Predictive analytics for 30-day hospital readmissions

Lu Xiong; Tingting Sun; Randall Green

doi:10.3934/mfc.2021035

Article Contents

2022, Volume 5, Issue 2: 93-111. Doi: 10.3934/mfc.2021035

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Predictive analytics for 30-day hospital readmissions

a.
Department of Mathematical Sciences Doctoral Program, Middle Tennessee State University, 1301 E. Main St., Murfreesboro, TN 37132, USA
b.
Computational and Data Science Doctoral Program, Middle Tennessee State University, 1301 E. Main St., Murfreesboro, TN 37132, USA
c.
Fidelis Analytics Healthcare Consulting, 7113 Commonwealth Circle, Nashville, TN 37221, USA

^* Corresponding author: Lu Xiong: lu.xiong@mtsu.edu
^* Corresponding author: Lu Xiong: lu.xiong@mtsu.edu

Received: March 31, 2021

Revised: July 31, 2021

Early access: December 2021

Published: May 2022

The first author is supported by MTSU FRCAC grant 2019

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Abstract

The 30-day hospital readmission rate is the percentage of patients who are readmitted within 30 days after the last hospital discharge. Hospitals with high readmission rates would have to pay penalties to the Centers for Medicare & Medicaid Services (CMS). Predicting the readmissions can help the hospital better allocate its resources to reduce the readmission rate. In this research, we use a data set from a hospital in North Carolina during the years from 2011 to 2016, including 71724 hospital admissions. We aim to provide a predictive model that can be helpful for related entities including hospitals, health insurance actuaries, and Medicare to reduce the cost and improve the clinical outcome of the healthcare system. We used R to process data and applied clustering, generalized linear model (GLM) and LASSO regressions to predict the 30-day readmissions. It turns out that the patient's age is the most important factor impacting hospital readmission. This research can help hospitals and CMS reduce costly readmissions.

Keywords:

Mathematics Subject Classification: Primary: 62P10, 62J05; Secondary: 91C20.

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Figure 1. Histogram of days between the admissions (DBA)

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Figure 2. Histogram of the log(DBA+1)

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Figure 3. Box plot of patient marital status VS log(DBA+1)

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Figure 4. The cluster dendrogram of $ \texttt{Doctor.Number}$. Each vertical line at Height 0 represents one doctor. The doctors inside the same red box are clustered as one

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Figure 5. Box plot of PATIENT.SEX.CODE VS log(DBA+1) split by inpatient (I) and outpatient (O)

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Figure 6. Box plot of Age vs log(DBA+1) split by inpatient (I) and outpatient (O)

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Figure 7. Residual vs Fitted. The left figure is for GLM with features selected from the above session, the right figure is for OLS with all predictors

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Figure 8. Q-Q plots of GLM (left) vs ordinary least squares regression (OLS)

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Table 1. The mean and median of seven levels of PATIENT.MARITAL.STATUS

PATIENT.MARITAL.STATUS	mean	median	n
D	4.06432	4.20469	8122
M	4.31861	4.48864	26568
P	4.84009	5.01728	21
S	4.42558	4.67283	22164
U	3.41953	2.83321	120
W	4.05355	4.11087	7196
X	4.05785	4.07754	1492

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Table 2. The largest loadings of related predictors in the first principal component (PC1)

Variable Name	PC1
ICD.PROCEDURE.CODE1	-0.38498161
HOSPITAL.SERVICE.CODEG	-0.38284437
ICD9$ \_ $DIAGNOST$ \_ $CODE3	-0.29296143
PATIENT.DDRG1	-0.19955252
ICD9$ \_ $DIAGNOST$ \_ $CODE2	0.38297941
ICD.PROCEDURE.CODE5	0.38210699
HOSPITAL.SERVICE.CODEB	0.36536618
PATIENT.DRG4	0.24330584

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Table 3. The results of GLM on training data generated by R

