Exploratory analysis

We first carry out an exploratory data analysis, in which we use three sets of variables to cluster patients with K-means clustering methods [30]. Clustering of patients or locations have been widely used in clinical and healthcare literature to make broad generalizable observations and analysis [31]. The objective of the clustering analysis is to discover evidence of encounter usage inequality across ZIP codes with varying sociodemographic characteristics, after adjusting for clinical measurements. The clustering process allows easy interpretability of results and understanding broad differences between clusters. In particular, patients are clustered into: (1) two groups based on their ZIP-code level socioeconomic information including income and education, (2) two groups based on their ZIP-code level racial distribution, and (3) four groups based on their individual clinical measurements (glucose and cholesterol). In particular, socioeconomic Cluster-1 has higher income and education level than socioeconomic Cluster-2; Racial Cluster-1 has a higher white percentage and lower African American percentage than Racial Cluster-2. Clinical Cluster-4 has the most severe diabetes condition, clinical Cluster-1 has the mildest diabetes condition, while the other two clinical clusters stay in the middle, with respect to disease severity. The descriptive statistics of the variables included in the study and for these three clustering results are shown in Table 1. Hypothesis tests were performed for the descriptive statistics to initially understand the center and variation of data. Description of the tests and the associated null hypotheses is given in Table 1.

Table 1

Data description and cluster descriptions.

	Mean / Total	Std. Dev	T-Stat / Chi-sq Stat	p-Value
Total Number of Patients	2124
FPG measure (mg/dl)	175.5	30.6	1.65 (H0: FPG≤125)	0.0495
			2.47 (H0: FPG≤100)	0.0068
LDL Cholesterol (mg/dl)	172.1	34.8	2.07 (H0: LDL≤100)	0.0192
Patient Gender
Male	50.3%		Chi-sq = 0.004 (df = 1)	0.9522
Female	49.7%
Patient Age (Years)	64.02	11.14
< = 40 Years	2.01%		Chi-sq = 33.17 (df = 5)	3.46E-06
41–50 Years	8.57%
51–60 Years	21.75%
61–70 Years	32.02%
71–80 Years	19.87%
>80 Years	15.78%
Patient Encounters
Six month encounter (physical)	3.97	6.03
Six month encounter (telephonic)	3.01	4.82
Health Insurance
13 Groups: Patients / Group	163.4	231.1	Chi-sq = 3921.4 (df = 12)	< 2.2E-16
Patient Clusters based on Clinical Conditions
4 Clusters (Between SS/Total SS)			73.9%
Cluster 1 (Percentage of Observations)	24.8%
Glucose	113.9	18.6
Cholesterol	145.4	21.3
Cluster 2 (Percentage of Observations)	26.8%
Glucose	169.2	20.9	Hotelling T^2 = 16756.4	< 2.2E-16
Cholesterol	145.1	22.8	(Compared to Cluster 1)
Cluster 3 (Percentage of Observations)	21.2%
Glucose	144.7	26.4	Hotelling T^2 = 15641.2	< 2.2E-16
Cholesterol	213.2	30.8	(Compared to Cluster 2)
Cluster 4 (Percentage of Observations)	27.2%
Glucose	261.9	46.5	Hotelling T^2 = 9801.2	< 2.2E-16
Cholesterol	190.8	52.7	(Compared to Cluster 3)
Community (Zip Code) Level Descriptives
Number of ZIP Codes	95
Number of Patients / ZIP code	22.4	44.7	Chi-sq = 8405.1 (df = 94)	< 2.2E-16
Population	6742	9618	Chi-sq = 1289800 (df = 94)	< 2.2E-16
Annual Income ($)	55822	12695
Highschool (%)	91.02%	5.62%
College Graduate (%)	22.62%	13.65%
Race—White (%)	43.82%	3.01%
Race—African American (%)	6.26%	4.09%
Zip Code Clusters: Socio-economic Clusters
2 Clusters (Between SS/Total SS)			64.1%
Cluster 1	42
Annual Income ($)	66465	9059
Highschool (%)	95.1%	2.17%
College Graduate (%)	28.8%	14.15%
Cluster 2	53
Annual Income ($)	47389	7918	Hotelling T^2 = 191.33	< 2.2E-16
Highschool (%)	87.8%	5.37%
College Graduate (%)	17.7%	11.11%
Zip Code Clusters: Race Based Cluster
2 Clusters (Between SS/Total SS)			81.4%
Cluster 1	25
White Percentage	48.70%	1.84%
African American Percentage	0.75%	1.94%
Cluster 2	70
White Percentage	42.10%	3.31%	Hotelling T^2 = 132.35	< 2.2E-16
African American Percentage	8.24%	4.61%

