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

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April 2019, 15(2): 947-962. doi: 10.3934/jimo.2018079

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

Fanwen Meng ^1,, , Kiok Liang Teow ^1, , Kelvin Wee Sheng Teo ^1, , Chee Kheong Ooi ^2, and Seow Yian Tay ^2,

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

Received October 2017 Revised January 2018 Published June 2018

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: Mixed integer programming, discriminant analysis, filter methods, emergency department reattendance, predict.

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

Citation: Fanwen Meng, Kiok Liang Teow, Kelvin Wee Sheng Teo, Chee Kheong Ooi, Seow Yian Tay. Predicting 72-hour reattendance in emergency departments using discriminant analysis via mixed integer programming with electronic medical records. Journal of Industrial & Management Optimization, 2019, 15 (2) : 947-962. doi: 10.3934/jimo.2018079

References:

[1]	E. A. Alessandrini, J. M. Lavelle, S. M. Grenfell, C. R. Jacobstein and K. N. Shaw, Return visits to a pediatric emergency department, Pediatr. Emerg. Care, 20 (2004), 166-171. Google Scholar
[2]	J. A. Anderson, Constrained discrimination between k populations, J. R. Stat. Soc. Series B, 31 (1969), 123-139. Google Scholar
[3]	D. Aujesky, M. K. Mor, M. Geng, R. A. Stone, M. J. Fine and S. A. Ibrahim, Predictors of early hospital readmission after acute pulmonary embolism, Arch. Intern. Med., 169 (2009), 287-293. doi: 10.1001/archinternmed.2008.546. Google Scholar
[4]	K. P. Bennett and O. L. Mangasarian, Robust linear programming discrimination of two linearly inseparable sets, Optim. Method Softw., 1 (1992), 23-34. doi: 10.1080/10556789208805504. Google Scholar
[5]	R. T. Boonyasai, O. M. Ijagbemi and J. C. Pham et al, Improving the Emergency Department Discharge Process, Agency for Healthcare Research and Quality, Rockville, Maryland, United States. 2014.Google Scholar
[6]	G. Brown, A. Pocock, M.-J. Zhao and M. Luján, Conditional likelihood maximisation: A unifying framework for information theoretic feature selection, J. Mach. Learn. Res., 13 (2012), 27-66. Google Scholar
[7]	CDC, ICD-9-CM official guidelines for coding and reporting, http://www.cdc.gov/nchs/data/icd/icd9cm＄_{-}＄guidelines＄_{-}＄2011.pdf (accessed on 20 March 2016).Google Scholar
[8]	R. J. Gallagher, E. K. Lee and D. A. Patterson, Constrained discriminant analysis via 0/1 mixed integer programming, Ann. Oper. Res., 74 (1997), 65-88. Google Scholar
[9]	E. Goksu, C. Oktay, M. Kartal, A. Oskay and A. V. Sayrac, Factors affecting revisit of COPD exacerbated patients presenting to emergency department, Eur. J. Emerg. Med., 17 (2010), 283-285. doi: 10.1097/MEJ.0b013e3283314795. Google Scholar
[10]	C. Y. Han, L. C. Chen, A. Barnard, C. C. Lin, Y. C. Hsiao and H. E. Liu et al, Early revisit to the emergency department: An integrative review, J. Emerg. Nurs., 41 (2015), 285-295 doi: 10.1016/j.jen.2014.11.013. Google Scholar
[11]	S. Hao, B. Jin and A. Y. Shin et al, Risk prediction of emergency department revisit 30 days post discharge: A prospective study, PLoS One, 10 (2015), e0117633. doi: 10.1371/journal.pone.0112944. Google Scholar
