Modelling of intensive care unit (ICU) length of stay as a quality measure: a problematic exercise

Background Intensive care unit (ICU) length of stay (LOS) and the risk adjusted equivalent (RALOS) have been used as quality metrics. The latter measures entail either ratio or difference formulations or ICU random effects (RE), which have not been previously compared. Methods From calendar year 2016 data of an adult ICU registry-database (Australia & New Zealand Intensive Care Society (ANZICS) CORE), LOS predictive models were established using linear (LMM) and generalised linear (GLMM) mixed models. Model fixed effects quality-metric formulations were estimated as RALOSR for LMM (geometric mean derived from log(ICU LOS)) and GLMM (day) and observed minus expected ICU LOS (OMELOS from GLMM). Metric confidence intervals (95%CI) were estimated by bootstrapping; random effects (RE) were predicted for LMM and GLMM. Forest-plot displays of ranked quality-metric point-estimates (95%CI) were generated for ICU hospital classifications (metropolitan, private, rural/regional, and tertiary). Robust rank confidence sets (point estimate and 95%CI), both marginal (pertaining to a singular ICU) and simultaneous (pertaining to all ICU differences), were established. Results The ICU cohort was of 94,361 patients from 125 ICUs (metropolitan 16.9%, private 32.8%, rural/regional 6.4%, tertiary 43.8%). Age (mean, SD) was 61.7 (17.5) years; 58.3% were male; APACHE III severity-of-illness score 54.6 (25.7); ICU annual patient volume 1192 (702) and ICU LOS 3.2 (4.9). There was no concordance of ICU ranked model predictions, GLMM versus LMM, nor for the quality metrics used, RALOSR, OMELOS and site-specific RE for each of the ICU hospital classifications. Furthermore, there was no concordance between ICU ranking confidence sets, marginal and simultaneous for models or quality metrics. Conclusions Inference regarding adjusted ICU LOS was dependent upon the statistical estimator and the quality index used to quantify any LOS differences across ICUs. That is, there was no “one best model”; thus, ICU “performance” is determined by model choice and any rankings thereupon should be circumspect.