T-test for a population mean is performed for FPG and LDL Cholesterol (H0 is reported with the test statistic). Chi-square goodness of fit test (H0: discrete uniform distribution) is performed for Patient Gender, Patient Age, Patient Health Insurance, Zip-code number of patients, and Zip-code population. Hotelling’s t-square test for independent population mean vectors (H0: two population mean vectors are equal) is performed for cluster mean vectors.

We next show how the distribution of patient encounters varies interactively across socioeconomic clusters and clinical clusters in the left panel of Fig 1. In general, patients in socioeconomic Cluster-2 have fewer physical encounters. In other words, after controlling for patients’ clinical status, patients who live in a ZIP-code with lower income and education level exhibit fewer physical encounters for diabetes treatment. The right panel in Fig 1 shows the distribution of physical encounters by different clinical clusters and racial clusters. Patients in the same clinical cluster have fewer physical encounters when they belong to Racial Cluster-2 (with lower white percentage and higher African American percentage). These results clearly indicate potential inequalities in patient encounters across ZIP-codes with varying sociodemographic characteristics, after controlling for patients’ clinical status.

Fig 1

Significant variation exists in patient encounters based on sociodemographic factors.

The clustering was done with K-means clustering. The advantage of K-means clustering is that it does not require distributional assumptions and can be done in a non-parametric setting. However, K-means depends on the initial starting points, and therefore tends to suffer from lack of stability in some cases [31]. Therefore, we performed the K-means with 25 random starts and used the most frequent clustering. For the study data, all random starts provided similar clustering results with less than 1% error on average. In addition, we re-estimated the K-means clustering multiple times to ensure stability. Furthermore, in the Appendix we provide a table comparing the clustering by K-means and by Latent Class Analysis (LCA). We find that the differences between the patient clusters are insignificant.

Model 1: Understanding the inequalities in encounters across ZIP-codes with different sociodemographic characteristics

Motivated by Fig 1, we study how patient encounters vary across ZIP-codes with different sociodemographic characteristics, after controlling for patients’ clinical status. Our objective is to identify patient subgroups (e.g., from a ZIP-code with particular sociodemographic characteristics) that are likely to have inadequate encounters for their diabetes control. We build zero-inflated Poisson models [32] for patients’ physical and telephonic encounters separately. Patients’ six-month count of physical encounters is the response variable in one of the models, while the six-month count of telephonic encounters is the response variable in another model. Poisson regression is often used to model a count response variable. In our data, there is a high frequency of zero counts. Patients may have zero encounter in a six-month period for various reasons such as missed appointments and traveling, which may not be accounted for by the independent variables, and therefore zero counts can be inflated. Hence, we adopt the zero-inflated Poisson model [32] to analyze such zero-inflated data. This model employs two processes to generate count data. One process follows a binomial distribution that generates structural zero counts. The other process follows a Poisson distribution that generates encounter counts given that at least one encounter takes place in a time period. To control for patient clinical status, we include patients’ previous time period’s clinical measurements of glucose and cholesterol as explanatory variables. Besides, patients’ encounters can largely depend on their insurance policy, so we include insurance policy as an explanatory variable. We then fit a zero-inflated Poisson regression model with the Poisson generating process described as follows. The estimated coefficients of the explanatory variables tell their effects on the rate of encounters.

In the equation, λ_t is the Poisson rate for the encounter counts at time period t. The coefficients β_i, α_j, and τ_i control for patients’ clinical status, insurance policy, and demographics. The coefficients γ_i show how ZIP-code level sociodemographic characteristics correlate with patient encounters.

To enhance the robustness of our data analysis, we then fit the above model within each clinical cluster. A different model, namely positive count model, is also fitted for robustness check. The results are essentially similar to that of the zero-inflated Poisson model, and are reported in the appendix.