[12]	S. C. Hu, Analysis of patient revisits to the emergency department, Am. J. Emerg. Med., 10 (1992), 366-370. Google Scholar
[13]	I. Imsuwan, Characteristics of unscheduled emergency department return visit patients within 48 hours in Thammasat university hospital, J. Med. Assoc. Thai., 94 (2011), S73-S80. Google Scholar
[14]	Y. Jenab, S. Haghani, A. Jalali and F. Darabi, Unscheduled return visits and leaving the chest pain unit against medical advice, Iran Red Crescent Med. J., 17 (2015), e18320. doi: 10.5812/ircmj.17(5)2015.18320. Google Scholar
[15]	K. D. Keith, J. J. Bocka, M. S. Kobernick, R. L. Krome and M. A. Ross, Emergency department revisits, Ann. Emerg. Med., 18 (1989), 964-968. doi: 10.1016/S0196-0644(89)80461-5. Google Scholar
[16]	M. Ko, Y. Lee, C. Chen, P. Chou and D. Chu, Incidence of and predictors for early return visits to the emergency department: a population-based survey, Medicine, 94 (2015), e1770. doi: 10.1097/MD.0000000000001770. Google Scholar
[17]	E. K. Lee, Y. Wang, M. S. Hagen, X. Wei, R. A. Davis and B. M. Egan, Machine learning: Multi-site evidence-based best practice discovery, in Machine Learning, Optimization, and Big Data. MOD 2016. Lecture Notes in Computer Science (eds. P. Pardalos, P. Conca, G. Giuffrida and G. Nicosia), Springer, Cham, (2016), 1-15. doi: 10.1007/978-3-319-51469-7_1. Google Scholar
[18]	E. K. Lee, Large-scale optimization-based classification models in medicine and biology, Ann. Biomed. Eng., 35 (2007), 1095-1109. doi: 10.1007/s10439-007-9317-7. Google Scholar
[19]	E. K. Lee, F. Yuan, D. Hirsh, M. Mallory and H. K. Simon, A clinical decision tool for predicting patient care characteristics: patients returning within 72 hours in the emergency department, AMIA Annu. Symp. Proc., (2012), 495-504. Google Scholar
[20]	E. K. Lee, R. J. Gallagher and D. A. patterson, A linear programming approach to discriminant analysis with a reserved-judgment region, INFORMS J. Comput., 15 (2003), 23-41. doi: 10.1287/ijoc.15.1.23.15158. Google Scholar
[21]	S. J. Liaw, M. J. Bullard, P. M. Hu, J. C. Chen and H. C. Liao, Rates and causes of emergency department revisits within 72 hours, J. Formos Med. Assoc., 98 (1999), 422-425. Google Scholar
[22]	J. A. Lowthian, A. J. Curtis and P. A. Cameron et al, Systematic review of trends in emergency department attendances: an Australian perspective, Emerg. Med. J., 28 (2011), 373-377. doi: 10.1136/emj.2010.099226. Google Scholar
[23]	F. Meng, C. K. Ooi, C. K. K. Soh, K. L. Teow and P. Kannapiran, Quantifying patient flow and utilization with patient flow pathway and diagnosis of an emergency in Singapore, Health Syst., 5 (2016), 140-148. doi: 10.1057/hs.2015.15. Google Scholar
[24]	F. Meng, J. Qi, M. Zhang, J. Ang, S. Chu and M. Siim, A robust optimization model for managing elective admission in a public hospital, Oper. Res., 63 (2015), 1452-1467. doi: 10.1287/opre.2015.1423. Google Scholar
[25]	A. S. Newton, S. Ali, D. W. Johnson, C. Haines, R. J. Rosychuk, R. A. Keaschuk, P. Jacobs, M. Cappelli and T. P. Klassen, Who comes back? Characteristics and predictors of return to emergency department services for pediatric mental health care, Acad. Emerg. Med., 17 (2010), 177-186. doi: 10.1111/j.1553-2712.2009.00633.x. Google Scholar
[26]	Y. Y. Ng, Optimal use of emegency services, SFP, 40 (2014), supplement 8-13. Google Scholar