Coefficients:	Estimate	Std. Error	t value	p-value	Significant Code
(Intercept)	5.99381	0.1633	36.7	< 2e-16	***
DOCTOR.NUMBER2	-0.60542	0.06983	-8.67	< 2e-16	***
DOCTOR.NUMBER3	-0.1012	0.04012	-2.52	0.01166	*
DOCTOR.NUMBER4	0.31089	0.03528	8.81	< 2e-16	***
DOCTOR.NUMBER5	0.52643	0.35486	1.48	0.13795	·
ServCode_DRG_ICD	-0.20195	0.00603	-33.48	< 2e-16	***
Age10-20	-0.26285	0.05948	-4.42	9.90E-06	***
Age100+	-1.86377	0.39675	-4.7	2.60E-06	***
Age20-30	-0.61615	0.05559	-11.08	< 2e-16	***
Age30-40	-0.66055	0.05605	-11.78	< 2e-16	***
Age40-50	-0.63653	0.05632	-11.3	< 2e-16	***
Age50-60	-0.63357	0.05637	-11.24	< 2e-16	***
Age60-70	-0.63019	0.05726	-11.01	< 2e-16	***
Age70-80	-0.60506	0.05855	-10.33	< 2e-16	***
Age80-90	-0.62985	0.06173	-10.2	< 2e-16	***
Age90-100	-0.6078	0.08093	-7.51	6.00E-14	***
Surgeon2	-0.27524	0.02279	-12.08	< 2e-16	***
Surgeon3	-0.18455	0.06706	-2.75	0.00592	**
Surgeon4	-0.36174	0.04333	-8.35	< 2e-16	***
Surgeon5	0.53341	0.34909	1.53	0.12652	·
PATIENT.MARITAL.STATUSM	0.16705	0.01716	9.73	< 2e-16	***
PATIENT.MARITAL.STATUSPS	0.05911	0.02037	2.9	0.00371	**
Nur.StatMS_CCU_ER_PC	0.02249	0.03593	0.63	0.53137	·
Nur.StatWS	0.2277	0.06175	3.69	0.00023	***
DISCHARGE.STATUSR	0.39629	0.0448	8.85	< 2e-16	***
DISCHARGE.STATUSY	0.43827	0.05653	7.75	9.20E-15	***
income_levellow	-0.11351	0.02611	-4.35	1.40E-05	***
income_levelmeduim	-0.09598	0.01506	-6.37	1.80E-10	***
Patient.Days20-30	-0.28387	0.04367	-6.5	8.10E-11	***
Patient.Days30+	-0.48626	0.32127	-1.51	0.13015	·
PATIENT.RACE.CODEBO	-0.18993	0.14455	-1.31	0.18887	·
PATIENT.RACE.CODEDH	-0.99651	0.20834	-4.78	1.70E-06	***
PATIENT.RACE.CODEWX	-0.11298	0.14369	-0.79	0.43171	·
IO_CODEO	-0.18799	0.04251	-4.42	9.80E-06	***
Significant codes: 0 '*' 0.001 '' 0.01 '*' 0.05 '.' 0.1 ' ' 1

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Table 4. The R output of the generalized linear model (GLM) on all data

