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Intensive care unit benchmarking
Prognostic models for length of stay and presentation of quality indicator values
Verburg, I.W.M.
Publication date
2018
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Citation for published version (APA):
Verburg, I. W. M. (2018). Intensive care unit benchmarking: Prognostic models for length of
stay and presentation of quality indicator values.
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associated with intensive
care unit characteristics?
Ilona W.M. Verburg, Rebecca Holman, Dave Dongelmans, Evert de Jonge and Nicolette F. de KeizerJournal of Critical Care 2017; 43:114-121
Abstract
Purpose: We described the association between intensve care unit (ICU)
charac-teristics and ICU length of stay, after correcting for patient characcharac-teristics. We also compared the predictive performances of models including either patient and ICU characteristics or only patient characteristics.
Materials and Methods We included all admissions of 38 ICUs
participat-ing in the Dutch National Intensive Care Evaluation foundation (NICE) between 2014 and 2016. We performed mixed effect regression including, one ICU charac-teristic in each model and a random intercept per ICU. Furthermore, we developed a prediction model containing multiple ICU characteristics and patients charac-teristics.
Results We found negative associations for the number of hospital beds; number
of ICU beds; availability of fellows in training for intensivist; full-time equivalent ICU nurses; and discharged in a shift with 100% bed occupancy. Furthermore, we found a U-shaped association with the nurses to patient ratio as spline function. The performance based on the squared Pearson's correlation coefficient R2 was between 0.30 and 0.32 for both the model containing only patient characteristics and the model also containing ICU characteristics.
Conclusion After correcting for patient characteristics, we found statistically
significant associations between ICU length of stay and six ICU characteristics, mainly describing staff availability. Furthermore, we conclude that including ICU characteristics did not significantly improve ICU length of stay prediction.
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4.1
Introduction
I
ntensive Care Units (ICUs) provide complex and expensive care and hospitalsface pressure to improve efficiency and reduce costs [23, 54]. Since costs are strongly related to ICU length of stay, shorter ICU length of stay generally equates to lower costs [23, 24, 103]. ICU length of stay is associated with patients' severity of illness [56, 104, 105] and hence case-mix adjustment is important when analyzing and modeling length of stay.Previously, we defined three main reasons for modeling ICU length of stay [104]. These were: 1) planning the number of beds and members of staff required to fulfil demand for ICU care within a given hospital or geographical area; 2) identifying individual patients or groups of patients with unexpectedly long ICU length of stay to drive direct quality improvement; and 3) comparing length of stay between ICUs when benchmarking. Although a range of models for predicting ICU length of stay using patient characteristics have been published, the clinical utility of these models for these purposes is suboptimal [104]. One reason for the suboptimal nature of these models may be the difficulty of approximating ICU length of stay using standard statistical distributions [56].
In a previous study we aimed to predict individual patient length of stay for benchmarking purposes by regression methods using patient characteristics at admission time only and concluded that it is difficult to predict ICU length of stay [56]. We hypothesize that information on ICU characteristics is required to model ICU length of stay for an individual ICU accurately.
Previous studies discussed the association between ICU length of stay and among others the number of ICU and hospital beds [64, 106]; the availability of step down or intermediate units [1, 107]; intensivist to bed ratios [108]; the presence of full-time intensivists [109, 110]; presence of fellows [111]; type of hospital [37, 64, 109, 112, 113]; types of care protocol [1, 37, 55]; and having clear admission and discharge policies [1]. Additional research has been performed on modeling ICU bed shortages [31, 114], but not on direct associations with ICU length of stay. However, not all these studies correct for patient characteristics as a base prior to analyse the association between ICU length of stay.
Our primary aim is to describe associations between ICU characteristics and ICU length of stay, correcting for patient characteristics. We also compare the predictive performance of a model including patient and ICU characteristics and one including only patient characteristics [56] for ICU length of stay. We used data collected in the Dutch National Intensive Care Evaluation foundation (NICE) registry [13].
4.2
Material and methods
4.2.1 The Dutch National Intensive Care Evaluation registry
The NICE registry exists since 1996 and collects data on patient characteristics, such as demographics, physiological and diagnostic data [13]. In addition, the registry records ICU characteristics and quality indicators for a subgroup of voluntary participating ICUs. Twice a year these ICUs report to the registry on staff resources, hospital type, ICU level, and the number of beds available. Four times a year they report on the availability of intensivists and policies to reduce the risk of medication errors. Every shift (day, evening, night), they report on availability of ICU nurses and operational ICU beds. The medical ethics committee of the Academic Medical Center stated that medical ethics approval for this study was not required under Dutch law (registration number W16_314).
4.2.2 Study data
We included ICUs, for which patient level information and characteristics recorded per shift was available for at least 23 complete months between January 1st 2014 and January 1st 2016 and the ICU characteristics recorded twice or four times a year were available and judged to be reliable by one of the authors (IV). ICU characteristics recorded twice a year or quarterly rarely change, since staff resources, hospital type, ICU level and number of available beds generally remain stable. We chose to use data on 2015 or the most recent data. We merged yearly and quarterly data on the ICUs to the patient record level data, using ICU as the merge variable. The maximum two records recorded for the half yearly data and four records recorded for the quarterly data were averaged to combine them into one record. Data recorded for each shift were merged to patient level data if the shift overlaps the patient admission period. ICU characteristics available on a shift level were averaged over the patients' admission period. We present a flow chart of ICU and patient inclusions in figure 4.1.
4.2.3 Identification of ICU characteristics for inclusion in the
regression analysis
To identify ICU characteristics for inclusion in the regression analysis an intensivist (DD) identified ICU characteristics recorded in the NICE registry, which he thought would have a clinically relevant association with ICU length of stay. We supported this work with a snowball literature search to identify ICU characteristics with an indication of association with ICU length of stay. We examined potential collinearity by calculating Pearson's correlation coefficients between pairs of ICU characteristics. Collinearity occurs if two predictors are highly linearly related. We defined collinearity if the correlation coefficient was smaller than -0.9 or larger than 0.9.
