Estimating medical costs has been a concern in countries where services are offered through a mean fee. However, many of the estimations have been imprecise. Some countries, like Peru, have undertaken methodologies to try to estimate the standard costs of the medical procedures that will then be incorporated into the Universal Health Benefits Plan ¹.

In Colombia, estimates have been made since 1993 of the medical cost that will be incurred during the following year by a population ensured with the General Social Security System (SGSS, for the term in Spanish), an estimation denominated: “ex ante approximation”, and legislatively called Capitation Payment Unit ”CPU”, articles 156 and 179 of Legislation 100 ² and with which the health promoter entities (EPS o HMO) must manage the offer of the health services hiring the network that provides these services to the population ensured, article 205 of Legislation 100 ². The Ministry of Health traditionally, since 1994 to date, has calculated this fee by using simple linear regression models (SLR).

This work proposed the search for cost estimation models that include independent variables, like the age and gender of the affiliate, as has usually been done by the Colombian Ministry of Health, as well as the inclusion of variables associated with the health-disease status of each affiliate cared for. Likewise, it sought to propose modelling techniques different from the traditional, like the SLR models to estimate costs, and included other models until achieving an adequate one with satisfactory performance in the valuation of statistical goodness of fit indicators, like the case of generalized linear models (GLM). This type of model measures goodness of fit with a couple of indicators: the Deviance indicator, which may be understood as a measurement of the lack of information available in the model to explain the phenomenon of interest in the response variable (the smaller the better), and the Akaike Information Criterion (AIC), an indicator that in its calculation involves the Deviance penalized by the number of parameters involved in the model (the smaller the better). The first model estimated, SLR, did not fulfill the basic validation assumptions, like normality and homoscedasticity in the dependent variable, additionally, no adequate goodness of fit indicators were obtained, given that the R² at most reached 6%. Thereafter, more robust estimation models were proposed, like the GLM applied in modelling two parts (estimating in the first part the probability of using the health services, and in the second part estimating the costs implied in said use), which has found considerable acceptance in the methodology of evaluating risks, thus, obtaining a general expenditure prediction for an individual, upon multiplying both predictions obtained from each part of the model ^3,4.

This work sought to find an ex ante prediction model that, besides estimating the POS medical cost, complies with more robust or adequate statistical criteria to the traditional, as well as a search for predictive methodologies of the medical costs that can serve to monitor the costs of health services required by the users of a health insurer without having the prior invoicing and only having demographic factors, variables appertaining to the insurance business, and the user risk classification variable.

This research contributes to and enhances the theory de the models to explain costs in health insurance, offers “methodological changes” gathering different categories of analytic approaches, like that expressed in the work on the strategy to estimate costs in EuroHOPE ¹⁶. The design of policies focused on implementing the use of these models is recommended in the insurance carriers and state entities.

The Ministry of Health traditionally, since 1994 to date, has calculated this fee by using SLR models, which reach R² determination coefficients that range from 2% to 12% of the medical care cost, besides, does not fulfill the statistical criteria of model fit, that is, the regressor variables do not contribute significantly in the explanation of the cost. The situation of estimating a CPU with such a low determination coefficient and with so few variables included from a health - multi-systemic disease model, like that proposed by Lalonde ¹⁷, gives rise to underestimated or overestimated cost values with the subsequent economic implications and of viability of the model of health insurance in Colombia.

In specific modelling exercises to estimate medical costs, it is noted that the linear regression models underestimate medical costs and do not fulfill statistic criteria to estimate from these; this is the case of the CPU calculation, or payment fee to the EPS for the health expense. Due to this, the major strength in this study is the application of generalized linear models segmented by age groups, given that these shows better goodness of fit to the estimation of the costs, according to a user’s average accident rate.

