Predictive Modeling of Emergency Department Wait Times for Abdominal Pain Patients

144 Pages·2010·4.47 MB·English

Predictive Modeling of Emergency Department Wait Times
for Abdominal Pain Patients
By
Pamela Lee-Kar Chan
A thesis submitted in conformity with the requirements
for the degree of Master’s of Applied Science
Department of Mechanical and Industrial Engineering
University of Toronto
© Copyright by Pamela Chan 2010
Predictive Modeling of Emergency Department Wait Times for
Abdominal Pain Patients
Pamela Lee-Kar Chan
Master’s of Applied Science
Department of Mechanical and Industrial Engineering
University of Toronto
2010
Abstract
Reducing emergency department (ED) wait times are a major priority for the Ontario
Government. Overcrowded EDs, cumulative effects of the delays in hospital processes and lack
of resources are manifested in the phenomenon of long wait times. This thesis aims to estimate in
real-time, a minimum wait time confidence interval for urgent abdominal pain patients on
weekdays based on ED operations, waiting room status and ED census indicators through
multivariate backwards stepwise regression modeling.
The ED wait times model accurately predicted a 95% wait time confidence interval for patients.
Common underlying factors attributed to long wait times include the total number of emergent
and urgent patients in the waiting room, the total number of patient waiting for a consultation and
the number of patients not seen within the Ontario Government’s target times. This information
is useful in managing patient expectations and appropriately allocating resources to improve wait
times.
ii
Acknowledgments

First and foremost, I would like to thank Prof. Michael Carter for providing me with endless
guidance throughout my university experience. Secondly, I would like to thank Dr. Thomas
Chan, the Emergency Department Chief at The Scarborough for leading the Enhancing
Emergency Services project, inspiring me with ideas and teaching me valuable life lessons.
This thesis would not have been possible without the help and support of Jenna Su and Louis
LeBlanc, Angie Ganter, Wol Bong Chung and Tazeem Ismail from the Scarborough Hospital. I
am grateful for their energy and advice throughout my thesis work.
I would like to take this opportunity to thank Ali Esenoy, Andriy Kolos, Somayeh Sadat and
Laura Tardif for their knowledge and enthusiasm during the more difficult periods.
Last, but certainly not least, I would like to thank my parents, Paul and Rosita Chan, for their
unwavering support. Caroline, you are certainly a force to be reckoned with. I admire your
strength and perseverance overcoming the challenging times in life. Megan, your wit and
opinions help me put things back into perspective. Richard, thank you for your inexhaustible
support and for inspiring me to follow my dreams.

Pamela Chan

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Table of Contents

Acknowledgments .......................................................................................................................... iii
Table of Contents ........................................................................................................................... iv
List of Tables ................................................................................................................................ vii
List of Figures ................................................................................................................................. x
List of Appendices ........................................................................................................................ xv
1 Introduction ................................................................................................................................ 1
1.1 Motivation ........................................................................................................................... 1
1.2 Context ................................................................................................................................ 4
1.2.1 The Scarborough Hospital Emergency Department ............................................... 4
1.2.2 Patient Inclusion Criteria ........................................................................................ 4
1.3 Emergency Department Process Flow ................................................................................ 5
1.4 Objectives ........................................................................................................................... 7
1.5 Thesis Organization ............................................................................................................ 7
2 Background ................................................................................................................................ 9
2.1 Emergency Department Overcrowding .............................................................................. 9
2.1.1 Sources of ED Overcrowding ............................................................................... 10
2.1.2 Detrimental Effects of Overcrowding ................................................................... 11
2.1.3 Solutions for Overcrowding .................................................................................. 12
2.1.4 Overcrowding Indicators ...................................................................................... 12
2.2 Exploratory Forecasting Methods ..................................................................................... 16
2.2.1 Discrete Event Simulation .................................................................................... 16
2.2.2 Queuing Theory .................................................................................................... 17
2.2.3 Time Series Analysis ............................................................................................ 17
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2.2.4 Multivariate Regression ........................................................................................ 18
2.3 Summary ........................................................................................................................... 19
3 Methodology ............................................................................................................................ 20
3.1 Conceptual Model Development ...................................................................................... 20
3.2 Developing the Wait Times Model ................................................................................... 21
3.2.1 Current Methodology Overview ........................................................................... 21
3.2.2 Data Source ........................................................................................................... 21
3.2.3 Data Partitioning ................................................................................................... 22
3.2.4 Data Preparation .................................................................................................... 24
3.2.5 Regression Model ................................................................................................. 26
3.2.6 Descriptive Analysis ............................................................................................. 27
3.3 Model Validation and Forecasting .................................................................................... 28
3.3.1 Model and Validation Data ................................................................................... 28
3.3.2 First Prediction Intervals ....................................................................................... 28
3.3.3 Second Prediction Interval .................................................................................... 29
3.3.4 Accuracy Testing .................................................................................................. 29
4 Results ...................................................................................................................................... 31
4.1 Introduction ....................................................................................................................... 31
4.2 Regression Model ............................................................................................................. 31
4.2.1 General Campus .................................................................................................... 31
4.2.2 Birchmount Campus ............................................................................................. 37
5 Discussion ................................................................................................................................ 44
5.1 Comparison of Wait Time Models ................................................................................... 44
5.2 Limitations ........................................................................................................................ 50
6 Conclusion................................................................................................................................ 51
6.1 Future Work ...................................................................................................................... 52
v
Bibliography ................................................................................................................................. 53

