Comparison of Regression Methods for Modeling Intensive Care Length of Stay

Intensive care units (ICUs) are increasingly interested in assessing and improving their performance. ICU Length of Stay (LoS) could be seen as an indicator for efficiency of care. However, little consensus exists on which prognostic method should be used to adjust ICU LoS for case-mix factors. This study compared the performance of different regression models when predicting ICU LoS. We included data from 32,667 unplanned ICU admissions to ICUs participating in the Dutch National Intensive Care Evaluation (NICE) in the year 2011. We predicted ICU LoS using eight regression models: ordinary least squares regression on untransformed ICU LoS, LoS truncated at 30 days and log-transformed LoS; a generalized linear model with a Gaussian distribution and a logarithmic link function; Poisson regression; negative binomial regression; Gamma regression with a logarithmic link function; and the original and recalibrated APACHE IV model, for all patients together and for survivors and non-survivors separately. We assessed the predictive performance of the models using bootstrapping and the squared Pearson correlation coefficient (R-2), root mean squared prediction error (RMSPE), mean absolute prediction error (MAPE) and bias. The distribution of ICU LoS was skewed to the right with a median of 1.7 days (interquartile range 0.8 to 4.0) and a mean of 4.2 days (standard deviation 7.9). The predictive performance of the models was between 0.09 and 0.20 for R-2, between 7.28 and 8.74 days for RMSPE, between 3.00 and 4.42 days for MAPE and between 22.99 and 1.64 days for bias. The predictive performance was slightly better for survivors than for non-survivors. We were disappointed in the predictive performance of the regression models and conclude that it is difficult to predict LoS of unplanned ICU admissions using patient characteristics at admission time only.