[27]	S. Nunëz, A. Hexdall and A. Aguirre-Jaime, Unscheduled returns to the emergency department: An outcome of medical errors?, Qual. Saf. Health Care., 15 (2006), 102-108. Google Scholar
[28]	K. O'Loughlin, K. A. Hacking, N. Simmons, W. Christian, R. Syahanee, A. Shamekh and N. J. Prince, Paediatric unplanned reattendance rate: A&E clinical quality indicators, Arch. Dis. Child., 98 (2013), 211-213. Google Scholar
[29]	L. Pereira, C. Choquet and A. Perozziello et al, Unscheduled return visits after an emergency department (ED) attendance and clinical link between both visits in patients aged 75 years and over: a prospective observational study, PloS One, 10 (2015), e0123803. doi: 10.1371/journal.pone.0123803. Google Scholar
[30]	H. Qiu, X. Chen, W. Liu, G. Zhou, Y. Wang and J. Lai, A fast11-solver and its applications to robust face recognition, J. Ind. Manag. Optim., 8 (2012), 163-178. Google Scholar
[31]	J. Ryan, J. Hendler and K. P. Bennett, Understanding emergency department 72-hour revisits among medicaid patients using electronic healthcare records, Big Data, 3 (2015), 238-248. doi: 10.1089/big.2015.0038. Google Scholar
[32]	Y. Saeys, I. Inza and P. Larrañaga, A review of feature selection techniques in bioinformatics, 23 (2007), 2507-2517. doi: 10.1093/bioinformatics/btm344. Google Scholar
[33]	G. Sauvin, Y. Freund, K. Saidi, B. Riou and P. Hausfater, Unscheduled return visits to the emergency department: Consequences for triage, Acad. Emerg. Med., 20 (2013), 33-39. doi: 10.1111/acem.12052. Google Scholar
[34]	Y. Sun, B. H. Heng, S. Y. Tay and K. B. Tan, Unplanned 3-day re-attendance rate at Emergency Department and hospital's bed occupancy rate, Int. J. Emerg. Med., 8 (2015), 324-329. doi: 10.1186/s12245-015-0082-3. Google Scholar
[35]	C. R. Trivedy and M. W. Cooke, Unscheduled-return-visits (URV) in adults to the emergency department (ED): A rapid evidence assessment policy review, Emerg. Med. J., 32 (2015), 324-329. doi: 10.1136/emermed-2013-202719. Google Scholar
[36]	S. J. J. Verelst, S. Pierloot, D. Desruelles, J.-B. Gillet and J. Bergs, Short-term unscheduled return visits of adult patients to the emergency department, J. Emerg. Med., 47 (2014), 131-199. doi: 10.1016/j.jemermed.2014.01.016. Google Scholar
[37]	A. K. C. Wai, C. M. Chor, A. T. C. Lee, Y. Sittambunka, C. A. Graham and T. H. Rainer, Analysis of trends in emergency department attendances, hospital admissions and medical staffing in a Hong Kong university hospital: 5-year study, Int J. Emerg. Med., 2 (2009), 141-148. doi: 10.1007/s12245-009-0098-7. Google Scholar
[38]	Y. Wang, G. Zhou, L. Caccetta and W. Liu, An alternative Lagrange-dual based algorithm for sparse signal reconstruction, IEEE Trans. Sig. Process., 59 (2011), 1895-1901. doi: 10.1109/TSP.2010.2103066. Google Scholar
[39]	C. Wei and X. Tang, A fuzzy group decision making approach based on entropy, similarity measure, Int. J. Inf. Technol. Decis. Mak., 10 (2011), 1111-1130. doi: 10.1142/S0219622011004737. Google Scholar
[40]	C. L. Wu, F. T. Wang, Y. C. Chiang, Y. F. Chiu, T. G. Lin and L. F. Fu et al, Unplanned emergency department revisits within 72 hours to a secondary teaching referral hospital in Taiwan, J. Emerg. Med., 38 (2010), 512-517. doi: 10.1016/j.jemermed.2008.03.039. Google Scholar