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List of Tables
Table 1 Indicators for wait times based on the input/throughput/output model ........................... 15
Table 2 General Campus: Percentage of patients with LOS greater than the Ministry benchmarks
....................................................................................................................................................... 31
Table 3 General Campus Regression Coefficients ....................................................................... 33
Table 4 Birchmount Campus: Percentage of patients with LOS greater than the Ministry
benchmarks ................................................................................................................................... 38
Table 5 Birchmount Campus Regression Coefficients ................................................................. 39
Table 6 EDM patient field definition ............................................................................................ 61
Table 7 Indicator descriptions ....................................................................................................... 62
Table 8 Frequency tables of MD waits ......................................................................................... 65
Table 9 Frequency table of consult waits ..................................................................................... 66
Table 10 Frequency table of ARQ waits ....................................................................................... 67
Table 11 Frequency table of CTAS 2 patients in the waiting room ............................................. 68
Table 12 Frequency table of regular CTAS 3 patients in the waiting room ................................. 69
Table 13 Frequency table of boarding patients ............................................................................. 70
Table 14 Frequency table of CTAS 2 patients in the ED ............................................................. 71
Table 15 Frequency table of CTAS 3 patients with ED LOS greater than 6 hours ...................... 72
Table 16 Frequency table of CTAS 4 & 5 patients with EDLOS greater than 4 hours ................ 73
Table 17 Regression model summary ........................................................................................... 79
Table 18 ANOVA summary ......................................................................................................... 80
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Table 19 Residual statistics ........................................................................................................... 80
Table 20 First estimate outliers ..................................................................................................... 83
Table 21 Descriptive information on first estimate ...................................................................... 83
Table 22 Second estimate outliers ................................................................................................ 90
Table 23 Descriptive information on second estimate .................................................................. 91
Table 24 Histogram of the range for the second estimated confidence interval ........................... 93
Table 25 Frequency table of consult waits ................................................................................... 96
Table 26 Frequency table of CTAS 2 patients in the waiting room ............................................. 97
Table 27 Frequency table of regular CTAS 4 & 5 patients in the waiting room .......................... 98
Table 28 Frequency table of regular CTAS 3 patients in the waiting room ................................. 99
Table 29 Frequency table of fast track CTAS 3 patients in the waiting room ............................ 100
Table 30 Frequency table of CTAS 1 patients in the ED ........................................................... 101
Table 31 Frequency table of CTAS 2 patients in the ED ........................................................... 102
Table 32 Frequency table of CTAS 3 patients with ED LOS greater than 6 hours .................... 103
Table 33 Frequency table of CTAS 4 & 5 patients with ED LOS greater than 4 hours ............. 104
Table 34 Regression Model Summary ........................................................................................ 110
Table 35 ANOVA summary ....................................................................................................... 111
Table 36 Coefficients table summary ......................................................................................... 111
Table 37 Summary on residual statistics .................................................................................... 112
Table 38 First estimate outliers ................................................................................................... 115
viii
Table 39 Descriptive information on first estimate .................................................................... 116
Table 40 Second estimate outliers .............................................................................................. 123
Table 41 Descriptive information on second estimate ................................................................ 124

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List of Figures
Figure 1 Most Frequent Emergency Department Chief Complaints ............................................ 23
Figure 2 ED Census Initialization Data – General Campus ......................................................... 25
Figure 3 General Campus: The relationship between wait times and change in predictor ........... 35
Figure 4 General Campus Regression Model Confidence Interval .............................................. 36
Figure 5 Birchmount Campus: The relationship between wait times and change in predictor
values ............................................................................................................................................ 41
Figure 6 Birchmount Campus Regression Model Confidence Interval ........................................ 42
Figure 7 ED Patient flow process ................................................................................................. 59
Figure 8 Data Initialization Warm-Up Period - Birchmount Campus .......................................... 64
Figure 9 Boxplot of MD waits on wait times ............................................................................... 65
Figure 10 Boxplot of consult waits on wait times ........................................................................ 66
Figure 12 Boxplot of ARQ waits on wait times ........................................................................... 67
Figure 13 Boxplot of CTAS 2 patients in the waiting room on wait times .................................. 68
Figure 14 Boxplot of regular CTAS 3 patients in the waiting room on wait times ...................... 69
Figure 15 Boxplot of boarding patients on wait times .................................................................. 70
Figure 16 Boxplot of CTAS 2 patients in the ED on wait times .................................................. 71
Figure 17 Boxplot of CTAS 3 patients with EDLOS greater than 6 hours on wait times ............ 72
Figure 18 Boxplot of CTAS 4 & 5 patients with EDLOS greater than 4 hours on wait times ..... 73
Figure 19 Boxplot of MD waits on the standardized residuals ..................................................... 74
Figure 20 Boxplot of consult waits on the standardized residuals ................................................ 74
x