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Open Access 01-12-2023 | Research

Statistical actuarial estimation of the Capitation Payment Unit from copula functions and deep learning: historical comparability analysis for the Colombian health system, 2015–2021

Authors: Oscar Espinosa, Valeria Bejarano, Jeferson Ramos, Boris Martínez

Published in: Health Economics Review | Issue 1/2023

Abstract

The Capitation Payment Unit (CPU) financing mechanism constitutes more than 70% of health spending in Colombia, with a budget allocation of close to 60 trillion Colombian pesos for the year 2022 (approximately 15.7 billion US dollars). This article estimates actuarially, using modern techniques, the CPU for the contributory regime of the General System of Social Security in Health in Colombia, and compares it with what is estimated by the Ministry of Health and Social Protection. Using freely available information systems, by means of statistical copulas functions and artificial neural networks, pure risk premiums are calculated between 2015 and 2021. The study concludes that the weights by risk category are systematically different, showing historical pure premiums surpluses in the group of 0–1 years and deficits (for the regions normal and cities) in the groups over 54 years of age.

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Of which people who have the ability to pay and contribute jointly and severally to the SGSSS are part (their respective beneficiaries are also included).

People who cannot pay their affiliation to the SGSSS (essentially people in conditions of vulnerability and poverty) are welcomed here, being subsidized by the State.

Unfortunately for the SR there is no public financial information to calculate its CPU. Historically, the EAHBPs belonging to this regime have had significant quality problems in their administrative records [31, 33].

Understanding by someone exposed to risk, an individual who was affiliated with the CR of the SGSSS for a full calendar year.

A wide review of other types of copula can be found in Nelsen [37] and Latorre [22].

\(\theta\) is the parameter of the Arquimedean copula, which is defined in the bivariate case as \(C\left(u,v\right)={\varphi }_{\theta }^{-1}\left({\varphi }_{\theta }\left(u\right)+{\varphi }_{\theta }\left(v\right)\right)\).

The monetary values of the pure risk premium, the proportion of distinct persons for each reference year and the values of the frequency/severity adjustment factors for each pricing year are presented in Appendix A (Tables A1, A2, A3, A4, A5, A6, A7).

The pure premium of the MHSP is found by multiplying the values of the CR-CPU set out in the resolutions of the entity by the percentage spent by the health insurance not allocated to utilities and administration, which is 0.90 in the case of the studied regime [26].

The analysis developed here make reference to the punctual estimations of the pure premium for the different categories, not to its confidence intervals.

In the year 2021, for the first time in the history of the country, the MHSP used proper information of the SR in the actuarial estimation of the CPU of 2022.

ADRES. (2020). Ejecución presupuestal URA a corte de 31 de diciembre 2020. Retrieved 18 February 2022, from https://servicios.adres.gov.co/La-Entidad/Información-financiera/URA/Ejecución-presupuestal-URA

Ayyildiz, E., Erdogan, M., & Taskin, A. (2021). Forecasting COVID-19 recovered cases with Artificial Neural Networks to enable designing an effective blood supply chain. Computers in Biology and Medicine, 139, 105029. https://doi.org/10.1016/j.compbiomed.2021.105029

Basto S, Bejarano V, Do Nascimento P, Espinosa O, Estrada K, Higuera S, … Barragán L. Producto 3. Estimación actuarial de la UPC del régimen subsidiado. Bogotá: Instituto de Evaluación Tecnológica en Salud y Ministerio de Hacienda y Crédito Público; 2021.

Bolívar, M. (2018). Ajuste de riesgo en la prima de capitación del sistema de aseguramiento en salud de Colombia para el régimen contributivo (Trabajo Final de Posgrado - Universidad de Buenos Aires). Retrieved from http://bibliotecadigital.econ.uba.ar/download/tpos/1502-1486_BolivarVargasMC.pdf

Cao Q, Leggio K, Schniederjans M. A comparison between Fama and French’s model and artificial neural networks in predicting the Chinese stock market. Comput Oper Res. 2005;32(10):2499–512. https://doi.org/10.1016/j.cor.2004.03.015.CrossRef

Charpentier A, editor. Computational actuarial science with R. Boca Raton: Chapman & Hall/CRC; 2015.