Guaranteeing the EPS’s solvency is fundamental for each of the SGGSS sectors ¹⁵ because these entities are in charge of managing health risk. This is one of the intrinsic premises of most studies on the economy of health conducted in Colombia on its SGSSS. Many of these studies segment the population into specific risk groups with a combination of gender, age group, geographic location, and diagnostic group. Including the diagnosis permits estimating more precisely the distribution of costs of the EPS ¹⁸. The results of applying the model in two parts, with one of them using GLM, shows an administrative plausibility in the majority of the coefficients of the independent variables. Understanding this term as an homologation to the term of causality in epidemiology, and which could be expressed herein in terms of the cultural acceptance within the health insurance of determinants of costs, for example, gender impacts upon the cost, exemplified in that women who use less services during non- reproductive years and that during these years, upon using more services (prenatal controls, hospitalizations due to deliveries) they begin to cost more than the men. Likewise, the model yielded plausible results when costs increased 4.1 times with comorbidities, like a patient with COPD risk + pathologies that increase cardio-cerebrovascular risk, like high blood pressure, diabetes, obesity, etc.

Color code. Red: factors impacting upon the cost positively; Green: factors diminishing the cost; Orange: factors impacting minimally upon the cost in positive manner; and White: factors with no significant incidence on the POS cost.

Another demonstration of the applicability of the model is constituted by the results howling that health costs have a “U” shaped behavior (Figure 3); high during the first year of life (secondary to the management of neonatal pathologies), descending until 15 years of age (school group and initial adolescent characterized by their scarce use of health services, and if these are used such are of low cost: general medicine consultation, vaccines, anticonception, others), and costs gradually start to increase until 65 years of age, as of which costs have an accelerated growth (onset of chronic, non-transmissible disease and - in many cases - of their chronic sequelae). This behavior is demonstrated by most insurance carriers globally.

For example, to calculate the CPU, almost all the results show that they vary significantly when including the health diagnosis ¹⁸. For this reason, not bearing in mind the epidemiological composition of the benefit plan insurers - EPS - for these calculations, may lead to defining economic results with very high insurance fees for the “healthier” population and very low for other EPSs with more ill-ridden population. This may occur because of the practice denominated skimming the market or “selection of risks” ¹⁸, that is, some insurance carriers limit affiliations of populations presumably of high demand of resources and, hence, in costs. Thereby, the authors consider that the disease burden should be included in modelling costs or in calculations for the CPU for the benefit plan insurers (EAPB) so that economic imbalance is avoided among them, which leads to confusing economic results for the SGSSS; some with large gains and others with large losses.

Since its beginning, the POS has been organized around a list of interventions and medications, and with respect to the estimation of the basic fee, which has been calculated annually in function of the records of activities, is adjusted with inflation, and since a few years back it has been adjusted by cities, where service offer problems could exist; in addition, it is adjusted ex-post by the High- Cost Account, given the presence of some catastrophic diseases.

Although we mention an insurance model, the fee calculated is based on the record of historical consumption of the previous year and does not effectively include any risk model or disease burden of the population of each EPS, given that beyond the adjustment made, a greater offer is obtained of services present in some cities, or in some catastrophic diseases.

The insurance carrier sector and the other sectors that construct the country’s economy need a model that explains better the population’s behavior and permits estimating adequately the fee to be paid into the system by each affiliate, based on epidemiological variables and not simply on the demographic variables. Thereby, classification models must be included according to the risks of each individual, and from these, it has been possible to demonstrate how the majority of the costs of an EPS concentrate on a small group of the population, Kaiser pyramid ¹⁹, as a scheme to explain the relationship between the number of affiliates and the total cost ^19-21. The Kaiser pyramid is the model most-often used to classify the population into categories of intervention, depending on its level of complexity. It was developed by Kaiser Permanente in the United States in 1945. On the base of the pyramid, Kaiser locates the healthy users of the population for which the promotion, prevention, and early and timely diagnosis of the disease are primordial. The second level classifies users who have some type of chronic disease, the achievement focuses on self-care, appropriate administration of medications, and education in healthy life habits. The third level has users classified as high cost or complex, who are set with risk programs guided by disease case management plans designed to mitigate inadequate use of specialized procedures and avoid hospital admissions and readmissions ²⁰.

This type of risk-stratification model emerged because of imbalance in economic conditions. To the extent the insurance carriers began using it to develop different types of products and tariff structures according to its users’ risk profiles, these economic imbalances began to disappear. In health systems, risk adjustment and stratification permit the differential retribution of medical care services and activities and, above all, of the resources, this is done to avoid an unfeasibility of the system ²¹. In other words, the models of risk stratification permit identifying and managing patients who merit more specialized interventions, for example, elderly individuals with more than two diseases diagnosed. In these particular cases, the stratification seeks to avoid hospital admissions not programmed, optimize the assignment of resources, promote the patient’s self-care, prioritize the intensity of interventions at all levels.

