{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T04:10:11Z","timestamp":1779250211416,"version":"3.51.4"},"reference-count":63,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2020,8,6]],"date-time":"2020-08-06T00:00:00Z","timestamp":1596672000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Although many authors have highlighted the importance of predicting people\u2019s health costs to improve healthcare budget management, most of them do not address the frequent need to know the reasons behind this prediction, i.e., knowing the factors that influence this prediction. This knowledge allows avoiding arbitrariness or people\u2019s discrimination. However, many times the black box methods (that is, those that do not allow this analysis, e.g., methods based on deep learning techniques) are more accurate than those that allow an interpretation of the results. For this reason, in this work, we intend to develop a method that can achieve similar returns as those obtained with black box methods for the problem of predicting health costs, but at the same time it allows the interpretation of the results. This interpretable regression method is based on the Dempster-Shafer theory using Evidential Regression (EVREG) and a discount function based on the contribution of each dimension. The method \u201clearns\u201d the optimal weights for each feature using a gradient descent technique. The method also uses the nearest k-neighbor algorithm to accelerate calculations. It is possible to select the most relevant features for predicting a patient\u2019s health care costs using this approach and the transparency of the Evidential Regression model. We can obtain a reason for a prediction with a k-NN approach. We used the Japanese health records at Tsuyama Chuo Hospital to test our method, which included medical examinations, test results, and billing information from 2013 to 2018. We compared our model to methods based on an Artificial Neural Network, Gradient Boosting, Regression Tree and Weighted k-Nearest Neighbors. Our results showed that our transparent model performed like the Artificial Neural Network and Gradient Boosting with an R2 of 0.44.<\/jats:p>","DOI":"10.3390\/s20164392","type":"journal-article","created":{"date-parts":[[2020,8,6]],"date-time":"2020-08-06T09:41:21Z","timestamp":1596706881000},"page":"4392","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Feature Selection for Health Care Costs Prediction Using Weighted Evidential Regression"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-1440-8192","authenticated-orcid":false,"given":"Belisario","family":"Panay","sequence":"first","affiliation":[{"name":"Department of Computer Science, Universidad de Chile, Santiago 8320000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0003-1608-6454","authenticated-orcid":false,"given":"Nelson","family":"Baloian","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Universidad de Chile, Santiago 8320000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 A.","family":"Pino","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Universidad de Chile, Santiago 8320000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergio","family":"Pe\u00f1afiel","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Universidad de Chile, Santiago 8320000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Horacio","family":"Sanson","sequence":"additional","affiliation":[{"name":"Allm Inc., Tokyo 150-0002, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicolas","family":"Bersano","sequence":"additional","affiliation":[{"name":"Allm Inc., Tokyo 150-0002, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,6]]},"reference":[{"key":"ref_1","unstructured":"WHO (2018). Public Spending on Health: A Closer Look at Global Trends, World Health Organization. Technical Report."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1257\/jep.22.4.27","article-title":"Is American health care uniquely inefficient?","volume":"22","author":"Garber","year":"2008","journal-title":"J. Econ. Perspect."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2431","DOI":"10.1007\/s10916-011-9710-5","article-title":"Data mining in healthcare and biomedicine: A survey of the literature","volume":"36","author":"Yoo","year":"2012","journal-title":"J. Med. