In this research we compare the current risk adjustment formula used by the Colombian Ministry of Health and Social Protection against alternative specifications that adjust for additional factors. The objective of a risk adjustment mechanism is to reduce the uncertainty of annual health spending by controlling variables that are not subject to manipulation by health insurers.
In this project we demonstrate that the current risk adjustment formula, which relies on demographic factors and their interactions, can only predict 30% of total health spending in the top quintile of the spending distribution. We also show that the government's formula could be significantly improved by conditioning according to a forecast rather than (ex ante) outcomes on indicators of long-term disease measures. In this research we estimate models based on machine learning and show that nonparametric methodologies such as boosted tree models perform better than linear regressions even when fitting on a smaller set of regressors. Finally, this project shows how risk adjustment policy in Colombia can redistribute its resources more efficiently by adjusting for the health status of enrollees ex ante and by using non parametric specification that capture the nonlinear relationship between risk factors better than linear models.
To predict the annual health care spending of contributory system enrollees in Colombia, we used the Sufficiency Base of the Ministry of Health and Social Protection for the years 2010 and 2011. We used the demographic characteristics and diagnoses received by each enrollee during 2010 to predict the annual health expenditure in 2011 adjusted by the number of days enrolled in this year. For each enrollee, we looked at gender, age, municipality of residence, insurer, provider, cost of service, and ICD-10 diagnosis. From an intersection of 13 million individuals, we create two mutually exclusive data sets by randomly selecting 500,000 enrollees each. One dataset is the training set where we will fit all our models and the other is the test set where we will estimate measures of fit.
Our results show that linear models, and in particular the government's current formula, tend to underestimate the total distribution of health spending by almost 11%. The underestimation is problematic because it leaves a portion of the health risk unwarranted. While the inclusion of ex ante morbidity risk adjustment with dummy variables for the 29 long-term diseases reduces the MAE and RMSE error measures substantially compared to the government formula, the inclusion of these techniques generates an increase in the overall predictive index. The machine learning-based models considered in this research were random forest (RF), boosted tree models (GBM) and artificial neural networks (ANN). All parameters of these models were obtained by cross-validation. The best model in this case we found to be the boosted tree model that fits on the set of variables chosen by the selection function (GMB FS), it achieves a more apt predictive index, and much lower errors, outperforming the linear models fitted on the whole set of regressors.
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