Statistical Model Comparisons for Prediction of Mental Health and Substance Abuse Cost in the Veterans Health Administration

• Activity Number: 295
• Type: Topic Contributed
• Date/Time: Wednesday, August 11, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Section on Health Policy Statistics
• Author(s): Maria E. Montez*+ and Cindy L. Christiansen and Susan Loveland and Susan L. Ettner and Priti Shokeen and Amy K. Rosen
• Companies: Boston University and Boston University and Boston University and University of California, Los Angeles and Boston University and Boston University
• Keywords: generalized linear models ; logged dependent variable ; retransformation ; risk adjustment

Abstract

Previous research shows that risk-adjustment (R-A) systems underestimate total health care costs for individuals with Mental Health & Substance Abuse (MH/SA) disorders. We examine how predictive ability of a R-A system depends on the statistical model chosen. The sample consists of 914,225 MH/SA patients. We regress four generalized linear models on untransformed cost, defined by distributional assumption and link function used: (1) Gaussian identity; (2) Gaussian log; (3) Gamma log; and (4) Gamma square root. A fifth model assumes a log-normal distribution. Regressors include age, sex, and 32 Adjusted Diagnostic Groups. Robust regression is used to account for variations in services within regions. Each model's predictive ability is evaluated using the root mean square error (RMSE) and mean absolute prediction error (MAPE). Predictive ratios (PRs) are calculated for 12 MH/SA categories. Models' performances do not differ when looking at the RMSE and MAPE. RMSEs range from 10036.3 to 10086.7 and MAPEs range from 2815.7 to 3076.9. The GLM model where a Gaussian distribution and a log link is assumed, has more PRs closer to 1.0 than the other four models.