Coefficients:	Estimate	Std. Error	t value	p-value	Significant Code
(Intercept)	5.84694	0.06366	91.84	< 2e-16	***
DOCTOR.GROUP2	-0.58933	0.06102	-9.66	< 2e-16	***
DOCTOR.GROUP3	-0.1105	0.03487	-3.17	0.00153	**
DOCTOR.GROUP4	0.28857	0.03085	9.36	< 2e-16	***
ServCode_DRG_ICD	-0.201	0.00528	-38.1	< 2e-16	***
Age10-20	-0.30656	0.05169	-5.93	3.00E-09	***
Age100+	-1.16735	0.35101	-3.33	0.00088	***
Age20-30	-0.63787	0.0482	-13.23	< 2e-16	***
Age30-40	-0.69793	0.04861	-14.36	< 2e-16	***
Age40-50	-0.67707	0.04885	-13.86	< 2e-16	***
Age50-60	-0.67009	0.04887	-13.71	< 2e-16	***
Age60-70	-0.66848	0.04966	-13.46	< 2e-16	***
Age70-80	-0.63585	0.05076	-12.53	< 2e-16	***
Age80-90	-0.63634	0.0536	-11.87	< 2e-16	***
Age90-100	-0.66369	0.07005	-9.47	< 2e-16	***
Surgeon2	-0.28085	0.01977	-14.21	< 2e-16	***
Surgeon3	-0.22311	0.0586	-3.81	0.00014	***
Surgeon4	-0.3631	0.03772	-9.63	< 2e-16	***
PATIENT.MARITAL.STATUSM	0.18697	0.01491	12.54	< 2e-16	***
PATIENT.MARITAL.STATUSPS	0.06817	0.01772	3.85	0.00012	***
Nur.StatWS	0.20997	0.04929	4.26	2.10E-05	***
DISCHARGE.STATUSR	0.41057	0.0387	10.61	< 2e-16	***
DISCHARGE.STATUSY	0.45851	0.04926	9.31	< 2e-16	***
income_levellow	-0.08182	0.02262	-3.62	0.0003	***
income_levelmeduim	-0.09786	0.01307	-7.49	7.20E-14	***
Patient.Days20-30	-0.22549	0.03781	-5.96	2.50E-09	***
PATIENT.RACE.CODEDH	-0.57857	0.13194	-4.39	1.20E-05	***
PATIENT.RACE.CODEWX	0.07868	0.01669	4.71	2.40E-06	***
IO_CODEO	-0.21764	0.02759	-7.89	3.10E-15	***
Significant codes: 0 '*' 0.001 '' 0.01 '*' 0.05 '.' 0.1 ' ' 1

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Table 5. Interpretation of the GLM results

Feature	Coefficients (β)	exp(β)-1	Interpretation
DOCTOR.GROUP = 2	-0.58933	-0.45	45% decrease in DBA compared to the base group DOCTOR.GROUP = 1. This means the group 2 of doctors are less effective in terms of improving the DBA (or reducing 30-day readmission) than group 1.
DOCTOR.GROUP = 3	-0.11050	-0.10	10% decrease in DBA compared to the group DOCTOR.GROUP = 1.
DOCTOR.GROUP = 4	0.28857	0.33	33% decrease in DBA compared to the group DOCTOR.GROUP = 1. Therefore group 4 of doctors are more effective in improving the DBA than group 1.
ServCode_DRG_ICD	-0.20100	-0.18	18% decrease in DBA for every 1.0 increase in the feature ServCode_DRG_ICD, which is the new artificial feature made using the PCA from the predictors PATIENT.DRG, HOSPITAL.SERVICE.CODE, ICD.PROCEDURE.CODE, ICD9_DIAGNOST_CODE
Age = 10-20	-0.30656	-0.26	26% decrease in DBA compared to Age 0-10. This makes sense because younger people are less likely to be readmitted.
Age = 20-30	-0.63787	-0.47	47% decrease compared to Age 0-10.
…
Age = 100+	-1.16735	-0.69	69% decrease compared to Age 0-10.
Surgeon = 2	-0.28085	-0.24	24% decrease of DBA compared with Surgeon = 1.
…
PATIENT.MARITAL.STATUS = M	0.205591	0.21	21% increase of DBA for patients in marriage compared with base-level MARITAL.STATUS = DUWXNA, which is the group for divorced, widowed, or unknown status. People in marriage usually can be taken care of better thus have better health.
PATIENT.MARITAL.STATUS = PS	0.06817	0.07	7% increase of DBA for patients with a domestic partner (P) or single (S) compared with base-level MARITAL.STATUS = DUWXNA.
income_level = low	-0.08182	-0.08	8% decrease of DBA for low-income patients compared to high-income patients. This makes sense because low-income patients may not afford enough healthcare to maintain good health.
income_level = medium	-0.09786	-0.09	9% decrease of DBA compared to high-income patients. The medium-income patients have even worse readmission days than low-income patients maybe because they have longer working hours, higher mental pressure.
Patient.Days = 20-30	-0.22549	-0.20	20% decrease compared to its base level, the visits whose Patient.Days smaller than 20 or greater than 30. This suggests the visits whose inpatient days are between 20-30 days are most likely to be readmitted with short readmission days.
PATIENT.RACE.CODE = WX	0.07868	0.08	8% increase of DBA for PATIENT.RACE.CODE is W or X compared to its base level PATIENT.RACE.CODE = AIMNT.

