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

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  • 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.

    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
     | Show Table
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    Table 2.  Top 15 Risk Factors Selected Using Filter Methods

    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
     | Show Table
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    Table 3.  Prediction Results Including Factor of Social Issues

    Set of risk factors Training set Test set
    sensitivity specificity overall sensitivity specificity overall
    S0 29.4% 86.2% 83.5% 29.3% 85.8% 83.3%
     | Show Table
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    Table 4.  Prediction Results Excluding Factor of Social Issues

    Set of risk factors Training set Test set
    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%
     | Show Table
    DownLoad: CSV

    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%
     | Show Table
    DownLoad: CSV
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