Cherubini U, Luciano E. Bivariate option pricing with copulas. Applied Mathematical Finance. 2002;9(2):69–85. https://doi.org/10.1080/13504860210136721a.CrossRef

Chiou, S., & Tsay, R. (2008). A copula-based approach to option pricing and risk assessment. Journal of Data Science, 6, 273–301. Retrieved from https://www.jds-online.com/files/JDS-503.pdf

Corte Constitucional de Colombia. (2018). Sentencia SU124/18. Retrieved 12 February 2022, from https://www.corteconstitucional.gov.co/relatoria/2018/SU124-18.htm

10.

Drummond M, Augustovski F, Bhattacharyya D, Campbell J, Chaiyakanapruk N, Chen Y, ... Yeung K. Challenges of health technology assessment in pluralistic healthcare systems: an ISPOR Council Report. Value in Health. 2022;25(8):1257–67. https://doi.org/10.1016/j.jval.2022.02.006.CrossRefPubMed

11.

Duarte G, Ozaki V. Pricing crop revenue insurance using parametric copulas. Rev Bras Econ. 2019;73(3):325–43. https://doi.org/10.5935/0034-7140.20190015.CrossRef

12.

Duncan I. Healthcare risk adjustment and predictive modelling. 2nd ed. New Hartford: Actex Publications; 2018.

13.

Erdemir Ö, Sucu M. A modified pseudo-copula regression model for risk groups with various dependency levels. J Stat Comput Simul. 2022;92(5):1092–112. https://doi.org/10.1080/00949655.2021.1985498.CrossRef

14.

Escarela D, Carriére J. A bivariate model of claim frequencies and severities. J Appl Stat. 2006;33(8):867–83. https://doi.org/10.1080/02664760600743969.CrossRef

15.

Frees E, Valdez E. Understanding relationships using copulas. North Am Actuarial J. 1998;2(1):1–25. https://doi.org/10.1080/10920277.1998.10595667.CrossRef

16.

Genest, C., Huang, W., & Dufour, J.-M. (2013). A regularized goodness-of-fit test for copulas. Journal de La Société Française de Statistique, 154(1), 64–77. Retrieved from https://jeanmariedufour.github.io/Genest_Huang_Dufour_2012_RevFrancaiseStat_RegularizedGoodnessFitTestCopulas.pdf

17.

Grønneberg S, Hjort N. The copula information criteria. Scand J Stat. 2014;41(2):436–59. https://doi.org/10.1111/sjos.12042.CrossRef

18.

Hofert M, Kojadinovic I, Mächler M, Yan J. Elements of copula modeling with R. Cham: Springer; 2018.CrossRef

19.

Kholifah A, Lestari D, Devila S. Premium calculation using marginal generalized linear model combined with copula. AIP Conf Proc. 2019;2168:020035. https://doi.org/10.1063/1.5132462.CrossRef

20.

Kularatne T, Li J, Pitt D. On the use of Archimedean copulas for insurance modelling. Ann Actuarial Sci. 2021;15(1):57–81. https://doi.org/10.1017/S1748499520000147.CrossRef

21.

Lancheros J. Ajuste por riesgo para el cálculo de la UPC en Colombia: ajuste desde las variables de estado de salud para las aseguradoras colombianas. 2019. https://doi.org/10.15332/tg.mae.2020.0664.

22.

Latorre L. Teoría de cópulas. Introducción y aplicaciones a Solvencia II. Madrid: Fundación MAPFRE; 2017.

23.

Lim B, Zohren S. Time-series forecasting with deep learning: a survey. Philos Trans A Math Phys Eng Sci. 2021;379(2194):20200209. https://doi.org/10.1098/rsta.2020.0209.CrossRefPubMed

24.