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1002\/hec.3003","article-title":"Measuring overfitting in nonlinear models: A new method and an application to health expenditures","volume":"24","author":"Bilger","year":"2015","journal-title":"Health Econ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1146\/annurev.publhealth.20.1.125","article-title":"Methods for analyzing health care utilization and costs","volume":"20","author":"Diehr","year":"1999","journal-title":"Annu. Rev. Public Health"},{"key":"ref_6","unstructured":"Kronick, R., Gilmer, T., Dreyfus, T., and Ganiats, T. (2020, May 02). CDPS-Medicare: The Chronic Illness and Disability Payment System Modified to Predict Expenditures for Medicare Beneficiaries. Available online: https:\/\/2.zoppoz.workers.dev:443\/http\/cdps.ucsd.edu\/CDPS_Medicare.pdf."},{"key":"ref_7","first-page":"1312","article-title":"Supervised Learning Methods for Predicting Healthcare Costs: Systematic Literature Review and Empirical Evaluation","volume":"Volume 2017","author":"Morid","year":"2017","journal-title":"AMIA Annual Symposium Proceedings"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"113262","DOI":"10.1016\/j.eswa.2020.113262","article-title":"Applying Dempster\u2013Shafer theory for developing a flexible, accurate and interpretable classifier","volume":"148","author":"Baloian","year":"2020","journal-title":"Expert Syst. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Shafer, G. (1976). A Mathematical Theory of Evidence, Princeton University Press.","DOI":"10.1515\/9780691214696"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0888-613X(03)00056-2","article-title":"Nonparametric regression analysis of uncertain and imprecise data using belief functions","volume":"35","year":"2004","journal-title":"Int. J. Approx. Reason."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1382","DOI":"10.1287\/opre.1080.0619","article-title":"Algorithmic prediction of health-care costs","volume":"56","author":"Bertsimas","year":"2008","journal-title":"Oper. Res."},{"key":"ref_12","unstructured":"Sushmita, S., Newman, S., Marquardt, J., Ram, P., Prasad, V., Cock, M.D., and Teredesai, A. (2020, May 03). Population Cost Prediction on Public Healthcare Datasets. Available online: https:\/\/2.zoppoz.workers.dev:443\/https\/dl.acm.org\/doi\/abs\/10.1145\/2750511.2750521."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1080\/10920277.2015.1110491","article-title":"Testing alternative regression frameworks for predictive modeling of health care costs","volume":"20","author":"Duncan","year":"2016","journal-title":"N. Am. Actuar. J."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Panay, B., Baloian, N., Pino, J.A., Pe\u00f1afiel, S., Sanson, H., and Bersano, N. (2019). Predicting Health Care Costs Using Evidence Regression. Proceedings, 31.","DOI":"10.3390\/proceedings2019031074"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1002\/hec.1653","article-title":"Review of statistical methods for analysing healthcare resources and costs","volume":"20","author":"Mihaylova","year":"2011","journal-title":"Health Econ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/S0167-6296(98)00032-0","article-title":"Modeling risk using generalized linear models","volume":"18","author":"Blough","year":"1999","journal-title":"J. Health Econ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0304-4076(94)01720-4","article-title":"On the choice between sample selection and two-part models","volume":"72","author":"Leung","year":"1996","journal-title":"J. Econ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2716","DOI":"10.1002\/sim.2728","article-title":"Estimating the costs for a group of geriatric patients using the Coxian phase-type distribution","volume":"26","author":"Marshall","year":"2007","journal-title":"Stat. Med."},{"key":"ref_19","unstructured":"Jones, A.M. (2009). Models for Health Care, University of York, Centre for Health Economics."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"677","DOI":"10.3346\/jkms.2004.19.5.677","article-title":"Comparison of hospital charge prediction models for colorectal cancer patients: Neural network vs. decision tree models","volume":"19","author":"Lee","year":"2004","journal-title":"J. Korean Med. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1017\/S1748499512000346","article-title":"Actuarial applications of multivariate two-part regression models","volume":"7","author":"Frees","year":"2013","journal-title":"Ann. Actuar. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1111\/j.1365-2656.2008.01390.x","article-title":"A working guide to boosted regression trees","volume":"77","author":"Elith","year":"2008","journal-title":"J. Anim. Ecol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/S0169-7161(04)24011-1","article-title":"Classification and regression trees, bagging, and boosting","volume":"24","author":"Sutton","year":"2005","journal-title":"Handb. Stat."},{"key":"ref_24","unstructured":"Zurada, J.M. (1992). Introduction to Artificial Neural Systems, West Publishing Company."