show all references

References:

[1]	E. A. Alessandrini, J. M. Lavelle, S. M. Grenfell, C. R. Jacobstein and K. N. Shaw, Return visits to a pediatric emergency department, Pediatr. Emerg. Care, 20 (2004), 166-171. Google Scholar
[2]	J. A. Anderson, Constrained discrimination between k populations, J. R. Stat. Soc. Series B, 31 (1969), 123-139. Google Scholar
[3]	D. Aujesky, M. K. Mor, M. Geng, R. A. Stone, M. J. Fine and S. A. Ibrahim, Predictors of early hospital readmission after acute pulmonary embolism, Arch. Intern. Med., 169 (2009), 287-293. doi: 10.1001/archinternmed.2008.546. Google Scholar
[4]	K. P. Bennett and O. L. Mangasarian, Robust linear programming discrimination of two linearly inseparable sets, Optim. Method Softw., 1 (1992), 23-34. doi: 10.1080/10556789208805504. Google Scholar
[5]	R. T. Boonyasai, O. M. Ijagbemi and J. C. Pham et al, Improving the Emergency Department Discharge Process, Agency for Healthcare Research and Quality, Rockville, Maryland, United States. 2014.Google Scholar
[6]	G. Brown, A. Pocock, M.-J. Zhao and M. Luján, Conditional likelihood maximisation: A unifying framework for information theoretic feature selection, J. Mach. Learn. Res., 13 (2012), 27-66. Google Scholar
[7]	CDC, ICD-9-CM official guidelines for coding and reporting, http://www.cdc.gov/nchs/data/icd/icd9cm＄_{-}＄guidelines＄_{-}＄2011.pdf (accessed on 20 March 2016).Google Scholar
[8]	R. J. Gallagher, E. K. Lee and D. A. Patterson, Constrained discriminant analysis via 0/1 mixed integer programming, Ann. Oper. Res., 74 (1997), 65-88. Google Scholar
[9]	E. Goksu, C. Oktay, M. Kartal, A. Oskay and A. V. Sayrac, Factors affecting revisit of COPD exacerbated patients presenting to emergency department, Eur. J. Emerg. Med., 17 (2010), 283-285. doi: 10.1097/MEJ.0b013e3283314795. Google Scholar
[10]	C. Y. Han, L. C. Chen, A. Barnard, C. C. Lin, Y. C. Hsiao and H. E. Liu et al, Early revisit to the emergency department: An integrative review, J. Emerg. Nurs., 41 (2015), 285-295 doi: 10.1016/j.jen.2014.11.013. Google Scholar
[11]	S. Hao, B. Jin and A. Y. Shin et al, Risk prediction of emergency department revisit 30 days post discharge: A prospective study, PLoS One, 10 (2015), e0117633. doi: 10.1371/journal.pone.0112944. Google Scholar
[12]	S. C. Hu, Analysis of patient revisits to the emergency department, Am. J. Emerg. Med., 10 (1992), 366-370. Google Scholar
[13]	I. Imsuwan, Characteristics of unscheduled emergency department return visit patients within 48 hours in Thammasat university hospital, J. Med. Assoc. Thai., 94 (2011), S73-S80. Google Scholar
[14]	Y. Jenab, S. Haghani, A. Jalali and F. Darabi, Unscheduled return visits and leaving the chest pain unit against medical advice, Iran Red Crescent Med. J., 17 (2015), e18320. doi: 10.5812/ircmj.17(5)2015.18320. Google Scholar
[15]	K. D. Keith, J. J. Bocka, M. S. Kobernick, R. L. Krome and M. A. Ross, Emergency department revisits, Ann. Emerg. Med., 18 (1989), 964-968. doi: 10.1016/S0196-0644(89)80461-5. Google Scholar
[16]	M. Ko, Y. Lee, C. Chen, P. Chou and D. Chu, Incidence of and predictors for early return visits to the emergency department: a population-based survey, Medicine, 94 (2015), e1770. doi: 10.1097/MD.0000000000001770. Google Scholar
[17]	E. K. Lee, Y. Wang, M. S. Hagen, X. Wei, R. A. Davis and B. M. Egan, Machine learning: Multi-site evidence-based best practice discovery, in Machine Learning, Optimization, and Big Data. MOD 2016. Lecture Notes in Computer Science (eds. P. Pardalos, P. Conca, G. Giuffrida and G. Nicosia), Springer, Cham, (2016), 1-15. doi: 10.1007/978-3-319-51469-7_1. Google Scholar
[18]	E. K. Lee, Large-scale optimization-based classification models in medicine and biology, Ann. Biomed. Eng., 35 (2007), 1095-1109. doi: 10.1007/s10439-007-9317-7. Google Scholar
[19]	E. K. Lee, F. Yuan, D. Hirsh, M. Mallory and H. K. Simon, A clinical decision tool for predicting patient care characteristics: patients returning within 72 hours in the emergency department, AMIA Annu. Symp. Proc., (2012), 495-504. Google Scholar
[20]	E. K. Lee, R. J. Gallagher and D. A. patterson, A linear programming approach to discriminant analysis with a reserved-judgment region, INFORMS J. Comput., 15 (2003), 23-41. doi: 10.1287/ijoc.15.1.23.15158. Google Scholar
[21]	S. J. Liaw, M. J. Bullard, P. M. Hu, J. C. Chen and H. C. Liao, Rates and causes of emergency department revisits within 72 hours, J. Formos Med. Assoc., 98 (1999), 422-425. Google Scholar
[22]	J. A. Lowthian, A. J. Curtis and P. A. Cameron et al, Systematic review of trends in emergency department attendances: an Australian perspective, Emerg. Med. J., 28 (2011), 373-377. doi: 10.1136/emj.2010.099226. Google Scholar
[23]	F. Meng, C. K. Ooi, C. K. K. Soh, K. L. Teow and P. Kannapiran, Quantifying patient flow and utilization with patient flow pathway and diagnosis of an emergency in Singapore, Health Syst., 5 (2016), 140-148. doi: 10.1057/hs.2015.15. Google Scholar
