Regional medical inter-institutional cooperation in medical provider network constructed using patient claims data from Japan

Abstract

The aging world population requires a sustainable and high-quality healthcare system. To examine the efficiency of medical cooperation, medical provider and physician networks were constructed using patient claims data. Previous studies have shown that these networks contain information on medical cooperation. However, the usage patterns of multiple medical providers in a series of medical services have not been considered. In addition, these studies used only general network features to represent medical cooperation, but their expressive ability was low. To overcome these limitations, we analyzed the medical provider network to examine its overall contribution to the quality of healthcare provided by cooperation between medical providers in a series of medical services. This study focused on: i) the method of feature extraction from the network, ii) incorporation of the usage pattern of medical providers, and iii) expressive ability of the statistical model. Femoral neck fractures were selected as the target disease. To build the medical provider networks, we analyzed the patient claims data from a single prefecture in Japan between January 1, 2014 and December 31, 2019. We considered four types of models. Models 1 and 2 use node strength and linear regression, with Model 2 also incorporating patient age as an input. Models 3 and 4 use feature representation by node2vec with linear regression and regression tree ensemble, a machine learning method. The results showed that medical providers with higher levels of cooperation reduce the duration of hospital stay. The overall contribution of the medical cooperation to the duration of hospital stay extracted from the medical provider network using node2vec is approximately 20%, which is approximately 20 times higher than the model using strength.

Fig 1. Conceptual diagram of regional inter-institutional medical cooperation for treating femoral neck fracture.

The red arrows represent the flow of patients. The blue arrows represent the service provision relationship. Patients with femoral neck fractures are hospitalized in the acute and recovery phase hospitals. Community hospitals and nursing homes provide long-term care (LTC) after discharge. The administration provides social services to maintain and improve the health of patients before and after a fracture.

Fig 2. Methods for calculating duration of hospital stay Dⁱⁿ.

(a) Extracting a series of medical records using two types of threshold τ₁ and τ₂. The threshold of hospital transfer τ₁ determines the inpatient transfer. The threshold of care continuity τ₂ is used to integrate pre-and post-hospitalization outpatient records into the series of medical records. (b) Calculating the duration of hospital stay Dⁱⁿ from each series of medical records. In the case of medical records with hospital transfers, the date of admission at the first medical provider to the date of discharge at the last medical provider is Dⁱⁿ. H denotes set of medical providers where a patient is hospitalized.

Fig 3. Network diagram of the medical provider network.

Number of nodes (medical providers) N = 644, number of edges L = 2756. The prefecture is divided into five medical administration areas, and the nodes are color-coded according to each area. The node size is based on the number of beds in the medical provider. The nodes located in the same area are close to each other on the network.

Fig 4. Empirical complementary cumulative distribution functions (CCDF) of degree and strength.

(a) Degree and (b) strength. Both are widely distributed. These figures show that the number of medical providers with which patients are shared and the level of medical cooperation with neighboring medical providers vary greatly among medical providers.

Fig 5. Distribution of duration of hospital stay Dⁱⁿ.

(a) Empirical cumulative distribution functions (CDF). (b) Empirical complementary cumulative distribution functions (CCDF). In the logarithmic plot, both tails are straight, which are similar to a power law distribution.

Fig 6. Result of linear regression model with duration of hospital stay Dⁱⁿ as output variable and geometric mean of strength μ_G(s) and age as input variables.

(a) Dⁱⁿ vs. μ_G(s) (R² = 0.0085). (b) Dⁱⁿ vs. μ_G(s) and age (R² = 0.011). These show the negative relationship between Dⁱⁿ and μ_G(s). In addition, the explanatory ability of the statistical model is increased by considering the effect of age on the duration of of hospital stay.

Fig 7. Comparison of measured duration of hospital stay Dⁱⁿ and predicted the duration of of hospital stay D^in by linear regression model with geometric mean of strength μ_G(s) and age as input variables.

(a) μ_G(s). (b) μ_G(s) and age. ${\widehat{D}}^{\text{in}}$ obtained by five-fold cross validation is shown. Both are underfitting and do not fully explain the variation in Dⁱⁿ.

Fig 8. Result of grid search of hyperparameters p and q of node2vec.

(a) p, q ∈ {1/8, 1/4, 1/2, 1, 2, 4, 8}, the number of iteration = 100. (b) p ∈ {4, 8, 16, 32, 64, 128} and q ∈ {1/128, 1/64, 1/32, 1/16, 1/8, 1/4}, the number of iteration = 300. Here, we set (t, l, w, d) = (7, 60, 13, 75), as determined by the pre-analysis. We evaluated the regression performance with the changes in parameters p and q using the root mean squared error (RMSE). Although the variation in RMSE with the change in parameters is not large, the regression performance tends to improve when p is large, and q is small. However, there is little change in RMSE in the range when p is sufficiently large and q is sufficiently small.

Fig 9. Comparison of measured duration of hospital stay Dⁱⁿ and predicted duration of hospital stay D^in calculated by linear regression model.

The predicted and the measured values calculated by the linear regression model with the average value of μ(v) of the feature representations by node2vec as the input variable. We select the best result comparing the coefficient of determination R² among all sets extracted through 300 iterations (R² = 0.17).

Fig 10. Relationship between geometric mean of strength μ_G(s) and network features of each community.

(a) μ_G(s) vs. the average distance normalized by the number of nodes 〈d〉/N. (b) μ_G(s) vs. the average clustering coefficient 〈C〉. (c) μ_G(s) vs. assortativity r. There is a linear relationship between each network feature and μ_G(s), indicating that there is a relationship between network structure and medical cooperation.

Fig 11. Comparison of measured duration of hospital stay Dⁱⁿ and predicted duration of hospital stay Dⁱⁿ calculated by regression tree ensemble model.

The predicted and measured values calculated by the regression tree ensemble model with the average value of μ(v) of the feature representations by node2vec as the input variable. We select the best result comparing the coefficient of determination R² among all sets extracted through 300 iterations (R² = 0.24).