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Number of ICUs that recorded data in the full period January 1st 2014 until December 31st 2015 and contractually participated the quality indicator registration: 54 ICUs
? ICU characteristics on availability of intensivists and medication policy, not recorded four times a year: 1 ICU
Reason:
q Unreliable data Used data from ICUs with no data over 2015: q 2012: 1 ICU
q 2014: 1 ICU Merge variable: ICU
? ICU characteristics on
resources, hospital type and level, not recorded twice a year: 2 ICUs Reasons:
q Unreliable data on staff resources
q Unreliable data on bed resources
Used data from ICUs with no data over 2015: q 2011: 1 ICU
q 2014: 4 ICUs Merge variable: ICU
No shift information at least 23 months: 13 ICUs
Reasons:
q Not recorded information on a shift level: 5 ICUs q More than one month
missing: 5 ICUs
(3.6% to 99.6% missing) q Registered no operational
beds or ICU nurses for several months: 3 ICUs
Merge variables: admission and discharge date and time
Admissions: 93,807 ICUs: 38
? APACHE IV exclusion criteria:
q Age less than 16 years: 315
qICU length of stay shorter than 4 hours: 3,503
q Died before ICU admission: 109
q ICU readmissions, within the same hospital admission: 5,945 q Admission from other critical care unit or ICU: 4,066
q Missing APACHE IV diagnose: 896 q Burns: 22
q Transplantations: 267
q Unknown admission type: 668 q Unknown gender: 8
q Unknown ICU length of stay: 2
q Unknown Glascow coma scale in the first 24 hours of ICU admission: 894 Unknown information about nurse resources or available beds (NA or 0):
qNurse resources equal to 0: 90
q Operational beds equal to 0: 110 q Operational beds not available: 57 q Nurse resources not available: 57 Additional exclusion criteria:
q Transferred to other critical care unit or ICU: 1,612 Total excluded: 14,985
? Admissions: 78,822 ICUs: 38
Figure 4.1: Flow diagram of ICU and patient inclusion.
4.2.4 Statistical analysis
To examine the shape of the association between individual ICU characteristics and ICU length of stay we used stacked histograms (digital content) and scatterplots. The patient and ICU characteristics examined are respectively presented in table 4.1 and table 4.2. We found an U-shaped relationship between ICU length of stay and nurse-to-patient ratio, presented in figure 4.1, and included it as spline, with four degrees of freedom in the regression models.
For each individual ICU characteristic we performed a mixed-effects ordinary least square regression with a random intercept per ICU and log-transformed ICU length of stay as the dependent variable [115]. A block of patients' characteristics and for each model one ICU characteristic were included as fixed-effects. There were two steps in our model building strategy. In the first step, we included the patient characteristics identified in a previous publication [56]. The model was subsequently simplified using stepwise backward selection and the Akaike Information Criterion (AIC) and the corresponding p-value based on the likelihood ratio test to test model improvement and used p>0.01 for exclusion. We viewed the patient characteristics in the resulting model as a fixed block of variables to be included in all further models. In the second step, we included the fixed block of patient case-mix characteristics and one ICU characteristic as fixed covariates and a random intercept for each ICU. We compared each model to the model with only patient characteristics by computing analysis of deviance tables and using the χ2-distribution to compare them. We defined improvement as a p-value smaller than 0.05 [116].
To examine the potential improvement of a prediction model for log-transformed ICU length of stay using both patient and ICU characteristics compared to a model correcting for patient characteristics only we performed another mixed effect regression analysis. We performed stepwise backward selection as described above starting with all ICU characteristics with p-value larger than 0.1 to exclude ICU characteristics. We included the patient characteristics as a fixed block of variables. We compared the difference in the residual deviances of the models to a chi-squared distribution as described above.
The models' performance was examined by analyzing statistics of the residuals of both models and deriving squared Pearson's correlation coefficient (R2) on a patient level using a general method for obtaining R2 for mixed-effect models [117]. Finally, we evaluated the performance by presenting a recalibration plot of 50 subgroups based on the mean predicted log-transformed ICU length of stay based on fixed-effects only. For each subgroup we plot the mean predicted log-transformed ICU length of stay against the mean observed log-transformed ICU length of stay.
We performed all statistical analyses using R statistical software, version 3.3.1 [97]. We used the lme4 package for mixed-effects models [118] and rms package for calculating restricted cubic splines [119].
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Table 4.1: Number of admissions and mean and standard deviation of ICU length of stay for patient characteristics included in the model - (1 of 2).
Patients with patient characteristic (yes) Patients without patient characteristic (no)
Patient case-mix characteristic
Admission count (%) Mean (sd) ICU length of stay in days Mean (sd) ICU length of stay in days
Number of ICU admissions 78,822 3.1 (6.6)
Age in years1 Up to 55 20,866 (26) 2.9 (6.3) 56 to 66 19,938 (25) 3.3 (7.1) 67 and 74 18,498 (23) 3.3 (6.8) Over 74 19,520 (25) 3.2 (6.2) Gender male 47,309 (60) 3.2 (6.9) 1.3 (2.2) Admission type Medical 35,646 (45) 4.1 (7.5) Urgent surgery 9,203 (12) 4.7 (9.2) Elective surgery 33,973 (43) 1.7 (3.9)
APACHE IV APS (quartiles)1
Up to 26 20,366 (26) 1.3 (2.2)
26 to 38 19,831 (25) 1.9 (3.6)
38 to 56 18,979 (24) 3.3 (6.3)
Over 56 19,646 (25) 6.2 (10.2)
Confirmed infection 11,501 (15) 6.2 (10.0) 2.6 (5.7)
Mechanical ventilation first 24h 37,809 (48) 4.5 (8.5) 1.9 (3.8)
Vasoactive medication 32,766 (42) 4.6 (8.6) 2.1 (4.5)
Lowest GCS first 24h 16,205 (21) 4.9 (8.7) 2.7 (5.9)
Chronic diagnoses
Cardio vascular insufficiency 3,698 (5) 3.0 (5.7) 3.2 (6.6)
Chronic renal insufficiency 4,370 (6) 3.8 (7.0) 3.1 (6.6)
Chronic dialysis 1,089 (1) 2.8 (4.9) 3.2 (6.6) Cirrhosis 1,110 (1) 4.2 (6.6) 3.1 (6.6) COPD2 11,014 (14) 3.6 (6.6) 3.1 (6.6) Diabetes 13,265 (17) 3.3 (6.6) 3.1 (6.6) Hematologic malignancy2 1,277 (2) 5.5 (8.7) 3.1 (6.5) Immunologic insufficiency 6,803 (9) 4.2 (7.8) 3.0 (6.5) Neoplasm 3,811 (5) 2.6 (5.1) 3.2 (6.7) Respiratory insufficiency 3,361 (4) 4.7 (8.4) 3.1 (6.5) 77
Table 4.1: Number of admissions and mean and standard deviation of ICU length of stay for patient characteristics included in the model - (2 of 2).
