Predicting 72-hour reattendance in emergency departments using discriminant analysis via mixed integer programming with electronic medical records

Fanwen Meng; Kiok Liang Teow; Kelvin Wee Sheng Teo; Chee Kheong Ooi; Seow Yian Tay

doi:10.3934/jimo.2018079

Article Contents

2019, Volume 15, Issue 2: 947-962. Doi: 10.3934/jimo.2018079

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Predicting 72-hour reattendance in emergency departments using discriminant analysis via mixed integer programming with electronic medical records

1.
Department of Health Services and Outcomes Research, National Healthcare Group, 138543, Singapore
2.
Department of Emergency Medicine, Tan Tock Seng Hospital, 308433, Singapore

* Corresponding author
* Corresponding author

Received: September 30, 2017

Revised: December 31, 2017

Early access: June 2018

Published: January 2019

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Abstract

The proportion of patients who reattended emergency department (ED) within 72 hours is an important indicator of quality of care. This study develops a practical framework to predict patients who will reattend ED in 72 hours from clinical perspectives. We analyze 328,733 ED patients from 1 January 2011 to 31 December 2013, with an average of 4.6% reattendances. We feature over 100 factors including demographics, diagnosis, patient acuity, chief complaints, selected laboratory tests, summarized vital signs. Using univariate analysis, a pool of risk variables is selected for subsequent factor selection. We then apply filter methods to derive a set of candidate factors. With these factors in combination with suggestions from ED clinicians, a mixed integer programming model based on discriminant analysis is proposed to determine a classification rule for 72-hour reattendance. In numerical experiments, various small subsets of risk factors are used for classification and prediction. The results show that favorable predicting performances can be achieved in both training and test sets.

Keywords:

Mathematics Subject Classification: Primary: 90C11, 90C90; Secondary: 62P10.

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Table 1. List of Potential Risk Factors

Index	Factor Name
1	Age
2	Gender
3	Race
4	Registration day of week (DOW)
5	Registration public holiday and Sunday (HAS)
6	CC¹ orthopaedic (ORTHO)
7	CC¹ gastrointestinal (GI)
8	CC¹ respiratory (RES)
9	CC¹ general & minor
10	CC¹ external causes of morbidity
11	CC¹ neurologic
12	CC¹ cardiovascular (CV)
13	CC¹ skin
14	CC¹ eye complaints (EC)
15	CC¹ ear, neck, throat
16	CC¹ substance misuse (SM)
17	CC¹ others
18	EDTC² category
19	Diagnosis: general symptoms (GM)
20	Diagnosis: acute respiratory infection (ARI)
21	Diagnosis: sprains and strains (SS)
22	Diagnosis: minor head injury (MHI)
23	Diagnosis: diseases of oesophagus, stomach, duodenum
24	Diagnosis: COPD³
25	Diagnosis: fracture upper limb (FUL)
26	Diagnosis: fracture lower limb (FLL)
27	Diagnosis: open wound upper limb (OWUL)
28	Diagnosis: superficial injuries (SIN)
29	Diagnosis: intestinal diseases (ID)
30	Diagnosis: rheumatism (RHE)
31	Diagnosis: diseases of ear and mastoid (DEM)
32	Diagnosis: open wound of head, neck, and trunk (OW of HNT)
33	Diagnosis: neurotic disorders (ND)
34	Diagnosis: viral diseases (VD)
35	Diagnosis: complications of care (COMC)
36	Diagnosis: open wound lower limb (OWLL)
37	Diagnosis: others in ICD-9-CM⁴ groups
38	PAC⁵ status
39	Social issues (SI)
40	National service full-time (NSTF)
41	Handover
42	Medical history diabetes
43	Medical history asthma
44	Medical history cardiovascular disease
45	Average temperature (ave temp.)
46	Average pulse
47	Diastolic blood pressure (DBP)
¹ CC stands for chief complaint ² EDTC stands for emergency diagnostic and therapeutic centre. Certain emergency patients are observed at EDTC for up to 24 hours before being admitted or discharged ³ COPD stands for chronic obstructive pulmonary disease ⁴ ICD-9-CM stands for international classification of diseases, 9th revision, clinical modification ⁵ PAC stands for patient acuity category

