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Health policyholder clustering using medical consumption

A useful tool for targeting prevention plans

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Abstract

On paper, prevention appears to be a good complement to health insurance. However, its implementation is often costly. To maximize the impact and efficiency of prevention plans, plans should target particular groups of policyholders. In this article, we propose a way of clustering policyholders that could be a starting point for the targeting of prevention plans. This two-step method considers mainly policyholder health consumption for classification. The dimension is first reduced using a nonnegative matrix factorization algorithm, producing intermediate health product clusters. Policyholders are then clustered using Kohonen’s map algorithm. This leads to a natural visualization of the results, allowing the simple comparison of results from different databases. The method is applied to two real French health insurer datasets. The method is shown to be easily understandable and able to cluster most policyholders efficiently.

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Notes

  1. The term health product is used for every item of health expenditure that may be refunded by the insurer (such as GP visits, nights at the hospital, medication and glasses).

  2. The legal retirement age in France is 62.

  3. More precisely, if H designs the frequency matrix as described above, the matrix \(log(H + 1)\) is computed.

  4. Six different implementations have been tested: those proposed by Lee and Seung (Lee, [37]), Brunet et al. (Brunet, [9]), Pascual-Montano et al. (nsNMF, [43]) and Badea (Offset, [4]) and the two proposed by Kim and Park (snmf/l and snmf/r, [31]). The “snmf/l” algorithm yields among the best results, while being significantly faster. Implementations from the R package “NMF”, developed by Gaujoux and Seoighe [19], were used in the analysis presented here.

  5. The R package “Kohonen”, developed by Wehrens et al. ([55]), was used in the analysis presented here.

  6. A well-known alternative is to choose the starting points via a PCA; however, Akinduko et al. show that this is not suitable for non-linear datasets [3].

  7. For the databases used here, dimension reduction dramatically improves clustering.

  8. These three concepts are quality indicators commonly measured for a clustering. Cophenetic correlation and dispersion aim to measure the stability and were introduced by Brunet et al. [9]. The silhouette was presented by Rousseeuw to test whether individuals are well clustered [49].

  9. The health product “Legal copayment” may be unfamiliar to the reader. In the French health system, many health products are partially reimbursed by the public insurer, “l’Assurance Maladie”. The price of health products is fixed by law (for example, a GP consultation costs 25 Euros). However, the public insurer does not refund all of this amount (only 16.5 Euros for GPs) to limit health consumption. Here, we call the 25–16.5 gap the “legal copayment”. Moreover, GPs are allowed to charge higher fees that are not covered by the public insurer. The reimbursement of the legal copayment is usually covered by private insurance.

  10. An individual can need glasses and have an operation in the same year. Such an individual would then belong to two clusters: the optic cluster and the hospitalization cluster. In this regard, the health sector is linked to a multi-label context.

  11. In fact, almost none of the 20 HPCs made using the PCA offer satisfying consistency.

  12. The \(R^{2}\) coefficient is given by \(R^{2} = 1 - \frac{\sum _{i=1}^{k} I_{C_{i}}}{I_{C}}\), with \(I_{C_{i}}\) denoting the inertia of the cluster \(C_{i}\). The inertia has been computed using the cosine similarity, following the recommendation of Huang [28].

  13. See Sect. 2 for a review of the subdatabases.

  14. According to Wikipedia, “Orthoptics is a profession allied to eye care professions whose primary emphasis is the diagnosis and non-surgical management of strabismus (wandering eyes), amblyopia (lazy eye) and eye movement disorders”.

  15. The same definition as that of Huang [28] has been used.

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Acknowledgements

The authors would like to thank Alexandra Barral for useful comments over the duration of this research, and Nabil Rachdi for technical advice. They are also grateful to Addactis in France for providing the data, and to everyone (including two reviewers) who had reread the paper. This research was carried out in the framework of the Chair Prevent'Horizon, supported by the risk foundation Louis Bachelier and in partnership with Claude Bernard Lyon 1 University, Addactis in France, AG2R La Mondiale, G2S, Covea, Groupama Gan Vie, Groupe Pasteur Mutualité, Harmonie Mutuelle, Humanis Prévoyance and La Mutuelle Générale. S. Loisel acknowledges support from the IDR Actuariat Durable sponsored by Milliman Paris, and the DAMI research chair sponsored by BNP Paribas Cardif.