Patients with patient characteristic (yes) Patients without patient characteristic (no)
Patient case-mix characteristic
Admission count (%) Mean (sd) ICU length of stay in days Mean (sd) ICU length of stay in days Acute diagnoses
Acute renal failure 6,196 (8) 7.1 (11.4) 2.8 (5.9)
CPR 3,391 (4) 5.7 (9.0) 3.0 (6.4)
CVA 3,238 (4) 4.8 (7.7) 3.1 (6.5)
Dysrhytmia 5,970 (8) 4.9 (8.3) 3.0 (6.4)
Gastro intestinal bleeding 1,574 (2) 2.8 (5.8) 3.2 (6.6)
Intracranial mass effect 3,950 (5) 4.6 (9.7) 3.1 (6.4)
APACHE IV diagnosis Non-operative Cardiovasculair 11,611 (15) 4.3 (7.5) Gastro-intestinal 2,697 (3) 3.4 (6.7) Genito-uritary 981 (1) 3.2 (5.2) Metabolic 1,219 (2) 2.1 (3.6) Musculoskeletal/skin 149 (0) 4.6 (9.1) Neurological 6,689 (8) 2.9 (6.5) Respiratory 9,590 (12) 5.3 (8.5) Trauma 2,348 (3) 3.8 (7.7) Operative Cardiovasculair 20,957 (27) 2.4 (5.7) Gastro-intestinal 7,318 (9) 2.8 (5.4) Genito-uritary 2,090 (3) 1.5 (2.9) Metabolic 188 (0) 1.8 (3.7) Musculoskeletal/skin 1,699 (2) 1.4 (2.4) Neurological 4,651 (6) 2.2 (4.9) Respiratory 4,198 (5) 1.8 (4.4) Transplant 406 (1) 2.4 (3.6) Trauma 1,673 (2) 4.1 (11.9)
Post- and non-operative
Hematological 358 (0) 4.3 (7.2)
Outcome measure
ICU death 6,150 (8) 5.8 (10.6) 2.9 (6.1)
Hospital death 8,878 (11) 5.7 (10.0) 2.8 (6.0)
APACHE IV=Acute Physiology and Chronic Health Evaluation IV; APS=Acute Physiology Score; GCS=Glasgow coma scale; COPD=chronic obstructive pulmonary disease;
CPR=cardiopulmonary resuscitation; CVA=cerebrovascular accident
1Continuous variables age and APACHE IV physiology score (APS) are presented in quartiles, but
they were included as splines in the regression analyses.
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Table 4.2: Number of admissions and mean and standard deviation of ICU length of stay for included ICU characteristics - (1 of 2).
ICU characteristic Admission count (%) Number of ICUs Mean (sd) length of stay in days ICU level 1 9,854 (13) 11 2.6 (5.1) 2 20,756 (26) 13 3.3 (6.7) 3 48,212 (61) 14 3.2 (6.8) Hospital type University affiliated 20,569 (26) 5 3.3 (7.2) Teaching 36,411 (46) 15 3.1 (6.5) General 21,842 (28) 18 3.1 (6.1)
Number of hospital beds1
Up to 382 12,992 (16) 10 2.7 (5.5)
383 to 482 12,743 (16) 9 3.6 (6.8)
483 to 660 17,779 (23) 9 3.3 (7.0)
Over 660 35,308 (45) 10 3.1 (6.6)
Number of ICU beds1
Up to 8 8,675 (11) 10 2.5 (4.7)
9 to 12 6,633 (8) 5 3.2 (6.9)
13 to 21 23,091 (29) 13 3.4 (6.8)
Over 21 40,423 (51) 10 3.1 (6.8)
Stepdown beds with supervision: no 41,249 (52) 23 3.1 (6.2)
Stepdown beds with supervision: yes 37,573 (48) 15 3.2 (7.0)
Stepdown beds without supervision: no 66,670 (85) 34 3.2 (6.7)
Stepdown beds without supervision: yes 12,152 (15) 4 2.8 (5.9)
PACU beds with mechanical ventilation: no 54,799 (70) 31 3.1 (6.3)
PACU beds with mechanical ventilation: yes 24,023 (30) 7 3.3 (7.1)
PACU beds without mechanical ventilation: no 59,148 (75) 28 3.0 (6.2)
PACU beds without mechanical ventilation: yes 19,674 (25) 10 3.5 (7.7)
CCU beds: no 70,406 (89) 34 3.1 (6.5)
CCU beds: yes 8,416 (11) 4 3.5 (7.2)
Calamity beds: no 29,290 (37) 12 3.0 (6.4)
Calamity beds: yes 49,532 (63) 26 3.2 (6.7)
Medication error prevention score
6 1,936 (2) 1 3.6 (6.2) 7 18,635 (24) 7 3.4 (7.5) 8 38,614 (49) 20 3.0 (6.2) 9 13,559 (17) 8 3.2 (6.1) 10 6,078 (8) 2 3.5 (7.0) 79
Table 4.2: Number of admissions and mean and standard deviation of ICU length of stay for included ICU characteristics - (2 of 2).
