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A Two-Compartment Mixed-Effects Gamma Regression Model for Quantifying Between-Unit Variability in Length of Stay among Children Admitted to Intensive Care


Address correspondence to Lahn Straney, Ph.D., Institute for Health Metrics and Evaluation, University of Washington, 2301 5th Avenue, Suite 600, Seattle, WA 98121; e-mail:



To quantify between-unit variability in mean length of stay (LoS) between intensive care units (ICUs) after adjusting for differences in case mix using a method that does not require arbitrary trimming of data.


An analysis of registry data from pediatric ICUs (PICUs) in Australia and New Zealand.

Study Design

The relationships between patient LoS and associated patient factors were modeled as a log-linear function of the covariates using two gamma distributions. The predicted distribution is estimated as a weighted average of the two distributions where the relative weighting is conditional on the patient's elective status.

Data Collection

Data for 12,763 admissions submitted to the Australian and New Zealand Paediatric Intensive Care Registry from the eight dedicated PICUs in Australia and New Zealand in 2007 and 2008.

Principal Findings

The two distributions of the mixture model accurately described the distribution of short- and long-stay patients in ICUs. After adjusting for patient case mix, several sites had a statistically significant effect on patient LoS.


The two-compartment model characterizes ICU LoS for short- and long-stay patients more effectively than a single-compartment model. There is significant site-level variation in the LoS among children admitted to ICUs in Australia and New Zealand. Differences in the site-level variation between short- and long-stay patients indicate differences in discharge practice.