters from simulated and benchmark data with known ground truth clustering, while varying the degree of missingness. We then used VaDER to successfully stratify patients with Alzheimer disease and patients with Parkinson disease into subgroups characterized by clinically divergent disease progression profiles. Additional analyses demonstrated that these clinical differences reflected known underlying aspects of Alzheimer disease and Parkinson disease.

Conclusions: We believe our results show that VaDER can be of great value for future efforts in patient stratification, and multivariate time-series clustering in general.

Keywords: clustering; deep learning; multivariate longitudinal data; multivariate time series; patient stratification.

Figure 1:

VaDER architecture.

Figure 2:

VaDER performance on simulated data, with varying degrees of clusterability and missingness. (a) Cluster purity [37] for clustering of simulated data as a function of the clusterability parameter λ, with higher λ implying a higher degree of similarity between profiles in the same cluster. Results are shown for VaDER as well as hierarchical clustering using 5 different distance measures, (i) Euclidean distance, (ii) Pearson correlation, (iii) the STS distance [40], (IV) multi-dimensional dynamic time warping (MD-DTW), [38] and (5) Global Alignment Kernels (GAK) [39]. (b) Cluster purity as a function of the fraction θ of values missing completely at random (MCAR), for various levels of the clusterability parameter λ, for both VaDER with implicit imputation and VaDER with pre-imputation. Confidence intervals were determined by repeating the clustering 100 times using newly generated random data and missingness patterns. (c) Cluster purity as a function of the fraction θ of values missing not at random (MNAR) (see Methods for details), for various levels of the clusterability parameter λ, for both VaDER with implicit imputation and VaDER with pre-imputation. Confidence intervals were determined by repeating the clustering 100 times using newly generated random data and missingness patterns.

Figure 3:

VaDER performance on benchmark data, for varying degrees of missingness. (a) Cluster purity [37] for clustering of benchmark data. Results are shown for VaDER as well as hierarchical clustering using 5 different distance measures, (i) Euclidean distance, (ii) Pearson correlation, (iii) the STS distance [40], (iv) multi-dimensional dynamic time warping (MD-DTW) [38], and (v) Global Alignment Kernels (GAK) [39]. For each dataset, the best performance across methods is marked by a horizontal dotted line. Confidence intervals were determined by bootstrapping the clustering 10³ times. (b) Cluster purity as a function of the fraction θ of values missing completely at random (MCAR), for both VaDER with implicit imputation and VaDER with pre-imputation. Confidence intervals were determined by repeating the clustering 5 times using newly generated random missingness patterns. (c) Cluster purity as a function of the fraction θ of values missing not at random (MNAR), for both VaDER with implicit imputation and VaDER with pre-imputation. Confidence intervals were determined by repeating the clustering 5 times using newly generated random missingness patterns.

Figure 4:

Normalized cluster mean trajectories relative to baseline (x-axis in months), as identified by VaDER from the ADNI cognitive assessment data.

Figure 5:

Normalized cluster mean trajectories relative to baseline (x-axis in months), as identified by VaDER from the PPMI motor/non-motor score data.