ICU characteristic Admission count (%) Number of ICUs Mean (sd) length of stay in days
Fellows in training to intensivist available: no 55,491 (70) 32 3.1 (6.4)
Fellows in training to intensivist available: yes 23,331 (30) 6 3.3 (7.1)
Full-time equivalent ICU doctors (non-intensivists)1
Up to 3.0 11,242 (14) 9 3.2 (6.3)
3.0 to 6.0 10,059 (13) 7 3.1 (6.8)
6.0 to 8.8 21,526 (27) 12 3.1 (6.6)
Over 8.8 35,995 (46) 10 3.2 (6.7)
Full-time equivalent ICU nurses1
Up to 6.5 10,269 (13) 23 2.6 (4.9)
6.5 to 10.9 11,285 (14) 26 3.1 (6.2)
10.9 to 17 19,145 (24) 26 3.4 (6.8)
Over 17 38,123 (48) 20 3.2 (7.0)
Full-time equivalent intensivists1
Up to 4.3 11,861 (15) 10 3.2 (6.3)
4.3 to 5.1 13,327 (17) 9 2.9 (6.0)
5.1 to 7.0 18,962 (24) 9 3.2 (6.6)
Over 7.0 34,672 (44) 10 3.2 (6.9)
Nurses to patient ratio1
Up to 0.6 20,579 (26) 38 2.7 (5.7)
0.6 to 0.7 19,266 (24) 38 3.6 (7.5)
0.7 to 0.8 19,025 (24) 38 3.5 (7.5)
Over 0.8 19,952 (25) 38 2.8 (5.5)
Intensivists to operational beds ratio1
Up to 0.3 25,872 (33) 9 3.1 (6.6)
0.3 to 0.4 15,209 (19) 10 3.2 (6.5)
0.4 to 0.5 18,844 (24) 9 2.8 (5.7)
Over 0.5 18,897 (24) 10 3.5 (7.5)
Hours intensivist present1
Up to 15 10,109 (13) 10 3.2 (6.3)
15 to 17 15,183 (19) 9 3.7 (7.9)
17 to 22 24,624 (31) 9 3.0 (6.1)
Over 22 28,906 (37) 10 3.0 (6.3)
Discharged in shift with 100% bed occupancy: no 63,836 (81) 38 3.1 (6.4)
Discharged in shift with 100% bed occupancy: yes 14,986 (19) 37 3.2 (7.2)
ICU=intensive care unit; PACU=post anesthesia care unit; CCU=coronary care unit
1Continues characteristics included as continuous or spline covariates are presented using
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4.3
Results
4.3.1 Identification of ICU characteristics for inclusion in the
regression analysis
Appendix 4.A, table 4.4, shows all ICU characteristics included in the analyses and identified as being clinically associated with ICU length of stay. Appendix 4.B, table 4.5, presents the Pearson's correlation coefficients between these variables. No pairs of ICU characteristics demonstrated collinearity, hence we included all variables in the univariate analyses.
4.3.2 Study data
A total of 84 ICUs participated in the NICE registry between January 1st 2014 and January 1st 2016. Of these, 54 (64%) participated in the ICU characteristics and quality indicator registration. We included 38 (70%) in this study. The remaining 16 ICUs provided unreliable data on one or more of the ICU characteristics examined in this paper. We included 93,807 ICU admissions, of which we included 78,822 (84%) in this study, figure 4.1. Table 4.1 and table 4.2 respectively present information about the number of admissions and ICU length of stay for each of the patient characteristics and each of the ICU characteristics.
4.3.3 Statistical analysis
We removed two variables from the block of patient characteristics during the backwards selection procedure. These were hematologic malignity (p=0.887) and chronic obstructive pulmonary disease (p=0.162). Table 4.1, contains the patient characteristics used in the model and appendix 4.C, table 4.6, presents the results of the regression analyses for patient characteristics. In table 4.3, we present the results of the regression analyses for individual ICU characteristics. Six demonstrated a statistically significant association with ICU length of stay: number of hospital beds; number of ICU beds; availability of fellows in training for intensivist; full-time equivalent ICU nurses; whether a patient was discharged in a shift with 100% bed occupancy; and nurse to patient ratio. Apart from the nurse to patient ratio, all characteristics had a negative association with ICU length of stay.
Examining the potential improvement of a model for log-transformed ICU length of stay by including ICU characteristics resulted in a model with number of ICU beds; full-time equivalent ICU nurses; and whether a patient was discharged in a shift with 100% bed occupancy, table 4.3. The fit statistics in 4.A, figure 4.4, presents the performance of the model with correction for case-mix characteristics and ICU characteristics. Comparing the performance of this full model with the model with only patient case-mix included, lead to R2 between 0.30 and 0.32 for both models. Furthermore, residuals showed biased results for patients with short and long ICU length of stay, but followed a normal distribution overall.
T able 4.3: Co efficien ts for ICU characteristics in the mixe d effects regression mo dels. Mo del including a single ICU characteristic Final mo del including m u ltiple ICU characteristics Characteristics P arameter (95% CI) P-v alue P ar ameter (95% CI) P-v alue ICU lev el (referen ce 1 (lo w est)) 0 .803 2 0 .030 (-0.088 to 0.150) 3 (highest) − 0 .003 (-0.119 to 0.110) Hospital typ e (reference General h ospital) 0 .093 ∗∗ T eac hing hospital − 0 .048 (-0.143 to 0.047) Univ ersit y affili a te d − 0 .148 (-0.285 to -0.012) Num b er of hospital b eds / 100 − 0 .017 (-0.034 to 0.001) 0 .040 ∗ Num b er of ICU b e ds / 10 − 0 .045 (-0.090 to -0.002) 0 .039 ∗ 0 .009 (0.002 to 0.014) <0.001 Step do wn b eds with sup ervision: y es − 0 .031 (-0.124 to 0.063) 0 .512 Step do wn b eds without sup ervision: y es − 0 .049 (-0.198 to 0.100) 0 .509 P A CU b eds with mec h anical v en tilation: y es − 0 .068 (-0.184 to 0.048) 0 .242 P A CU b eds without mec hanical v en tilation: y e s 0 .033 (-0.071 to 0.137) 0 .522 CCU b eds: y es 0 .008 (-0.142 to 0.159) 0 .912 Calamit y b eds: y es 0 .037 (-0.062 to 0.135) 0 .456 F ello ws in training to in tensivist a v ailable: y es − 0 .145 (-0.261 to -0.035) 0 .016 ∗ F ull-time equiv alen t ICU do ctors (non-in tensivists) − 0 .004 (-0.011 to 0.003) 0 .227 F ull-time equiv alen t ICU n urses − 0 .017 (-0.021 to -0.013) < 0 .001 ∗ − 0 .030 (-0.034 to -0.025) <0.001 F ull-time equiv alen t in tensivists − 0 .010 (-0.021 to 0.000) 0 .058 ∗ In tensivists to op erational b eds ratio 0 .000 (-0.317 to 0.320) 0 .999 Nurses to patien t ratio (npr) (spline) 1 < 0 .001 ∗ Hours in tensivist presen t − 0 .005 (-0.014 to 0.003) 0 .221 Disc harged in a shift with 100% b ed o ccupancy − 0 .054 (-0.071 to -0.037) < 0 .001 ∗ 0 .035 (0.017 to 0.054) <0.001 Medication error prev en tion score 0 .001 (-0.054 to 0.056) 0 .965 ICU admission in w eek end − 0 .004 (-0.021 to 0.013) 0 .668 ICU=in te nsiv e care unit, CI=confidence in terv al, PA CU=p ost anesthesia care unit, CCU=coronary care unit. ∗p<0.05 significan t ∗∗ Inclusion in a m ultiv ariate mo del w as based on p<0.1. Using step wise bac kw ard selec tion p>0.1 w as used for exclusion. 1Regression form ula for spline variables npr is: 2 .573 · npr − 28 .358 ·( npr − 0 .491) 3+ 64 .672 ·( npr − 0 .627) 3− 36 .508 ·( npr − 0 .735) 3 − 0 .193 ·( npr − 1 .061) 3 A graphical result is sho wn in figur e 4.2.
