Visit Entropy Associated with Hospital Readmission Rates

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Figure 1.
Multivariate odds ratio forest plot for independent variables and continuity measures associated with 30-day readmission. CI, confidence interval; ED, emergency department; UPC, usual provider continuity; COC, dispersion continuity of care; SECON, sequence continuity; VE, visit entropy.
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Figure 2.
Prior 12-month continuity measures versus 30-day readmission.

Table 1.

Formula Used to Calculate Continuity Measures

Measure	Definition
Density (UPC)	max where N = total visits
	n_i = number visits to i^th provider
Dispersion (COC)	where N = total visits
	n_i = total visits to i^th provider
	p = total number of providers
Sequence (SECON)	where N = total visits

Entropy/Disorganization (VE)
	where
	n_i = the number of visits to the i^th provider
	k = the total number of possible providers
	N = the total number of visits

COC, dispersion continuity of care; SECON, sequence continuity; UPC, usual provider continuity; VE, visit entropy.

Table 2.

Value of Continuity Measures for Various Visit Patterns

Visit Pattern	UPC	COC	SECON	VE
A) No visits	Undefined	Undefined	Undefined	4.14
B) 1 primary physician visit	1.00	Undefined	Undefined	2.72
C) 1 primary physician visit, 1 ED visit, 1 dermatology visit, 1 Urgent care visit	0.25	0.00	0.00	2.37
D) 1 primary physician visit, 1 cardiology visit, 1 primary physician visit, 1 cardiology visit (different specialist)	0.50	0.17	0.33	2.11
E) 2 primary physician visits	1.00	1.00	1.00	1.99
F) 1 primary physician visit, 1 cardiology visit, 1 primary physician visit, 1 cardiology visit (same referral)	0.50	0.33	0.00	1.85
G) 2 nurse practitioner visits, 1 primary physician visit, 1 nurse practitioner visit (same NP)	0.50	0.17	0.33	1.74
H) 4 primary physician visits	1.00	1.00	1.00	1.31

COC, dispersion continuity of care; ED, emergency department; SECON, sequence continuity; UPC, usual provider continuity; VE, visit entropy.

Table 3.

Descriptive Statistics of Independent Variables for the Cohort by Group

Characteristic	Not Readmitted	Readmitted	P-Value^*
N	12,965	1697
Age, mean (SD)	61.2 (19.3)	64.1 (19.3)	<.001
Sex
Female (%)	7034 (54.3%)	901 (53.1%)
Male (%)	5931 (45.7%)	796 (46.9%)	.379
Marital status
Not married (%)	5114 (39.4%)	734 (43.3%)
Married (%)	7851 (60.6%)	963 (56.7%)	.003
Carlson Comorbidity Index, mean (SD)	3.3 (3.3)	4.9 (3.7)	<.001
Length of stay, mean (SD), days	3.2 (3.6)	4.7 (6.2)	<.001
Previous 6 months ED Visits, mean (SD)	0.8 (1.6)	1.2 (2.2)	<.001
Previous 12 months Hospitalizations, mean (SD)	0.1 (0.5)	0.3 (1.0)	<.001
Previous 12 months Outpatient Visits, mean (SD)	9.8 (9.2)	12.4 (12.3)	<.001
No. Distinct providers, 12 months, mean (SD)	6.4 (5.1)	7.7 (6.5)	<.001
UPC, mean (SD)	0.39 (0.22)	0.37 (0.22)	<.001
COC, mean (SD)	0.12 (0.16)	0.12 (0.16)	.101
SECON, mean (SD)	0.15 (0.19)	0.14 (0.19)	.869
VE, mean (SD)	3.49 (0.68)	3.54 (0.70)	<.001

Abbreviations: COC, dispersion continuity of care; SECON, sequence continuity; UPC, usual provider continuity; VE, visit entropy.
↵* P-values are Fishers exact test for two valued nominal variables, Chi-Square test for multiple valued nominal variables, and Wilcoxon rank sum for continuous variables.