Additionally, this methodological proposal could serve as the base to construct tools or instruments that permit continuous monitoring of the costs of health services demanded by the users of a health insurance carrier, without having the prior invoicing and only having the demographic factors, variables appertaining to the insurance business, and risk classification variable that aims to comply with one of the “Standards of monitoring and evaluation of the comprehensive networks of health services offer” that EPSs in Colombia must comply according to that disposed in Resolution 1441 of 2016 ²².

The accumulated distribution of health costs has a ‘peak’ at zero. This corresponds to an important percentage of individuals who have no variable medical costs in the POS; in the case of this study, this cost is constant through the figure of hiring through capitation of the basic level of care, that is, these people are managed by a third party at a fixed cost. For those people who do have medical costs, the distribution of costs is quite slanted to the right with the variance not constant. That is, there tends to be greater variability among the medical costs of the individuals when these are large than when these are small costs.

From the statistics point of view, we suggest modelling with other non- parametric alternatives, like the Generalized Additive Models - GAM ^23,24, which would permit seeing the model integrated as a single one, not by segments, as well as without the possibility of estimating the magnitude with which the factors contribute to explaining costs.

As an opportunity for future improvement of the present study, or as a starting point for future research, we could think of a classification that would consider the classification in the diagnostic-related groups (DRG), according to the number of contacts per types of services, as suggested by Vivas et al ²⁵.

For improvement purposes, the model was carried out with data from 2012 to 2013, during the transition of the modification of the tariff plan in which some procedures and activities that were then considered outside the obligatory health plan (POS), as of 2014 these were included in the POS. Similarly, other updates of this model must consider the inclusion of other independent variables, like time affiliated to the EPS, type of affiliation regime (contributive, subsidized), especially to recognize the theme of mobility, the users who go from being subsidized by the state (subsidized regime) when they are unemployed and which began in effect for Colombia as of 2014, according to Decree 3047 of 2013 ²⁶.

For pathologies whose risk coefficient is beneficial to the cost, it may be explained by an efficiency problem in the care opportunity of the patient and in the monitoring of the cost, which in this study was of one year. It may be that the intervention is late, and although the risk is present, affiliates initially do not consume, but in the long term we could evidence the effect of consumption.

Statistics: the “medical POS cost” is a variable not distributed formally and, although the transformation was made with Natural Logarithm, normality was not achieved, nor stability in the residual variance, which induces the search for other alternative methods to transform data, whose exploration and way of distributing these suggest a transformation of the exponential family; a necessary condition to model or treat the data through generalized linear models (GLM) segmented by age groups.

Due to the aforementioned, a good statistical model adjusted to the behavior of an insurance carrier’s cost is a GLM, which best fits to explain an abnormal variable, like the medical cost. Additionally, it included independent variables, like comorbidities and insurance variables, as well as the traditional sociodemographic variables (age, gender, and zone).

Applicable to a health model: the variables “favoring medical costs”, depending on the geographic region where the user is cared for are: being a woman in extreme groups of the vital cycle; having less than six months of affiliation to the EPS; being in wage range 2; belonging to regions different from the Pacific and South (except for males in age groups 15 to 18 years in the Andean and Northeast regions).

The variables associated most with increased costs are:

Patients with high-cost pathologies (CKD, HIV-AIDS, Cancer, rare diseases), being poly-consultant, having been reported as user with ex-ante risks and with current comorbidities, affiliates whose contributor is in wage range 3, being beneficiary for ages between 19 and 44 years, having COPD risks, risks of neoplastic origin, risk of mental illness, maternal perinatal users, CCRV risk, risk of chronic pathologies.

To validate the model, with 2014 budget data, and using the statistical model proposed for 2013, we have that the increase on the traditional model to estimate the mean cost for 2014, after indexing, was 12% above the value observed with an interval going from 2% above and 23% for the period comprised between October 2013 and September 2014.

Likewise, with a modelling exercise during a subsequent period and with data from 2015, effectiveness is achieved on the estimation performed by the model of 4.8% above the value observed.