Upload
richard-francis
View
220
Download
0
Tags:
Embed Size (px)
Citation preview
Comparison of different statistical methods to predict Intensive Care Length of Stay
Ilona VerburgNicolette de Keizer
Niels Peek
Dept. Of Medical InformaticsAcademic Medical CenterUniversity of Amsterdam
The Netherlands
ESCTAIC 2012,Timisoara
Background
Intensive Care Units (ICUs) assess their performance to improve quality and reduce costs
4-10-2012 2
Background
Background and objective
mortality
length of stay
Case mixEffectiveness of care
Efficiency of care
4-10-2012 3
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
ICU Length of stay is influenced by case mix.
Example:
Background and objective
Background and objective
4-10-2012 4
Observed outcome
Predictive model
Expected outcome
ICU
Case mix
Com
pare
Case mix
4-10-2012 5
ObjectiveCompare the performance of different statistical regression methods to predict ICU LoS.
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
Data
4-10-2012 6
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
Identifying quality of care problems
Quality assurance
Database
Data
4-10-2012 7
Exclusion criteria
APACHE IV exclusion criteria
elective surgery
Data
Patients admitted to ICUs participating NICE
2009 - 2011
84 ICUs
81,190 (86.1%) survivors
94,251 (42.4%) admissions
13,061 (13.9%) non-survivors
Included patients
Length of stay
4-10-2012 8
Distribution of Length of Stay in fractional days
ICU survivors (n= 81,190) ICU non-survivors (n= 13,061)
Median: 1.7 (days)Mean: 4.2 Standard deviation: 8.2Maximum: 326.6
Median: 2.4 (days)Mean: 5.9Standard deviation: 10.2Maximum: 139.0
9
ICU Length of Stay
Distribution of discharge time
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
4-10-2012 10
4-10-2012 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
4-10-2012 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
4-10-2012 13
Selection of covariates
Starting with large set of variables
Known relationship with LoS (literature)
Stepwise backwards elimination of variables
Modeling ICU length of stay
Included case mix
Demographics
Age
Gender
Admission type
Diagnoses (APACHE IV)
Severity of illness (APACHE IV severity-of-illness score)
Different comorbidities (21)
4-10-2012 14
Performance measures
Validation
Squared Pearson correlation = R2 =
Root Mean squared prediction error (RMSPE) =
Relative BIAS =
Relative mean absolute prediction error (MAPE) =
2
)ˆ()(
)ˆ,(
YY
YYCov
k
kk yEyn
21
kk
kk
kk
yn
yn
Eyn
1
11
kk
kkk
yn
yEyn
1
1
Good prediction
High ↑
Low ↓
Low ↓- or +
Low ↓
Validation
4-10-2012 15
Validation
Performance measures calculated on original data
Correcting for optimistic bias
100 bootstrap samples
4-10-2012 16
Covariates survivorsOLS reg los
OLS reg log los
GLM: gaussian
GLM: poisson
GLM: negative binomial
GLM: Gamma
Cox PH
chronic dialysis -1.04 -0.16 -0.25 -0.26 -0.28 -0.28 0.31cva 0.74 0.1 0.13 0.18 0.26 0.26 -0.3diabetes -0.34 -0.01 -0.07 -0.06 -0.04 -0.04 0.03resperatory insufficient 0.38 0.03 0.06 0.09 0.15 0.15 -0.11spline Aps (1) 5.55 0.64 1.74 1.65 1.61 1.61 -1.52spline Aps (2) 11.07 1.09 3.16 2.78 2.64 2.64 -2.57spline Aps (3) 15.98 0.99 2.07 2 2.08 2.08 -1.79
Results coefficients
Covariates non-survivorsOLS reg los
OLS reg log los
GLM: gaussian
GLM: poisson
GLM: negative binomial
GLM: Gamma
Cox PH
chronic dialysis 0.15 0.08cva -0.68 -0.18 -0.15 -0.12 -0.12 0.09diabetes 0.35 0.03 0.05 0.05 0.06 0.06 -0.05resperatory insufficient -0.51 -0.03 -0.11 -0.1 -0.09 -0.09 0.07spline Aps (1) -5.59 -0.43 -0.94 -0.84 -0.8 -0.8 0.7spline Aps (2) -6.08 -0.73 -1.09 -1.26 -1.53 -1.55 1.54spline Aps (3) -6.47 -0.84 -1.64 -1.76 -1.87 -1.88 1.83
R2 RMSPE Relative BIAS Relative MAPE
OLS regression (LoS) 0.174 7.448 0.008 0.812
OLS regression (log(LoS)) 0.183 7.714 -0.400 0.674
GLM Gaussian 0.197 7.335 0.001 0.771
GLM Poisson 0.194 7.349 0.000 0.769
GLM Negative Binomial 0.186 7.388 0.005 0.773
GLM Gamma 0.184 7.407 0.005 0.773
Cox PH regression 0.097 9.002 -0.693 0.938
Results validation
4-10-2012 17
ICU survivors
Mean observed > mean expectedUnderestimation of mean LoS
R2 RMSPE Relative BIAS Relative MAPE
OLS regression (LoS ) 0.107 9.618 0.005 0.891
OLS regression (log(LoS)) 0.107 10.213 -0.510 0.762
GLM Gaussian 0.134 9.462 -0.009 0.868
GLM Poisson 0.128 9.504 0.000 0.872
GLM Negative Binomial 0.12 9.545 -0.001 0.872
GLM Gamma 0.112 9.602 -0.001 0.877
Cox PH regression 0.075 11.388 -0.808 0.906
Results validation
4-10-2012 18
ICU non-survivors
Conclusion and discussion
GLM models shows best performance
Poorest performance found for Cox PH regression
Large relative bias was found for OLS regression of log-transformed LoS
4-10-2012 19
Difficult to predict ICU LoS
Influenced by admission and discharge policy
Seasonal pattern for admission and discharge time
Skewed to the right
Differences in performance between models not statistically tested
Conclusion and discussion
4-10-2012 20
Similar study for CABG patients (Austin et al.), with comparable results
Different patient type
Different distribution of length of stay
Future research
Different models for survivors and non-survivors
combining with mortality in one prediction
Statistical methods to predict ICU LoS
developing a model for benchmarking purposes
4-10-2012 21
Questions?
Thank you for your attention!
APACHE IV Exclusiecriteria
4-10-2012 22
• 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