Mahmoud, A., & Mohammed, A. (2021). A survey on deep learning for time-series forecasting. In A. Hassanien & A. Darwish (Eds.), Machine learning and big data analytics paradigms: analysis, applications and challenges (pp. 365–392). https://doi.org/10.1007/978-3-030-59338-4_19

25.

Ministerio de Salud y Protección Social. Estudio de la suficiencia y de los mecanismos de ajuste de riesgo para el cálculo de la Unidad de Pago por Capitación para garantizar el Plan Obligatorio de Salud en el año 2006. Bogotá, D.C.; 2006.

26.

Ministerio de Salud y Protección Social. Ley 1438 de 2011. Por medio de la cual se reforma el Sistema General de Seguridad Social en Salud y se dictan otras disposiciones. 2011.

27.

Ministerio de Salud y Protección Social. Resolución 5593 de 2015. Por la cual se fija el valor de la Unidad de Pago por Capitación (UPC) para la cobertura del Plan Obligatorio de Salud de los Regímenes Contributivo y Subsidiado para la vigencia 2016 y se dictan otras disposiciones. Bogotá D.C.; 2015a.

28.

Ministerio de Salud y Protección Social. Resolución 5925. Bogotá D.C.; 2015b.

29.

Ministerio de Salud y Protección Social. Resolución 6411 de 2016. Por la cual se fija el valor de la Unidad de Pago por Capitación -UPC para la cobertura del Plan de Beneficios en Salud de los Regímenes Contributivo y Subsidiado en la vigencia 2017 y se dictan otras disposiciones. Bogotá D.C.; 2016.

30.

Ministerio de Salud y Protección Social. Resolución 5268 de 2017. Por la cual se fija el valor de la Unidad de Pago por Capitación - UPC para el Plan de Beneficios en Salud de los Regímenes Contributivo y Subsidiado para la vigencia 2018 y se dictan otras disposiciones. Bogotá D.C.; 2017.

31.

Ministerio de Salud y Protección Social. Estudio de suficiencia y de los mecanismos de ajuste del riesgo para el cálculo de la Unidad de Pago por Capitación para garantizar el Plan de Beneficios en Salud para el año 2019. In Ministerio de Salud y Protección Social. Bogotá D.C.; 2019a.

32.

Ministerio de Salud y Protección Social. Resolución 3513 de 2019. Por la cual se fijan los recursos de la Unidad de Pago por Capitación - UPC para financiar los servicios y tecnologías de salud, de los Regímenes Contributivo y Subsidiado para la vigencia 2020 y se dictan otras disposiciones. Bogotá D.C.; 2019b.

33.

Ministerio de Salud y Protección Social. Estudio de suficiencia y de los mecanismos de ajuste del riesgo para el cálculo de la Unidad de Pago por Capitación, recursos para garantizar la financiación de tecnologías y servicios de salud en los regímenes Contributivo y Subsidiado. Año 2020. Bogotá D.C.; 2020a.

34.

Ministerio de Salud y Protección Social. Resolución 2503. Bogotá D.C.; 2020b.

35.

36.

Ministerio de Salud y Protección Social. Resolución 2381. Bogotá D.C.; 2021b.

37.

Nelsen R. An introduction to copulas (Second Edi). Portland: Springer; 2006.

38.

Novales, A. (2017). Cópulas. Retrieved from https://www.ucm.es/data/cont/media/www/pag-41459/Copulas.pdf

39.

Oh R, Ahn J, Lee W. On copula-based collective risk models: from elliptical copulas to vine copulas. Scand Actuar J. 2021;2021(1):1–33. https://doi.org/10.1080/03461238.2020.1768889.CrossRef

40.

Parra, L. (2015). Modelamiento conjunto del número de siniestros y pagos por reclamación en seguros mediante una cópula mixta desde la perspectiva frecuentista y bayesiana. Retrieved from https://repositorio.unal.edu.co/bitstream/handle/unal/55421/32297645_2015.pdf?sequence=1

41.