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Appendix 4.B, figure 4.5, presents a calibration plot comparing predicted and observed values for 50 subgroups based on mean predicted log-transformed ICU length of stay. For the model including ICU characteristics, we found that the total predicted ICU length of stay was slightly closer to the total observed values and that ICU level differences were associated with the number of ICU nurses available.
Nurses to patient ratio
Predicted log-transformed ICU length of
stay 0 1 2 3 4 5 -1.5 -1.0 0 0.5 -0.5
Figure 4.2: Predicted log-transformed ICU length of stay by nurses to patient ratio. Log-transformed ICU length of stay is adjusted for patient characteristics and nurses to patient ratio included as spline. A smoothing curve was derived using generalized additive model method. Grey zones represent 95% confidence intervals.
4.4
Discussion
In this study, we examined the association between ICU characteristics available in the NICE registry and ICU length of stay, after correcting for patient charac-teristics. The results of our study show statistically significant associations for the number of hospital beds; the number of ICU beds; full-time equivalent ICU nurses; whether fellows in training for intensivist were available; nurse to patient ratio; and whether a patient was discharged in a shift with 100% bed occupancy. Adding these characteristics to a multivariate prediction model with patient characteristics
[56] only slightly improved the predictive performance. Adding these characteris-tics to a multivariate prediction model with patient characterischaracteris-tics did not improve the performance of the model. We hypothesized that case-mix corrected ICU length of stay is associated with these characteristics. Hence, our data show that adding ICU characteristics will not substantially improve predictive performance for planning beds and staff requirements, identifying patients with unexpected long length of stay or benchmarking ICUs.
We found that as the numbers of hospital or ICU beds increase ICU length of stay decreases. A previous study found no associations between ICU length of stay and number of hospital beds in five categories after case-mix adjustment [64]. An explanation could be that larger hospitals care for more severely ill patients. Another study found no change in ICU length of stay reducing the number of ICU beds and when severity of illness stayed constant [106]. One of the explanations could be the increase in nurses per bed. We also found that the availability of fellows resulted in an increase of ICU length of stay. Previously, ICU length of stay has been shown to be longer [111], unaffected [120] or shortened [121] at pediatric ICUs after correcting for patient case-mix in the presence of fellows. Furthermore, we found that the ICU length of stay increased as the number of ICU nurses decreased. This is conform a systematic literature review which indicates that the presence ICU nurses is associated with reduced ICU length of stay [122]. We found no association between ICU length of stay and the ratio of intensivists to operational beds, but the ICU length of stay was associated with the ratio of nurses to patients. A previous study has shown that an increase in the bed to physician ratio was associated with an decrease in ICU length of stay [108]. One study developed a quality indicator for ICU length of stay and classified ICUs in two groups based on efficiency [32]. They analyzed the association between efficiency and ICU characteristics. They found a significant negative association for the number of physicians, intensivist per bed and the availability of intensivist. They found a significant positive association for nurses to bed ratio. However, these association were not significant in a multivariate model.
We found that 'discharged in a shift with 100% bed occupancy' was associated with shorter ICU stay. The reason could be that there was pressure to discharge patients somewhat faster to make bed capacity available. This is in line with previous research, which showed that delays in discharging patients from the ICU decreased when bed occupancy increased [34] and in the event of bed shortage admissions and discharges are triaged, increasing the number of rejected admission requests and shortening the length of stay [114, 123].
Step-down units are intermediate levels of care between ICU and general wards [1, 33]. The availability of step-down units may reduce ICU length of stay [37, 55, 107]. Step-down units were available among the top 10 performing ICUs in United States [1]. We found no association between the availability of step-down beds on the ICU and ICU length of stay in our data. However, the NICE registry only records the number of step-down beds under responsibility of an intensivist.
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Previously, researchers have reported that having a full time intensivist [109, 110] or being able to call an intensivist [124] decreases ICU length of stay and the absence of a full time intensivist prolonged ICU length of stay [125]. Furthermore, studies found that teaching hospitals had longer [37, 64, 112] or shorter [109, 113] ICU length of stay. However, following correction for patient characteristics, we found no statistically significant associations between ICU length of stay and the average hours of intensivist availability, the availability of intensivists on weekdays or at weekends, the ability to call an intensivist, type of hospital or ICU level. A strength of this study is the large amount of patient level data available in the NICE registry. Although not all Dutch ICUs register data on their structure and logistics processes, we believe that the ICUs included in this study were representative for all Dutch ICUs as we found similar distribution of ICU level and hospital type among the included and excluded ICUs. A limitation of this study is that we did not have information on the availability of intermediate care or step-down units in the hospitals or on other factors, which may be associated with ICU length of stay. These include whether ICUs: had open or closed management models [126–128]; standardized care by following guidelines [37, 55] using clinical pathways [37] or process related guidelines and protocols [1, 37]; or had discharge policies for when ICU or general beds are scarce. Discharge policies may influence ICU length of stay predictions, but may not directly mean low utility in terms of identifying outliers [105]. Another limitation of this study is that although, none of the ICU characteristics showed a correlation coefficient smaller than -0.9 and larger than 0.9 which were chosen as cut-off values for collinearity, it is likely that several characteristics are not independent predictors. For example, the number of ICU beds and the total number of ICU nurses were related. Interestingly, both the number of ICU beds and number of ICU nurses appeared to be independent predictors in multivariate analysis. Furthermore, the direction of the regression coefficient changed for both the number of ICU beds and the 100% bed occupancy, which may be caused by associations between the three ICU characteristics in-cluded in the full model. Since the purpose of the full model was to predict ICU length of stay, including these correlated ICU characteristics is not a problem.
4.5
Conclusions
After correcting for patient characteristics, we found statistically significant asso-ciations between ICU length of stay and six ICU characteristics. These character-istics mainly describe staff availability. Adding ICU charactercharacter-istics to a prediction model for ICU length of stay already containing patient characteristics did not substantially improve the performance of the model. This indicates that the use of ICU characteristics have little additional utility above the use of only patient characteristics, when predicting ICU length of stay.
