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A review of statistical estimators for risk-adjusted length of stay: analysis of the Australian and New Zealand intensive care adult patient data-base, 2008-2009

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dc.contributor.authorMoran, J.
dc.contributor.authorSolomon, P.
dc.date.issued2012
dc.descriptionExtent: 17p.
dc.description.abstract<h4>Background</h4>For the analysis of length-of-stay (LOS) data, which is characteristically right-skewed, a number of statistical estimators have been proposed as alternatives to the traditional ordinary least squares (OLS) regression with log dependent variable.<h4>Methods</h4>Using a cohort of patients identified in the Australian and New Zealand Intensive Care Society Adult Patient Database, 2008-2009, 12 different methods were used for estimation of intensive care (ICU) length of stay. These encompassed risk-adjusted regression analysis of firstly: log LOS using OLS, linear mixed model [LMM], treatment effects, skew-normal and skew-t models; and secondly: unmodified (raw) LOS via OLS, generalised linear models [GLMs] with log-link and 4 different distributions [Poisson, gamma, negative binomial and inverse-Gaussian], extended estimating equations [EEE] and a finite mixture model including a gamma distribution. A fixed covariate list and ICU-site clustering with robust variance were utilised for model fitting with split-sample determination (80%) and validation (20%) data sets, and model simulation was undertaken to establish over-fitting (Copas test). Indices of model specification using Bayesian information criterion [BIC: lower values preferred] and residual analysis as well as predictive performance (R2, concordance correlation coefficient (CCC), mean absolute error [MAE]) were established for each estimator.<h4>Results</h4>The data-set consisted of 111663 patients from 131 ICUs; with mean(SD) age 60.6(18.8) years, 43.0% were female, 40.7% were mechanically ventilated and ICU mortality was 7.8%. ICU length-of-stay was 3.4(5.1) (median 1.8, range (0.17-60)) days and demonstrated marked kurtosis and right skew (29.4 and 4.4 respectively). BIC showed considerable spread, from a maximum of 509801 (OLS-raw scale) to a minimum of 210286 (LMM). R2 ranged from 0.22 (LMM) to 0.17 and the CCC from 0.334 (LMM) to 0.149, with MAE 2.2-2.4. Superior residual behaviour was established for the log-scale estimators. There was a general tendency for over-prediction (negative residuals) and for over-fitting, the exception being the GLM negative binomial estimator. The mean-variance function was best approximated by a quadratic function, consistent with log-scale estimation; the link function was estimated (EEE) as 0.152(0.019, 0.285), consistent with a fractional-root function.<h4>Conclusions</h4>For ICU length of stay, log-scale estimation, in particular the LMM, appeared to be the most consistently performing estimator(s). Neither the GLM variants nor the skew-regression estimators dominated.
dc.description.statementofresponsibilityJohn L Moran and Patricia J Solomon
dc.identifier.citationBMC Medical Research Methodology, 2012; 12(1):1-17
dc.identifier.doi10.1186/1471-2288-12-68
dc.identifier.issn1471-2288
dc.identifier.issn1471-2288
dc.identifier.orcidMoran, J. [0000-0003-2311-0440]
dc.identifier.orcidSolomon, P. [0000-0002-0667-6947]
dc.identifier.urihttp://hdl.handle.net/2440/75890
dc.language.isoen
dc.publisherBioMed Central Ltd.
dc.rights© 2012 Moran and Solomon; licensee BioMed Central Ltd.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
dc.source.urihttps://doi.org/10.1186/1471-2288-12-68
dc.subjectANZICS Centre for Outcome and Resource Evaluation (CORE) of the Australian and New Zealand Intensive Care Society (ANZICS)
dc.subjectHumans
dc.subjectCritical Care
dc.subjectLength of Stay
dc.subjectAPACHE
dc.subjectSeverity of Illness Index
dc.subjectData Interpretation, Statistical
dc.subjectModels, Statistical
dc.subjectRegression Analysis
dc.subjectDatabases, Factual
dc.subjectIntensive Care Units
dc.subjectAustralia
dc.subjectNew Zealand
dc.titleA review of statistical estimators for risk-adjusted length of stay: analysis of the Australian and New Zealand intensive care adult patient data-base, 2008-2009
dc.typeJournal article
pubs.publication-statusPublished

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