Are generalized additive models for location, scale, and shape an improvement on existing models for estimating skewed and heteroskedastic cost data?

Abstract

Generalized additive models for location, scale, and shape (GAMLSS) are a class of semi-parametric models with potential applicability to health care cost data. We compared the bias, accuracy, and coverage of GAMLSS estimators with two distributions [gamma and generalized inverse gaussian (GIG)] using a log link to the generalized linear model (GLM) with log link and gamma family and the log-transformed OLS. The evaluation using simulated gamma data showed that the GAMLSS and GLM gamma model had similar bias, accuracy, and coverage and outperformed the GAMLSS GIG. When applied to simulated GIG data, the GLM gamma was similar or improved in bias, accuracy, and coverage compared to the GAMLSS GIG and gamma; furthermore, the GAMLSS estimators produced wildly inaccurate or overly-precise results in certain circumstances. Applying all models to empirical data on health care costs after a fall-related injury, all estimators produced similar coefficient estimates, but GAMLSS estimators produced spuriously smaller standard errors. Although no single alternative was best for all simulations, the GLM gamma was the most consistent, so we recommend against using GAMLSS estimators using GIG or gamma to test for differences in mean health care costs. Since GAMLSS offers many other flexible distributions, future work should evaluate whether GAMLSS is useful when predicting health care costs.