4.6
Acknowledgements
We acknowledge all participating ICUs in the National Intensive Care Registry for their participation and hard work to collect and improve their processes based on these data.
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App
endix
4.A:
ICU-c
haracteristics
T able 4.4: List of ICU characteristics, the frequency with whic h they are record ed and ho w these in analyses v ariables are included -(1 of 3). ICU characteristics 1 Description / defini tion Supply frequency Exp ert kno wl edge Literature Included in the study V ariable typ e as included in the mo del (categories; reference) ICU lev el ICU lev el as gran ted in visitation by NVIC 3. Lev el 3 is the most-equipp ed and lev el 1 the least eq uipp ed ICU. T wic e a year Y es Y es Discrete (3, lev el 1) Hospital typ e This variable con sist of three hospital typ es: 1. univ ersi ty affiliated; 2. teac hing hospitals; and 3. general hospitals. T wic e a year Y es Y es Discrete (3, typ e 3) Num ber of hospital beds T otal num ber of authorized hospit al beds during the observ ation perio d (six mon ths). T wic e a year Y es Y es Con ti nuous Num ber of ICU beds Maxim um num ber av ailable beds at the ICU. T wice a year Y es Y es Rational cubic spline 4 knots Step-do wn with sup ervision Num ber of beds whic h could be used as step do wn bed with in tensivist sup er vision in a sepparate step do wn unit (medium or sp ecial care, but no pacu or ccu) or part of the ICU. Included as >0=1 and 0=0 variable. T wic e a year Y es Y es Y es Binary (2, no) Step-do wn without sup ervision Num ber of beds whic h could be used as step do wn bed without in tensivist sup er vision in a sepparate step do wn unit (medium or sp ecial care, but no pacu or ccu) or part of the ICU. Included as >0=1 and 0=0 variable. T wic e a year Y es Y es Y es Binary (2, no) PA CU beds with mec hanical ven tilation Num ber of beds at the 24 hours post anesthesia care unit (P A CU) with mec hanical ven tilation possibilit y. Included as >0=1 and 0=0 variable. T wic e a year Y es Y es Y es Binary (2, no) PA CU beds without mec hanical ven tilation Num ber of beds at the 24 hours pa cu without mec hanical ven tilation possibilit y. Included as >0=1 and 0=0 variable. T wic e a year Y es Y es Y es Binary (2, no) CCU beds Num ber of co ronary car e unit (CCU) beds with mec hanical ven tilation possibilit y on a separate CCU or on the ICU. Included as >0=1 and 0=0 variable. T wic e a year Y es Y es Y es Binary (2, no) 87T able 4.4: List of ICU characteristics, the frequency with whic h they are recorde d and ho w th ese v ariables are included in analyses -(2 of 3). ICU characteristics 1 Description / defini tion Supply frequency Exp ert kno wl edge Literature Included in the study V ariable typ e as included in the mo del (categories; reference) Calamit y beds A vailabilit y of aditional beds offering monitoring and mec hanical ven tilation equipmen t, but no sc heduled staf, whic h can be used in an ca lami ty situation. Included as >0=1 and 0=0 variable. T wic e a year Y es Y es Y es Binary (2, no) Fel lo ws in training to in tensivist av ailable Fte medical sp ecialists in training to in te nsivist (fello ws). Included as >0=1 and 0=0 variable. T wic e a year Y es Y es Y es Binary (2, no) Fte ICU do ctors Fte medical sp ecialists at the ICU (no fello ws). T wice a year yes Y es Con tin uous Fte sp ecialist ICU nurse s Num ber of graduated ICU nurses av ailable per shift. This num ber is av eraged ov er all shifts during admission time. Eac h shift Y es Y es Con tin uous Fte in tensivists Fte in tensivists w orking at the ICU. T wice a year Y es Y es Con tin uous In tensivists to num ber of beds ratio Ratio bet w een the fte in tensivist and op erational be ds on a patien t lev el. T wic e a year Y es Y es Con ti nuous Nurses to patien t ratio Ratio bet w een graduated ICU nurses av ailable per shift and num ber of patien ts admi tted at the ICU at that shift. This ratio is av eraged ov er all shifts during admission time. Eac h shift Y es Y es Rational cubic spline 4 knots Hours in tensivist presen t A ve rage num ber of hours of in tensivist prese nt during the w eek (0 to 24), calc ul ate d as 5 times the num ber of hours of in tensivist av ailabilit y at w eek da ys + 2 times the num ber of hours of in tensivist av ailabilit y in the w eek end)/7. T wic e a year Y es Y es Con ti nuous In tensivist presen t w eek end Presence of an in tensivist during 24 hours in the w eek ends. T wice a year Y es No 4 In tensivist presen t w orkw eek Presence of an in tensivist during 24 hours at w orkda ys. T wice a year Y es No 4 Disc harg ed in a shift with 100% bed oc cupa nc y2 Disc harg e of a patien ts in a shift with 100% bed occupancy . Eac h shift Y es Y es Binary (2, no)