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Table 2. Top 15 Risk Factors Selected Using Filter Methods

JMI	MIFS	CMIM	MRMR	ICAP	CIFE	DISR	CMI	ConDred
SI	SI	SI	SI	SI	SI	SI	SI	SI
PAC	PAC	PAC	PAC	PAC	PAC	diag: COPD	PAC	PAC
DBP	diag:ID	DBP	diag:ID	DBP	ave pulse	CC stance	ave SM	DBP
ave pulse	reg HAS	ave pulse	reg HAS	ave pulse	DBP	diag:ND	DBP	EDTC
diag:COPD	diag:COMC	diag:COPD	diag:OWLL	diag:COPD	age	diag:OWLL	reg DOW	CC others
age	diag:OWLL	age	diag:OW of HNT	age	reg DOW	handover	age	diag:MHI
CC RES	diag:OW of HNT	handover	diag:COMC	gender	race	CC RES	race	age
gender	diag:VD	gender	diag:ND	handover	diag:COPD	diag:OWUL	ave temp.	NSFT
ave temp.	diag:DEM	ave temp.	diag:DEM	ave temp.	ave temp.	diag:FLL	gender	ave pulse
handover	CC SM	CC RES	ave temp.	CC GI	gender	diag:OW of HNT	CC ORTHO	CC ORTHO
race	diag:RHE	CC EC	diag:FLL	race	CC RES	PAC	diag:GM	diag:GM
EDTC	diag:SIN	CC ORTHO	diag:RHE	NSFT	handover	EDTC	diag:others in ICD9	CC CV
NSFT	diag:FLL	race	diag:OWUL	reg DOW	NSFT	diag:DEM	CC RES	diag:ARI
CC ORTHO	diag:FUL	NSFT	diag:SIN	diag:ND	diag:GM	diag:ID	CC GI	CC RES
reg DOW	diag:OWUL	diag:ND	gender	diag:GM	medical history asthma	CC EC	NSFT	diag:SS

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Table 3. Prediction Results Including Factor of Social Issues

Set of risk factors	Training set			Test set
Set of risk factors	sensitivity	specificity	overall	sensitivity	specificity	overall
S₀	29.4%	86.2%	83.5%	29.3%	85.8%	83.3%

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Table 4. Prediction Results Excluding Factor of Social Issues

Set of risk factors	Training set			Test set
Set of risk factors	sensitivity	specificity	overall	sensitivity	specificity	overall
S₁	41.1%	74.2%	72.5%	40.3%	74.1%	72.4%
S₂	40.6%	74.5%	72.8%	40.1%	74.1%	72.6%
S₃	40.6%	74.4%	72.7%	40.1%	74.2%	72.7%
S₄	40.3%	74.4%	72.8%	39.9%	74.4%	72.8%

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Table 5. Prediction Results Using Logistic Regression

	Training set: 211,160			Test set: 117,573
Hosmer-Lemeshow test	p < 0.001			p < 0.001
C-statistic of ROC curve	0.67			0.66
Predictive accuracy	sensitivity	specificity	overall	sensitivity	specificity	overall
70% cutoff	1.7%	99.9%	95.4%	1.0%	99.9%	95.5%
50% cutoff	4.6%	99.9%	95.5%	2.4%	99.9%	95.5%
20% cutoff	11.9%	99.3%	95.2%	7.2%	99.4%	95.2%
10% cutoff	18.5%	96.3%	92.7%	14.1%	96.1%	92.4%
5% cutoff	51.6%	72.2%	71.2%	51.0%	70.8%	69.9%

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