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Breiman, L. (2017). Classification and Regression Trees, Routledge.","DOI":"10.1201\/9781315139470"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Tanuseputro, P., Wodchis, W.P., Fowler, R., Walker, P., Bai, Y.Q., Bronskill, S.E., and Manuel, D. (2015). The health care cost of dying: A population-based retrospective cohort study of the last year of life in Ontario, Canada. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0121759"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.jhealeco.2017.11.001","article-title":"Health care expenditures, age, proximity to death and morbidity: Implications for an ageing population","volume":"57","author":"Howdon","year":"2018","journal-title":"J. Health Econ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1186\/s13561-019-0224-z","article-title":"Proximity to death and health care expenditure increase revisited: A 15-year panel analysis of elderly persons","volume":"9","year":"2019","journal-title":"Health Econ. Rev."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Friedman, J., Hastie, T., and Tibshirani, R. (2001). The Elements of Statistical Learning, Springer.","DOI":"10.1007\/978-0-387-21606-5"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"131","DOI":"10.3233\/IDA-1997-1302","article-title":"Feature selection for classification","volume":"1","author":"Dash","year":"1997","journal-title":"Intell. Data Anal."},{"key":"ref_31","unstructured":"Yu, L., and Liu, H. (2020, May 04). Redundancy Based Feature Selection for Microarray Data. Available online: https:\/\/2.zoppoz.workers.dev:443\/http\/www.cs.binghamton.edu\/~lyu\/publications\/Yu-Liu04KDD.pdf."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2383","DOI":"10.1016\/j.patcog.2005.11.001","article-title":"Incremental wrapper-based gene selection from microarray data for cancer classification","volume":"39","author":"Ruiz","year":"2006","journal-title":"Pattern Recognit."},{"key":"ref_33","unstructured":"Guyon, I., Gunn, S., Nikravesh, M., and Zadeh, L.A. (2008). Feature Extraction: Foundations and Applications, Springer."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Benesty, J., Chen, J., Huang, Y., and Cohen, I. (2009). Pearson correlation coefficient. Noise Reduction in Speech Processing, Springer.","DOI":"10.1007\/978-3-642-00296-0_5"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Goutte, C., and Gaussier, E. (2005). A probabilistic interpretation of precision, recall and F-score, with implication for evaluation. European Conference on Information Retrieval, Springer.","DOI":"10.1007\/978-3-540-31865-1_25"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2208","DOI":"10.1016\/j.ins.2009.02.014","article-title":"A wrapper method for feature selection using support vector machines","volume":"179","author":"Maldonado","year":"2009","journal-title":"Inf. Sci."},{"key":"ref_37","first-page":"18","article-title":"Classification and regression by randomForest","volume":"2","author":"Liaw","year":"2002","journal-title":"R News"},{"key":"ref_38","unstructured":"Xu, Z., Huang, G., Weinberger, K.Q., and Zheng, A.X. (2020, May 04). Gradient Boosted Feature Selection. Available online: https:\/\/2.zoppoz.workers.dev:443\/https\/alicezheng.org\/papers\/gbfs.pdf."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1023\/A:1025667309714","article-title":"Theoretical and empirical analysis of ReliefF and RReliefF","volume":"53","author":"Kononenko","year":"2003","journal-title":"Mach. Learn."},{"key":"ref_40","unstructured":"Navot, A., Shpigelman, L., Tishby, N., and Vaadia, E. (2020, May 04). Nearest Neighbor Based Feature Selection for Regression and Its Application to Neural Activity. Available online: https:\/\/2.zoppoz.workers.dev:443\/https\/papers.nips.cc\/paper\/2848-nearest-neighbor-based-feature-selection-for-regression-and-its-application-to-neural-activity.pdf."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1016\/j.knosys.2018.10.004","article-title":"Weighted nearest neighbors feature selection","volume":"163","author":"Bugata","year":"2019","journal-title":"Knowl.-Based Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.ijar.2015.12.009","article-title":"Dempster\u2019s rule of combination","volume":"79","author":"Shafer","year":"2016","journal-title":"Int. J. Approx. Reason."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1016\/j.ymssp.2008.08.004","article-title":"Dempster\u2013Shafer regression for multi-step-ahead time-series prediction towards data-driven machinery prognosis","volume":"23","author":"Niu","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.eswa.2017.04.035","article-title":"Prediction of industrial equipment remaining useful life by fuzzy similarity and belief function theory","volume":"83","author":"Baraldi","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_45","unstructured":"WHO (2001). International Classification of Functioning, Disability and Health: ICF, World Health Organization."