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Table 6. Data Dictionary

Variable Name	Definition	Date type and values
PATIENT.DRG Patient	diagnosis-related group	Integer 0-999
NurStat	Nurses Station	Letters code representing the type of nurses station, with majority values missing.
DOCTOR.NUMBER	ID of the doctor	Integer
Surgeon	ID of the surgen	Integer
IO_CODE	Inpatient or outpatient	I: inpatient O: outpatient
HOSPITAL.SERVICE.CODE	A code representing the type of healthcare service	Letters code. No missing value.
ADMIT.SOURCE	The code indicating the source of the referral for the admission or visit.	1:Physician Referral 2:Clinic Referral 3:HMO Referral 4:Transfer from a Hospital 6:Transfer from Another Health Care Facility 8:Court/Law Enforcement 9:Information Not Available
DISCHARGE.STATUS	Patient discharge status	Integer code
PATIENT.SEX.CODE	A$\cdot$code$\cdot$indicating the$\cdot$sex$\cdot$of the$\cdot$patient.	F:Female M:Male U: Unknown
PATIENT.MARITAL.STATUS	Marital status	D: divorced S:single M:married W:widowed U:unknown P:partnered X:legally Separated
PATIENT.RACE.CODE	Code$\cdot$indicating the$\cdot$racial$\cdot$or ethnic background of a person.	A:Asian or Pacific Islander B:Black D:Subcontinent Asian American H:Hispanic I:American Indian or Alaskan Native N:Black(Non-Hispanic) O:White(Non-Hispanic) W:widow X:legally separated
ICD.PROCEDURE.CODE	ICD-10 Procedure Coding	Integer code
ICD9_DIAGNOST_CODE	ICD-9-CM Diagnosis Codes	Integer code
PATIENT ZIP	Patient zip code	Integer code
DBA	days between the admissions	Non-negative integer

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Table 7. Levels combined for predictors

Variable Name	Levels before combined	Levels after combined
Nur.Stat	isNA MS CCU ER PC	isNA
Nur.Stat	WS	WS
Patient.Days	0-19 30+	0-19or30+
Patient.Days	20-30	20-30
HOSPITAL.SERVICE.CODE	OPS CTH NB	Y
	DX MED OBS OPB OPV EOB	R
	WND IVT SO WWC NP	B
	ER	G
ADMIT.SOURCE	9	9
	1 6	16
	8	8
	4	4
	2 5	25
PATIENT.SEX.CODE	M U	M
PATIENT.SEX.CODE	F	F
PATIENT.MARITAL.STATUS	M	M
	P S	PS
	D U W X NA	DUWXNA
PATIENT.RACE.CODE	W X	WX
	A I M N T B O	AIMNT
	D H	DH
DISCHARGE.STATUS	1 7 30	R
	2 5 43 62 63 65 70 72	Y
	3 4 6 9 21 50 51 64 81 82 83	G

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Table 8. The mean and median of log(DBA+1) within three levels of Patient.Days

Patient.Days	Mean of log(DBA+1)	Median of log(DBA+1)
0-19	4.34939	4.54329
30+	3.86552	3.98744
20-30	2.59868	2.07944

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