New models for old questions: generalized linear models for cost prediction

Generalized linear models (GLMs) have recently been introduced into cost data analysis. GLMs, transformations of the linear regression model, are characterized by a particular response distribution from one of the exponential family of distributions and monotonic link function which relates the response mean to a scale on which additive model effects operate.

This study compared GLMs and ordinary least squares regression (OLS) in predicting individual patient costs in adult intensive care units (ICUs) and sought to define the utility of the inverse Gaussian distribution family within GLMs.

A prospective 'ground-up' utilization costing study was performed in three adult university associated ICUs, enrolling consecutive ICU admissions over a 6-month period in 1991. ICU utilization, patient demographic and ICU admission day data were recorded by dedicated data collectors. Model performance was assessed by prediction error [mean absolute error (MAE), root mean squared error (RMSE)] and residual analysis.

The cohort, 1098 patients surviving ICU, was of mean (SD) age 56 (19.5) years and 41% female. Patient costs per ICU episode (1991 A$) were A$6311 (9689), with range A$106 to A$95602. Prediction error for mean costs was minimal (MAE 4780; RMSE 8965) with OLS using heteroscedastic retransformation of log costs and GLM with Gaussian family and log link (MAE 4798; RMSE 8907). Residual analysis suggested optimal overall performance for the above two models and a GLM with inverse Gaussian family and log link.

Traditional cost models of OLS with (log) cost transformation may be supplemented by appropriately specified GLM which more closely model the error structure.