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T able 4.4: List of ICU characteristics, the frequency with whic h they are recorde d and ho w th ese v ariables are included in analyses -(3 of 3). ICU characteristics 1 Description / defini tion Supply frequency Exp ert kno wl edge Literature Included in the study V ariable typ e as included in the mo del (categories; reference) Early disc harge scarcit y ICU be ds Early disc harge with reason scarcit y of ICU beds. Calculated from the ICU dis charge reason. Eac h admission Y es No 5 Dela yed disc harge scarcit y nursery departmen t beds Dela yed disc harge with reason scarcit y of nursery departmen t beds. Calculated from the ICU disc harge reason. Eac h admission Y es No 5 Medication error prev en tion score Num ber of items scored with yes based on policy to prev en t medication errors (0 to 10). The total num ber of items av ailable is ten (ref ). In the practical data se t this score ranged from 6 to 10. Eac h quarter of a year Y es Y es Discrete (5,score 6) Da y of ICU admission Da y of the w eek ICU admission to ok place 1Pubmed w as searc hed fo r publications on predictors for ICU LoS. W e searc hed on terms for 'in tensiv e care unit '(in tensiv e care unit; ICU; and critical ca re unit), 'length of sta y' (length of sta y; and LOS), and 'c ha racte ri stics '(predictors; factors; and determinan ts). The terms are com bined with 'and '. Go ogle sc holar w as also used to searc h for articles . The follo wing searc h phrases w ere used as opp osed to the se arc h terms: 1. ICU length of sta y; 2. determinan ts of IC U duration; 3. variables affecting length of sta y in ICU; 4. factors influencing length of ICU sta y; and 5. Prolonged ICU sta y. 2Within the NICE registry the bed occupancy per shift is calculated using the num ber of av ailable ICU be ds during a shift and the num ber of admitted patien ts during that shift. 3Nederlandse V ereniging vo or In te nsiv e Care (NVIC), https://n vic.nl/ 4Hours in tensivist presen t included in the study . Correlation w as 0.64 with hours in tensivist presen t. In tensivist presen t at w eek ends are the same hospitals as in tensivist presen t at w orkw eeks. p-v alue of this characteristic in the mo del w as 0.53. 5Not reliable in NICE registry (optionally pro vided). 89T able 4.5 P ear son correlation co efficien ts b et w een ICU characteristics a v ailable in the NICE registration. ICUlev el Hospitalt ype Number ofhospital beds Number ofICU beds Stepdo wnwith supervision Stepdo wnwithout supervision PA CUwith mechanical ven tilation PA CUwithout mechanical ven tilation CCUb eds Calamity beds Fel lows available Full-time equivalen tICU doctors Full-tim eequiv alent ICUn urses Full -ti meequiv alent intensivists Intensivists ton umber ofb edsratio Nursesto patient ratio Hoursin tensivistpresen t Discharged when100% bed occupancy Medicationerror preven tion score Day ofICU admissionw eekend ICU lev el 1.00 -0.65 0.63 0.77 0.39 0. 07 0.46 0. 02 0.07 -0.07 0.49 0.63 0.73 0.64 -0.29 -0.29 0.59 -0.14 -0.01 -0.17 Hospital typ e 1.00 -0.75 -0.73 -0.40 -0.17 -0.43 -0.04 -0.17 0.01 -0.73 -0.71 -0.73 -0.76 0.02 0.31 -0.35 -0.05 -0.14 0. 30 Num ber of hospital beds 1.00 0.72 0.28 0.10 0.34 -0.06 0.12 -0.08 0.50 0.69 0.74 0.80 -0.02 -0.13 0.41 -0.26 0.11 -0.19 Num ber of ICU beds 1.00 0.18 0.25 0.57 0.01 0.05 -0.15 0.64 0.76 0.89 0.76 -0.35 -0.09 0.48 -0.15 0.05 -0.35 Step do wn with sup ervision 1. 00 -0.10 0.31 0.37 -0.10 -0.03 0.09 0.20 0.15 0.08 -0.14 -0.21 0.23 -0.03 -0.27 0.02 Step do wn without sup ervision 1.00 0.28 -0.01 -0.12 0.05 0.32 0.23 0.26 0.23 0.05 -0.03 0.08 0.06 -0.13 -0.05 PA CU with mec hanical ven tilation 1.00 0.49 -0.16 0.03 0.54 0.47 0.49 0.38 -0.31 0.05 0.04 0.15 -0.29 -0.11 PA CU without mec hanical ven tilation 1.00 0.18 0.15 0.07 -0.10 -0.04 -0.19 -0.30 0.12 -0.11 0.16 -0 .1 3 0.15 CCU beds 1.00 0. 05 0.32 -0.02 0.15 0.15 0.05 0.14 -0.02 -0.09 0. 48 -0.02 Calamit y beds 1.00 -0.02 -0.10 -0.02 -0.06 0.06 0.23 -0 .1 4 -0.05 0.06 0.16 Fel lo ws av ailable 1.00 0.58 0.70 0.71 0.00 -0.13 0.21 0.23 0.05 -0.28 Full -ti me equiv alen t ICU do ctors 1.00 0. 72 0.86 0. 09 -0.21 0.28 -0.10 -0.07 -0.35 Full -ti me equiv alen t ICU nurses 1.00 0.8 3 -0.20 -0.04 0.41 -0.20 0.03 -0.29 Full-ti me equiv alen t in tensivists 1.00 0.24 -0.10 0.37 -0.12 0.04 -0.30 In tensivists to num ber of beds ra tio 1.00 -0.09 -0.15 0.18 -0.05 -0.12 Nurses to patien t ratio 1.00 -0.10 -0.41 0.15 0.11 Hours in tensivist presen t 1.00 -0.25 -0.04 -0.27 Disc harg ed when 100% bed occupancy 1.00 -0.15 -0.13 Medication error prev en tion score 1.00 -0.12 Da y of ICU admission w eek end 1.00 ICU=in te nsiv e care unit; PA CU=p ost anesthesia car e unit; CCU=coronary care unit.
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0 1 2 3 4 5 0 1 2 3 4 5 Density Hospital type University Teaching General 0 2 4 6 0 1 2 3 4 5Number of hospital beds Up to 382 383 to 482 483 to 660 Over 660 0 2 4 6 0 1 2 3 4 5 Density
Number of ICU beds Up to 8 9 to 12 13 to 21 Over 21 0 1 2 3 0 1 2 3 4 5 Fellows available No Yes 0 2 4 6 0 1 2 3 4 5 Density Full−time equivalent specialist ICU nurses
Up to 6.5 6.5 to 10.9 10.9 to 17.0 Over 17 0 2 4 6 0 1 2 3 4 5 Full−time equivalent intensivists Up to 4.3 4.3 to 5.1 5.1 to 7.0 Over 7.0 0 2 4 6 0 1 2 3 4 5
ICU length of stay
Density
Nurses to patient ratio Up to 0.6 0.6 to 0.7 0.7 to 0.8 Over 0.8 0 1 2 3 0 1 2 3 4 5
ICU length of stay
100% bed occupancy at discharge
No Yes
Figure 4.3: Stacked histograms to show the relationship between ICU length of stay and the significant ICU characteristics.
App
endix
4.B:
Mo
del
p
erformance.
