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

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.

Keywords: Actuarial science; Artificial neural networks; Copulas; Health system; Pure risk premium.

Fig. 1

Frequency of people served by the CR by region, 2013–2019

Fig. 2

CR severity by region, 2013–2019 (2020 prices)

Fig. 3

Number of people exposed to CR risk, 2013–2019

Fig. 4

Distribution of those exposed to CR risk by region, 2013–2019

Fig. 5

Pure premiums estimated via copulas for the years 2015 to 2021, versus what was calculated by the MSHP

Fig. A1

Frequency of people served by the CR by age/sex group, 2013–2019

Fig. A2

CR severity by age/sex group, 2013–2019 (2020 prices)

Fig. A3

Distribution of those exposed to CR risk by age/sex group, 2013–2019