Comparison of different statistical methods to predict Intensive Care Length of Stay

1. Comparison of different statistical methods to predict Intensive Care Length of Stay IlonaVerburg Nicolette de Keizer Niels Peek Dept. Of Medical Informatics Academic Medical Center University of Amsterdam The Netherlands ESCTAIC 2012,Timisoara

2. Background and objective Background Intensive Care Units (ICUs) assess their performance to improve quality and reduce costs Background Effectiveness of care Efficiency of care Case mix mortality length of stay

3. Background and objective ICU Length of stay is influenced by case mix. Example: Length of stay (mean) 10 days 5 days Age (mean) 68 57 Medical vs surgical 80% medical 40% medical admission type (%) 20% surgical 60% surgical

4. Background and objective Observed outcome ICU Compare Case mix Predictive model Expected outcome Case mix

5. Background and objective Background • Models exist to predict ICU mortality (example APACHE IV) • Few models exist to predict ICU Length of Stay (LoS) • No consensus about best modelling method Objective Compare the performance of different statistical regression methods to predict ICU LoS.

6. Data NICE registry • Dutch National Intensive Care Evaluation (NICE) • Registry of ICU admissions in the Netherlands (since 1996) • All admissions from (voluntary) participating ICUs (>90%) • Evaluating (systematically) the effectiveness and efficiency of ICUs in the Netherlands • Identifyingquality of care problems • Qualityassurance Database

7. Data Data • Patients admitted to ICUs participating NICE • 2009 - 2011 • 84 ICUs Included patients 94,251 (42.4%) admissions Exclusion criteria • APACHE IV exclusion criteria • elective surgery 81,190 (86.1%) survivors 13,061 (13.9%) non-survivors

8. Length of stay Distribution of Length of Stay in fractional days ICU non-survivors (n= 13,061) ICU survivors (n= 81,190) Median: 2.4 (days) Mean: 5.9 Standard deviation: 10.2 Maximum: 139.0 Median: 1.7 (days) Mean: 4.2 Standard deviation: 8.2 Maximum: 326.6

9. ICU Length of Stay Distribution of discharge time

10. Modeling ICU length of stay Different methods to model ICU length of stay (in fractional days) • Ordinary least square (OLS) regression • LoS and Log-transformed LoS • Most frequently used method in literature

11. Modeling ICU length of stay Different methods to model ICU length of stay (in fractional days) • Ordinary least square (OLS) regression • LoS and Log-transformed LoS • General linear models (GLM) • Gaussian - difference with OLS is the log link function • Gamma - LoS time until discharge - depending on chosen parameters positively skewed • Poisson - LoS count data `-depending on chosen parameters positively skewed - property: expectation = variance → overdispersion • Negative binomial - count data -depending on chosen parameters positively skewed - generalisation of poisson

12. Modeling ICU length of stay Different methods to model ICU length of stay (in fractional days) • Ordinary least square (OLS) regression • LoS and Log-transformed LoS • General linear models (GLM) 4 different families • Gaussian • Gamma • Poisson • negative binomial • Cox proportional Hazard (Cox PH) regression • No assumptions on the shape of the distribution • Omits the need of transform the outcome

13. Modeling ICU length of stay Selection of covariates • Starting with large set of variables • Known relationship with LoS (literature) • Stepwise backwards elimination of variables • Included case mix • Demographics • Age • Gender • Admission type • Diagnoses (APACHE IV) • Severityof illness(APACHE IV severity-of-illness score) • Different comorbidities (21)

14. Validation Good prediction Performance measures Squared Pearson correlation = R2 = High ↑ Low ↓ Root Mean squared prediction error (RMSPE) = Low ↓ - or + Relative BIAS = Low ↓ Relative mean absolute prediction error (MAPE) =

15. Validation Validation • Performance measures calculated on original data • Correcting for optimistic bias • 100 bootstrap samples

16. Results coefficients

17. Results validation ICU survivors Mean observed > mean expected Underestimation of mean LoS

18. Results validation ICU non-survivors

19. Conclusion and discussion • Difficulttopredict ICU LoS • Influencedbyadmissionand discharge policy • Seasonalpatternforadmissionanddischarge time • Skewedtothe right • GLM models shows best performance • Poorest performance found for Cox PH regression • Large relative bias was found for OLS regression of log-transformed LoS • Differences in performance between models not statistically tested

20. Conclusionand discussion • Similarstudyfor CABG patients (Austin et al.), withcomparableresults • Different patient type • Different distribution of length of stay • Future research • Different modelsforsurvivorsand non-survivors • combiningwithmortality in oneprediction • Statistical methodstopredict ICU LoS • developinga model for benchmarking purposes

21. Thank you for your attention! Questions?

22. APACHE IV Exclusiecriteria • Age < 16 • ICU admission < 4 hours • Hospital admission >365 days • Died during admission • Readmissions • Admissions from CCU/IC other hospital • No diagnose • Burns • Transplantations • Missing hospital discharge