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Authors and Affiliations

  1. Université de Lyon, Université Claude Bernard Lyon 1, ISFA, LSAF, Lyon, France

    Romain Gauchon, Stéphane Loisel & Jean-Louis Rullière

  2. Addactis France, Tassin-la-Demi-Lune, France

    Romain Gauchon

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  1. Romain Gauchon
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  2. Stéphane Loisel
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Appendix

Appendix

1.1 Appendix 1: Comparing the clusters obtained using the proposed method with those obtained using a very basic approach

See Figs. 12 and 13.

Fig. 12
figure 12

Detailed statistics for all classes

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Fig. 13
figure 13

Consumption if consuming at least some of a particular health product and overall consumption

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1.2 Appendix 2: An example of another map obtained from the same data

See Fig. 14.

Fig. 14
figure 14

Self-organizing map obtained from the same data as in Fig. 6, using a different seed

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1.3 Appendix 3: Test of the algorithm on a database with known clusters

While several tests have been carried out to test the relevance of the results obtained in health insurance databases, it is impossible to compute an objective error metric because the underlying clusters are unknown. To process this kind of test, it is thus necessary to use a dataset coming from another field. For example, the text mining field offers many databases with known clusters. Moreover, it is a common practice in this field to work with a word frequency matrix, making it realistic to apply the NMF/Kohonen process to a text-mining dataset.

The 20-newsgroups dataset is chosen to perform this test. This is a well-known text-mining dataset and has been used for various text-mining tasks, such as word embedding (e.g., [25, 54]), unsupervised clustering (e.g., [17, 28]) and supervised classification (e.g., [47, 50]). The training test dataset has been used, representing 11 293 texts from 20 different newsgroups. For this study, we use the dataset as pre-processed by Cardoso Cachopo [11] (the “no-short” dataset). The objective is to find the original newsgroup of each document.

As text mining is not one of the goals of this paper, the results presented below come from the first run of the algorithm, without attempts to calibrate the model or improve the results. The dimension is first reduced to 60 before clustering, and the frequency matrix is pre-processed using the tf-idf method, which is a common practice in text mining. Since the 20-newsgroups dataset contains 20 different natural clusters, the HAC has been calibrated to obtain 20 different classes.

From the Kohonen map (Fig. 15), it is possible to see that clusters 2 and 10 are spread out. Moreover, clusters 6 and 9 seem significantly larger than the others. Their purity score confirms that they are less homogeneous than the other clusters (purity is shown in Fig. 17). Except for in these four clusters and cluster 18, purity is acceptable. The overall purity is 62%, and the total entropyFootnote 15 is 0.4, which is significantly better than the results obtained by Huang from the same dataset [28], even though we do not aim to achieve a good score.

Fig. 15
figure 15

Kohonen’s map using the 20-Newsgroups Dataset. Cluster 10 cannot be constructed

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Comparing Figs. 16 and 17, even though the algorithm does not identify all of the documents in a given cluster, the resulting clusters are still reliable. This means that if one wants to identify all of the policyholders with psychiatric medication (for example), this algorithm is not very appropriate. However, if a psychiatric class is identified, it is reliable enough to justify the targeting of a prevention plan.

Fig. 16
figure 16

Newsgroup reconstitution capacity

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Fig. 17
figure 17

Cluster purity

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To summarize, the method produces acceptable results for the 20-newsgroup dataset. Most of the clusters represent a specific newsgroup. However, the method cannot differentiate between very similar newsgroups, such as IBM and Mac computers. This produces large clusters containing most of the documents the method cannot differentiate.

This clustering method is thus able to construct meaningful policyholder clusters. However, large classes (such as the everyday-care cluster) are heterogeneous and should not be used to target prevention plans: they contain policyholders who cannot be differentiated by the algorithm.

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Gauchon, R., Loisel, S. & Rullière, JL. Health policyholder clustering using medical consumption. Eur. Actuar. J. 10, 599–626 (2020). https://doi.org/10.1007/s13385-020-00244-z

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