T able 4.6: Co efficien ts for patien t characteristics in the mixed effects regression mo dels (1 of 3). Results mo del case-mix only Results mo del patien t case-mix with m ultiv ariate ICU characteristics Characteristics Co efficien t 1 P-v alue 2 Co efficien t 1 P-v alue 2 In tercept − 0 .839 (-0.92 to -0.759) − 2 .144 (-2.308 to -1.981) Gender: male 0 .016 (0.004 to 0.028) 0 .011 0 .014 (0.002 to 0.026) 0 .025 A dmission typ e < 0 .001 < 0 .001 Urgen t surgery − 0 .036 (-0.299 to 0.227) − 0 .019 (-0.277 to 0.239) Electiv e surgery − 0 .246 (-0.509 to 0.018) − 0 .222 (-0.480 to 0.036) Age (splines) < 0 .001 < 0 .001 Spline 1 0 .132 (0.102 to 0.162) 0 .137 (0.108 to 0.166) Spline 2 0 .066 (-0.023 to 0.155) 0 .072 (-0.016 to 0.16) Spline 3 − 0 .497 (-0.564 to -0.43) − 0 .488 (-0.553 to -0.423) AP A CHE IV ph ysiology score (APS) (splines) < 0 .001 < 0 .001 Spline 1 1 .804 (1.756 to 1.851) 1 .778 (1.731 to 1.824) Spline 2 0 .660 (0.550 to 0.770) 0 .643 (0.535 to 0.751) Spline 3 − 0 .809 (-0.943 to -0.675) − 0 .816 (-0.948 to -0.684) Confirmed infection (y es) 0 .252 (0.233 to 0.272) < 0 .001 0 .246 (0.227 to 0.265) < 0 .001 Mec hanical v e n tilation first 24 hours (y es) 0 .354 (0.338 to 0.370) < 0 .001 0 .349 (0.334 to 0.365) < 0 .001 V as oactiv e d rug use first 24-hours of admission (y es) 0 .259 (0.244 to 0.275) < 0 .001 0 .257 (0.242 to 0.272) < 0 .0014
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T able 4.6: Co efficien ts for patien t characteristics in the mixed effects regression mo dels -(2 of 3). Results mo del case-mix only Results mo del patien t c ase-mix with m ultiv ariate ICU characteristics Characteristics Co efficien t 1 P-v alue 2 Co efficien t 1 P-v alue 2 Lo w est GCS the first 24-hours of ICU admission < 0 .001 < 0 .001 GCS: 4 0 .306 (0.223 to 0.390) 0 .306 (0.223 to 0.388) GCS: 5 0 .312 (0.225 to 0.398) 0 .318 (0.233 to 0.403) GCS: 6 0 .337 (0.273 to 0.400) 0 .333 (0.270 to 0.396) GCS: 7 0 .395 (0.333 to 0.456) 0 .383 (0.323 to 0.443) GCS: 8 0 .478 (0.413 to 0.544) 0 .464 (0.400 to 0.529) GCS: 9 0 .307 (0.241 to 0.372) 0 .292 (0.228 to 0.357) GCS: 10 0 .445 (0.383 to 0.507) 0 .432 (0.371 to 0.493) GCS: 11 0 .397 (0.336 to 0.457) 0 .385 (0.325 to 0.444) GCS: 12 0 .401 (0.340 to 0.461) 0 .400 (0.340 to 0.459) GCS: 13 0 .431 (0.378 to 0.484) 0 .418 (0.366 to 0.470) GCS: 14 0 .432 (0.388 to 0.475) 0 .421 (0.378 to 0.463) GCS: 15 0 .401 (0.362 to 0.440) 0 .395 (0.356 to 0.433) 93T able 4.6: Co efficien ts for patien t characteristics in the mixed effects regression mo dels -(3 of 3). Results mo del case-mix only Results mo del patien t case-mix with m ultiv ariate ICU characteristics Characteristics Co efficien t 1 P-v alue 2 Co efficien t 1 P-v alue 2 A cute diagnoses (y es) A cute renal fail ure 0 .146 (0.120 to 0.173) < 0 .001 0 .145 (0.119 to 0.171) < 0 .001 CPR 0 .166 (0.128 to 0.204) < 0 .001 0 .173 (0.135 to 0.210) < 0 .001 CV A 0 .257 (0.223 to 0.291) < 0 .001 0 .247 (0.214 to 0.281) < 0 .001 Dysrh ytmia 0 .032 (0.007 to 0.058) 0 .012 0 .030 (0.005 to 0.055) 0 .018 Gastro in testinal b leeding − 0 .215 (-0.266 to -0.164) < 0 .001 − 0 .213 (-0.263 to -0.164) < 0 .001 In tracranial mass e ffect 0 .256 (0.222 to 0.291) < 0 .001 0 .256 (0.222 to 0.290) < 0 .001 Chronic diagnoses (y es) Cardio v ascul ar insufficien cy − 0 .035 (-0.064 to -0.006) 0 .018 − 0 .032 (-0.061 to -0.004) 0 .027 Chronic renal insufficiency − 0 .064 (-0.095 to -0.033) < 0 .001 − 0 .065 (-0.095 to -0.035) < 0 .001 Chronic dialysis − 0 .262 (-0.321 to -0.202) < 0 .001 − 0 .260 (-0.318 to -0.202) < 0 .001 Chronic resp eratoir insufficiency 0 .101 (0.070 to 0.132) < 0 .001 0 .097 (0.066 to 0.127) < 0 .001 Cirrhosis − 0 .059 (-0.113 to -0.004) 0 .034 − 0 .053 (-0.106 to 0.001) 0 .053 Diab etes − 0 .035 (-0.052 to -0.019) < 0 .001 − 0 .034 (-0.05 to -0.018) < 0 .001 Imm unologic insufficiency (y e s) 0 .054 (0.032 to 0.077) < 0 .001 0 .054 (0.032 to 0.076) < 0 .001 Neoplasm − 0 .141 (-0.171 to -0.112) < 0 .001 − 0 .145 (-0.174 to -0.116) < 0 .001 GCS=Glasgo w coma scale; CPR=cardiopulmonary resuscitation; CV A=cerebro vascular acciden t 1Fixed effect regression co efficie nts and W ald typ e confidence in terv als. 2P-v alue based on the χ 2-test.
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Figure 4.4: Performance of the model based on statistics of the residuals.
● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ●● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Case-mix only 1.7 1.3 0.9 0.5 0.1 -0.3 -0.7
Mean predicted log-transformed ICU LoS
Mean observ
ed log-transf
ormed ICU LoS
1.7 1.3 0.9 0.5 0.1 -0.3 -0.7
ICU characteristics included
Figure 4.5: Calibration plot of mean predicted log-transformed ICU length of stay against mean observed log-transformed ICU length of stay, based on 2% percentiles of predicted log-transformed ICU length of stay.