},{"key":"ref_46","first-page":"55","article-title":"The Claim Database in Japan","volume":"6","author":"Matsuda","year":"2014","journal-title":"Asian Pac. J. Dis. Manag."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/s10115-012-0487-8","article-title":"A review of feature selection methods on synthetic data","volume":"34","year":"2013","journal-title":"Knowl. Inf. Syst."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Aggarwal, C.C., Hinneburg, A., and Keim, D.A. (2001). On the surprising behavior of distance metrics in high dimensional space. International Conference on Database Theory, Springer.","DOI":"10.1007\/3-540-44503-X_27"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1145\/2347736.2347755","article-title":"A few useful things to know about machine learning","volume":"55","author":"Domingos","year":"2012","journal-title":"Commun. ACM"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/s11075-007-9072-8","article-title":"On choosing \u201coptimal\u201d shape parameters for RBF approximation","volume":"45","author":"Fasshauer","year":"2007","journal-title":"Numer. Algorithms"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1137\/11S010840","article-title":"Choosing basis functions and shape parameters for radial basis function methods","volume":"4","author":"Mongillo","year":"2011","journal-title":"SIAM Undergrad. Res. Online"},{"key":"ref_52","unstructured":"Yager, R., Fedrizzi, M., and Kacprzyk, J. (1994). What is Dempster-Shafer\u2019s model. Advances in the Dempster-Shafer Theory of Evidence, Wiley."},{"key":"ref_53","unstructured":"Johnson, J., Douze, M., and J\u00e9gou, H. (2020, May 06). Billion-Scale Similarity Search with GPUs. Available online: https:\/\/2.zoppoz.workers.dev:443\/https\/arxiv.org\/pdf\/1702.08734.pdf."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1109\/TIT.1978.1055865","article-title":"The uniform convergence of nearest neighbor regression function estimators and their application in optimization","volume":"24","author":"Devroye","year":"1978","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Atkeson, C.G., Moore, A.W., and Schaal, S. (1997). Locally weighted learning. Lazy Learning, Springer.","DOI":"10.1007\/978-94-017-2053-3_2"},{"key":"ref_56","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_57","unstructured":"Ruder, S. (2016). An overview of gradient descent optimization algorithms. arXiv."},{"key":"ref_58","first-page":"1","article-title":"Multivariate adaptive regression splines","volume":"19","author":"Friedman","year":"1991","journal-title":"Ann. Stat."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Koller, D., Sch\u00f6n, G., Sch\u00e4fer, I., Glaeske, G., van den Bussche, H., and Hansen, H. (2014). Multimorbidity and long-term care dependency\u2014A five-year follow-up. BMC Geriatr., 14.","DOI":"10.1186\/1471-2318-14-70"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"James, G., Witten, D., Hastie, T., and Tibshirani, R. (2013). An Introduction to Statistical Learning, Springer.","DOI":"10.1007\/978-1-4614-7138-7"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"S5","DOI":"10.1007\/s00125-002-0858-x","article-title":"Revealing the cost of Type II diabetes in Europe","volume":"45","year":"2002","journal-title":"Diabetologia"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1498","DOI":"10.1007\/s00125-006-0277-5","article-title":"The cost burden of diabetes mellitus: The evidence from Germany\u2014The CoDiM study","volume":"49","author":"Ihle","year":"2006","journal-title":"Diabetologia"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1002\/hec.831","article-title":"Time to include time to death? The future of health care expenditure predictions","volume":"13","author":"Stearns","year":"2004","journal-title":"Health Econ."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.mdpi.com\/1424-8220\/20\/16\/4392\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:57:16Z","timestamp":1760176636000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.mdpi.com\/1424-8220\/20\/16\/4392"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,6]]},"references-count":63,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2020,8]]}},"alternative-id":["s20164392"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/s20164392","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,6]]}}}