[24]	F. Meng, J. Qi, M. Zhang, J. Ang, S. Chu and M. Siim, A robust optimization model for managing elective admission in a public hospital, Oper. Res., 63 (2015), 1452-1467. doi: 10.1287/opre.2015.1423. Google Scholar
[25]	A. S. Newton, S. Ali, D. W. Johnson, C. Haines, R. J. Rosychuk, R. A. Keaschuk, P. Jacobs, M. Cappelli and T. P. Klassen, Who comes back? Characteristics and predictors of return to emergency department services for pediatric mental health care, Acad. Emerg. Med., 17 (2010), 177-186. doi: 10.1111/j.1553-2712.2009.00633.x. Google Scholar
[26]	Y. Y. Ng, Optimal use of emegency services, SFP, 40 (2014), supplement 8-13. Google Scholar
[27]	S. Nunëz, A. Hexdall and A. Aguirre-Jaime, Unscheduled returns to the emergency department: An outcome of medical errors?, Qual. Saf. Health Care., 15 (2006), 102-108. Google Scholar
[28]	K. O'Loughlin, K. A. Hacking, N. Simmons, W. Christian, R. Syahanee, A. Shamekh and N. J. Prince, Paediatric unplanned reattendance rate: A&E clinical quality indicators, Arch. Dis. Child., 98 (2013), 211-213. Google Scholar
[29]	L. Pereira, C. Choquet and A. Perozziello et al, Unscheduled return visits after an emergency department (ED) attendance and clinical link between both visits in patients aged 75 years and over: a prospective observational study, PloS One, 10 (2015), e0123803. doi: 10.1371/journal.pone.0123803. Google Scholar
[30]	H. Qiu, X. Chen, W. Liu, G. Zhou, Y. Wang and J. Lai, A fast11-solver and its applications to robust face recognition, J. Ind. Manag. Optim., 8 (2012), 163-178. Google Scholar
[31]	J. Ryan, J. Hendler and K. P. Bennett, Understanding emergency department 72-hour revisits among medicaid patients using electronic healthcare records, Big Data, 3 (2015), 238-248. doi: 10.1089/big.2015.0038. Google Scholar
[32]	Y. Saeys, I. Inza and P. Larrañaga, A review of feature selection techniques in bioinformatics, 23 (2007), 2507-2517. doi: 10.1093/bioinformatics/btm344. Google Scholar
[33]	G. Sauvin, Y. Freund, K. Saidi, B. Riou and P. Hausfater, Unscheduled return visits to the emergency department: Consequences for triage, Acad. Emerg. Med., 20 (2013), 33-39. doi: 10.1111/acem.12052. Google Scholar
[34]	Y. Sun, B. H. Heng, S. Y. Tay and K. B. Tan, Unplanned 3-day re-attendance rate at Emergency Department and hospital's bed occupancy rate, Int. J. Emerg. Med., 8 (2015), 324-329. doi: 10.1186/s12245-015-0082-3. Google Scholar
[35]	C. R. Trivedy and M. W. Cooke, Unscheduled-return-visits (URV) in adults to the emergency department (ED): A rapid evidence assessment policy review, Emerg. Med. J., 32 (2015), 324-329. doi: 10.1136/emermed-2013-202719. Google Scholar
[36]	S. J. J. Verelst, S. Pierloot, D. Desruelles, J.-B. Gillet and J. Bergs, Short-term unscheduled return visits of adult patients to the emergency department, J. Emerg. Med., 47 (2014), 131-199. doi: 10.1016/j.jemermed.2014.01.016. Google Scholar
[37]	A. K. C. Wai, C. M. Chor, A. T. C. Lee, Y. Sittambunka, C. A. Graham and T. H. Rainer, Analysis of trends in emergency department attendances, hospital admissions and medical staffing in a Hong Kong university hospital: 5-year study, Int J. Emerg. Med., 2 (2009), 141-148. doi: 10.1007/s12245-009-0098-7. Google Scholar
[38]	Y. Wang, G. Zhou, L. Caccetta and W. Liu, An alternative Lagrange-dual based algorithm for sparse signal reconstruction, IEEE Trans. Sig. Process., 59 (2011), 1895-1901. doi: 10.1109/TSP.2010.2103066. Google Scholar
[39]	C. Wei and X. Tang, A fuzzy group decision making approach based on entropy, similarity measure, Int. J. Inf. Technol. Decis. Mak., 10 (2011), 1111-1130. doi: 10.1142/S0219622011004737. Google Scholar
[40]	C. L. Wu, F. T. Wang, Y. C. Chiang, Y. F. Chiu, T. G. Lin and L. F. Fu et al, Unplanned emergency department revisits within 72 hours to a secondary teaching referral hospital in Taiwan, J. Emerg. Med., 38 (2010), 512-517. doi: 10.1016/j.jemermed.2008.03.039. Google Scholar

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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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

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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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

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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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%

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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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%

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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	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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2018 Impact Factor: 1.025

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2018 Impact Factor: 1.025

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2018 Impact Factor: 1.025

American Institute of Mathematical Sciences