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 |
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.
Citation: |
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 |
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 |
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 |
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 |
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. |
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 |
Table 7. Levels combined for predictors
Variable Name | Levels before combined | Levels after combined |
Nur.Stat | isNA MS CCU ER PC |
isNA |
WS | WS | |
Patient.Days | 0-19 30+ |
0-19or30+ |
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 |
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 |
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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Histogram of days between the admissions (DBA)
Histogram of the log(DBA+1)
Box plot of patient marital status VS log(DBA+1)
The cluster dendrogram of
Box plot of PATIENT.SEX.CODE VS log(DBA+1) split by inpatient (I) and outpatient (O)
Box plot of Age vs log(DBA+1) split by inpatient (I) and outpatient (O)
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
Q-Q plots of GLM (left) vs ordinary least squares regression (OLS)