Analysis of healthcare service utilization after transport-related injuries by a mixture of hidden Markov models

Abstract

Background: Transport injuries commonly result in significant disease burden, leading to physical disability, mental health deterioration and reduced quality of life. Analyzing the patterns of healthcare service utilization after transport injuries can provide an insight into the health of the affected parties, allow improved health system resource planning, and provide a baseline against which any future system-level interventions can be evaluated. Therefore, this research aims to use time series of service utilization provided by a compensation agency to identify groups of claimants with similar utilization patterns, describe such patterns, and characterize the groups in terms of demographic, accident type and injury type.

Methods: To achieve this aim, we have proposed an analytical framework that utilizes latent variables to describe the utilization patterns over time and group the claimants into clusters based on their service utilization time series. To perform the clustering without dismissing the temporal dimension of the time series, we have used a well-established statistical approach known as the mixture of hidden Markov models (MHMM). Ensuing the clustering, we have applied multinomial logistic regression to provide a description of the clusters against demographic, injury and accident covariates.

Results: We have tested our model with data on psychology service utilization from one of the main compensation agencies for transport accidents in Australia, and found that three clear clusters of service utilization can be evinced from the data. These three clusters correspond to claimants who have tended to use the services 1) only briefly after the accident; 2) for an intermediate period of time and in moderate amounts; and 3) for a sustained period of time, and intensely. The size of these clusters is approximately 67%, 27% and 6% of the number of claimants, respectively. The multinomial logistic regression analysis has showed that claimants who were 30 to 60-year-old at the time of accident, were witnesses, and who suffered a soft tissue injury were more likely to be part of the intermediate cluster than the majority cluster. Conversely, claimants who suffered more severe injuries such as a brain head injury or anon-limb fracture injury and who started their service utilization later were more likely to be part of the sustained cluster.

Conclusion: This research has showed that clustering of service utilization time series is an effective approach for identifying the main user groups and utilization patterns of a healthcare service. In addition, using logistic regression to describe the clusters in terms of demographic, injury and accident covariates has helped identify the salient attributes of the claimants in each cluster. This finding is very important for the compensation agency and potentially other authorities as it provides a baseline to improve need understanding, resource planning and service provision.

Fig 1. “Stacked plot” of the number of monthly utilizations of the psychology service.

This figure shows the 788 times series as a “stacked plot. The height of each colored bar is proportional to the number of time series with that given number of utilizations.

Fig 2. Stacked plots of the number of monthly utilizations of the psychology service for cluster 1 (528 claimants), cluster 2 (211 claimants) and cluster 3 (49 claimants).

Based on the trends in the plots, we qualitatively describe these clusters as “brief”, “intermediate”, and “sustained”.

Fig 3. Stacked “state paths” for the three clusters of the psychology service.

This figure shows the stacked “state paths” (i.e., the traversed sequences of states) of the claimants in each cluster. These plots confirm the different utilization trends in the three clusters.

Fig 4. HMM state diagrams for the three clusters of the psychology service.

Each state of each HMM is represented by a pie chart. The number of utilizations associated with the state are displayed as slices of the pie, with the size of each slice proportional to how frequent each number appears. The pies are connected by edges which represent how long the state typically lasts, and how frequently it instead changes to another state (i.e., the transition probabilities).

Fig 5. Comparing the clusters obtained with MHMM, PAM, CLARA and FCM MHMM.

The clusters are plotted in 2D using multidimensional scaling.