Petropoulos F, Apiletti D, Assimakopoulos V, Babai M, Barrow D, Ben Taieb S, Ziel F. Forecasting: theory and practice. Int J Forecast. 2022. https://doi.org/10.1016/j.ijforecast.2021.11.001.CrossRefPubMedPubMedCentral

42.

Rao, K., Vecino, A., Roberton, T., López, A., & Noonan, C. (2022). Future health spending in Latin America and the Caribbean: health expenditure projections & scenario analysis. Washington, D.C.

43.

Riascos A, Alfonso E, Romero M. The performance of risk adjustment models in Colombian competitive health insurance market. SSRN Electron J. 2014. https://doi.org/10.2139/ssrn.2489183.CrossRef

44.

Riascos, A., Romero, M., & Serna, N. (2018). Risk adjustment revisited using machine learning techniques. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 6(2). https://doi.org/10.2139/ssrn.2973514

45.

Richman R, Wüthrich M. A neural network extension of the Lee-Carter model to multiple populations. Ann Actuarial Sc. 2021;15(2):346–66. https://doi.org/10.1017/S1748499519000071.CrossRef

46.

Shemyakin, A., Zhang, H., Benson, S., Burroughs, R., & Mohr, J. (2019). Copula models of economic capital for life insurance companies. Retrieved from https://www.soa.org/globalassets/assets/files/resources/research-report/2019/copula-models-economic-capital.pdf

47.

Shi P, Feng X, Boucher J-P. Multilevel modeling of insurance claims using copulas. Ann Appl Stat. 2016;10(2):834–63. https://doi.org/10.1214/16-AOAS914.CrossRef

48.

Shi, P., & Lee, G. (2022). Copula regression for compound distributions with endogenous covariates with applications in insurance deductible pricing. Journal of the American Statistical Association, 1–38. https://doi.org/10.1080/01621459.2022.2040519

49.

Shi P, Zhang W. Managed care and health care utilization: specification of bivariate models using copulas. North Am Actuarial J. 2013;17(4):306–24.CrossRef

50.

Sklar A. Fonctions de répartition à n dimensions et leurs marges. Pub Inst Statist Univ Paris. 1959;8:229–31.

51.

Tamraz M. Mixture copulas and insurance applications. Ann Actuarial Sci. 2018;12(2):391–411. https://doi.org/10.1017/S174849951800012X.CrossRef

52.

Torres J, Hadjout D, Sebaa A, Martínez-Álvarez F, Troncoso A. Deep learning for time series forecasting: a survey. Big Data. 2021;9(1):3–21. https://doi.org/10.1089/big.2020.0159.CrossRefPubMed

53.

Werner, G., & Modlin, C. (2016). Basic ratemaking (Vol. 4; Casualty Actuarial Society, Ed.).

54.

Xie Y, Yang J, Jiang C, Cai Z, Adagblenya J. Incidence, dependence structure of disease, and rate making for health insurance. Math Probl Eng. 2018;2018:1–13. https://doi.org/10.1155/2018/4265801.CrossRef

55.

Young, V. (2014). Premium principles. In Wiley StatsRef: Statistics Reference Online. https://doi.org/10.1002/9781118445112.stat04727

56.

Zhao, X., & Zhou, X. (2012). Estimation of medical costs by copula models with dynamic change of health status. Insurance: Mathematics and Economics, 51(2), 480–491. https://doi.org/10.1016/j.insmatheco.2012.07.007

Title: Statistical actuarial estimation of the Capitation Payment Unit from copula functions and deep learning: historical comparability analysis for the Colombian health system, 2015–2021
Authors: Oscar Espinosa
Valeria Bejarano
Jeferson Ramos
Boris Martínez
Publication date: 01-12-2023
Publisher: Springer Berlin Heidelberg
Published in: Health Economics Review / Issue 1/2023
Electronic ISSN: 2191-1991
DOI: https://doi.org/10.1186/s13561-022-00416-5

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Statistical actuarial estimation of the Capitation Payment Unit from copula functions and deep learning: historical comparability analysis for the Colombian health system, 2015–2021

Abstract

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