Model 2: Estimate the effect of encounters on glucose transition

First, diabetic patients’ health status can be majorly reflected by their glucose measurements. Second, encounters may play an important role in controlling diabetic patients’ glycemic levels. On the one hand, more encounters mean patients are under improved oversight of their service providers and better informed about their health issues. On the other hand, fewer encounters than needed can mean less attention to healthcare, poorer information, and less education for disease control, and as a result, lead to worse health status. Finally, the ZIP-code level variables record the average values of sociodemographic characteristics of the population around a patient’s home, and thus they can partially and indirectly describe the patient’s sociodemographic characteristics.

We classify every patient’s glucose measurements in each six-month time period into three health states following the common standard: N (<100 mg/dl), P (100–125 mg/dl), and D (>125 mg/dl). These three states, as mentioned in the introduction, correspond to normal, prediabetes, and diabetes diagnoses, respectively. A patient who is already diagnosed with type 2 diabetes may have their glucose measurement varying among the three states over time. In other words, a patient in any state in time period t may transit to N, P, or D in time period t+1. The transition of glucose states tells if a patient’s clinical status is improving, worsening, or staying the same. For example, a transition from N to P means a patient’s glucose level gets worse, while a transition from D to P means an improvement in glucose level. The chance that a patient in state i (N, P, or D) at time t will transit to state j (N, P, or D) at time t+1 can be quantified by a transition probability, denoted by $$ P_{i\to j}^t$$. The larger the transition probability $$ P_{i\to j}^t$$, the higher the chance that the patient will transit from state i to state j, as time goes from t to t+1. Both healthcare providers and patients desire higher probabilities of the transitions that improve the glucose level (e.g., P to N, D to N, and D to P), and lower probabilities of the transitions that worsen the glucose level (e.g., N to P, N to D, and P to D).

The transition probabilities depict how the health risk changes may depend on a patient’s engagement via physical and telephonic encounters, as well as the patient’s sociodemographic characteristics, which are partially characterized by the ZIP-code level variables. We then build a multinomial logistic regression model [33] to estimate the effect of encounters on glucose status transitions, including ZIP-code level sociodemographic variables and their interactions with the encounter variables. Multinomial logistic regression is a well-developed tool for modeling transitions among a finite number of states, and has been widely adopted in various scientific fields [34–36]. Using the transition of glycemic state as a dependent variable has the advantage of model flexibility such that the effect of an explanatory variable is allowed to vary by different transitions. In contrast, directly using the change in glucose value as a response variable assumes unvaried effect of an explanatory variable, regardless of a patient’s current glycemic state. The multinomial logistic regression model for glucose state transitions is stated as follows.

In the above model, the left-hand side is the logarithm of the odds ratio of the transition from i to j to the transition from D to D, where i, j can be any of {D, P, N}. The coefficient α_1,ij indicates the effect of a physical encounter on the log odds of transition from i to j. For example, the larger the value of α_1,ij, the bigger the effect of a physical encounter on the probability of transitioning from i to j.

Identify ZIP codes with inadequate encounters

The estimates of Model 1 are shown in Table 2. According to the results, all coefficients show statistical significance when the model is fitted on the entire data to explain physical encounters. Sociodemographic characteristics of a ZIP-code significantly correlate to the number of physical encounters of patients from the ZIP code, after adjusting for patients’ clinical measures, gender, age, and insurance policy. Specifically, a smaller population (coef = −0.21, p<0.001), higher percentage of white (coef = 13.71, p<0.001), lower percentage of African Americans (coef = −7.18, p<0.001), higher income (coef = 0.43, p<0.01), higher percentage of high-school graduates (coef = 4.14, p<0.01), and higher percentage of college graduates (coef = 4.59, p<0.001) correlate to a higher number of physical encounters. Besides ZIP-code level variables, other significant factors for predicting physical encounters include dummy variables of clinical clusters 3 and 4 (coef = 0.46, p<0.01; coef = 0.58, p<0.01), log cholesterol in the previous time period (coef = 0.6, p<0.01), log age (coef = 1.96, p<0.001), and male indicator (coef = −0.26, p<0.001).

