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PLoS One. 2019 Mar 6;14(3):e0213258. doi: 10.1371/journal.pone.0213258. eCollection 2019.

Exploring the use of machine learning for risk adjustment: A comparison of standard and penalized linear regression models in predicting health care costs in older adults.

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Center for Population Health IT, Department of Health Policy and Management, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, United States of America.



Payers and providers still primarily use ordinary least squares (OLS) to estimate expected economic and clinical outcomes for risk adjustment purposes. Penalized linear regression represents a practical and incremental step forward that provides transparency and interpretability within the familiar regression framework. This study conducted an in-depth comparison of prediction performance of standard and penalized linear regression in predicting future health care costs in older adults.


This retrospective cohort study included 81,106 Medicare Advantage patients with 5 years of continuous medical and pharmacy insurance from 2009 to 2013. Total health care costs in 2013 were predicted with comorbidity indicators from 2009 to 2012. Using 2012 predictors only, OLS performed poorly (e.g., R2 = 16.3%) compared to penalized linear regression models (R2 ranging from 16.8 to 16.9%); using 2009-2012 predictors, the gap in prediction performance increased (R2:15.0% versus 18.0-18.2%). OLS with a reduced set of predictors selected by lasso showed improved performance (R2 = 16.6% with 2012 predictors, 17.4% with 2009-2012 predictors) relative to OLS without variable selection but still lagged behind the prediction performance of penalized regression. Lasso regression consistently generated prediction ratios closer to 1 across different levels of predicted risk compared to other models.


This study demonstrated the advantages of using transparent and easy-to-interpret penalized linear regression for predicting future health care costs in older adults relative to standard linear regression. Penalized regression showed better performance than OLS in predicting health care costs. Applying penalized regression to longitudinal data increased prediction accuracy. Lasso regression in particular showed superior prediction ratios across low and high levels of predicted risk. Health care insurers, providers and policy makers may benefit from adopting penalized regression such as lasso regression for cost prediction to improve risk adjustment and population health management and thus better address the underlying needs and risk of the populations they serve.

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Conflict of interest statement

I have read the journal's policy and the authors of this manuscript have the following competing interests: This study applied algorithms for grouping diagnosis codes and prescription drugs from the ACG case-mix/risk adjustment methodology, developed at Johns Hopkins Bloomberg School of Public Health. The Johns Hopkins University receives royalties for non-academic use of the software based on the ACG methodology. Dr. Kan, Dr. Chang, Dr. Kharrazi, Dr. Bodycombe, Dr. Lemke and Dr. Weiner receive a portion of their salary support from this revenue. This does not alter our adherence to all PLOS ONE policies on sharing data and materials.

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