Table 2

Zero-inflated poisson model estimated for physical and telephonic encounters.

Response: Physical Encounters
	All Patients		Clinical Cluster 1		Clinical Cluster 2		Clinical Cluster 3		Clinical Cluster 4
Patient Level
Log(Cholesterol(t-1))	0.6 (0.17, 1.03)	**	2.00 (0.18, 3.82)	*	0.9 (0.21, 1.59)	**	0.83 (0.14, 1.52)	*	1.43 (0.49, 2.37)	**
Log(Glucose(t-1))	0.34 (-0.03, 0.71)	+	1.85 (-0.17, 3.87)	+	0.63 (-0.21, 1.47)		1.02 (0.47, 1.57)	***	0.33 (-0.28, 0.94)
Log(PatientAge(t-1))	1.96 (1.55, 2.37)	***	3.91 (0.87, 6.95)	*	1.83 (1.14, 2.52)	***	2.46 (1.68, 3.24)	***	0.97 (0.21, 1.73)	*
Patient Gender—Male	-0.26 (-0.4, -0.12)	***	-0.57 (-1.26, 0.12)		-0.21 (-0.43, 0.01)	.	-0.3 (-0.52, -0.08)	**	-0.35 (-0.66, -0.04)	*
Clinical Cluster 2	0.35 (-0.02, 0.72)	+
Clinical Cluster 3	0.46 (0.13, 0.79)	**
Clinical Cluster 4	0.58 (0.17, 0.99)	**
Insurance	S		S		S		S		S
Community Level (Zip Code)
Log(Population)	-0.21 (-0.33, -0.09)	***	0.58 (0.11, 1.05)	*	0.35 (0.17, 0.53)	***	0.14 (-0.04, 0.32)		0.14 (-0.15, 0.43)
Percentage White	13.71 (7.42, 20)	***	20.96 (-13.91, 55.83)		0.49 (-9.68, 10.66)		22.97 (12.66, 33.28)	***	8.42 (-6.16, 23)
Percentage African American	-7.18 (-11.32, -3.04)	***	13.02 (-9.97, 36.01)		2.49 (-4.29, 9.27)		-11.54 (-18.42, -4.66)	**	1.04 (-8.68, 10.76)
Log(Income)	0.43 (0.16, 0.7)	**	-1.22 (-2.69, 0.25)		0.11 (-0.36, 0.58)		0.45 (-0.02, 0.92)	+	0.62 (0.09, 1.15)	*
Percentage High School	4.14 (1.08, 7.2)	**	1.45 (-7.66, 10.56)		3.22 (-2.31, 8.75)		4.9 (-1.04, 10.84)		7.9 (1.53, 14.27)	*
Percentage Graduate	4.58 (3.23, 5.93)	***	7.46 (0.72, 14.2)	*	3.13 (0.93, 5.33)	**	5.32 (3.24, 7.4)	***	2.75 (-0.86, 6.36)
Number of Patients	2124		526		569		451		578
N-Observations	12533		3104		3357		2661		3411
Theta (Zero Inflation Factor)	0.88		0.85		0.94		0.93		0.91
Log-Lik	-2.96E+04		-7.28E+03		-9.24E+03		-6.72E+03		-6.92E+03
Response: Telephonic Encounters
	All Patients		Clinical Cluster 1		Clinical Cluster 2		Clinical Cluster 3		Clinical Cluster 4
Patient Level
Log(Cholesterol(t-1))	-0.02 (-0.31, 0.27)		0.49 (-0.2, 1.18)		-0.17 (-0.68, 0.34)		0.56 (0.07, 1.05)	*	0.76 (0.07, 1.45)	*
Log(Glucose(t-1))	-0.01 (-0.26, 0.24)		-0.25 (-1.13, 0.63)		0.23 (-0.44, 0.9)		-0.22 (-0.61, 0.17)		0.25 (-0.2, 0.7)
Log(PatientAge(t-1))	1.15 (0.88, 1.42)	***	1.27 (0.45, 2.09)	**	1.22 (0.71, 1.73)	***	1.44 (0.97, 1.91)	***	0.65 (0.12, 1.18)	*
Patient Gender—Male	0.06 (-0.04, 0.16)		0.21 (-0.12, 0.54)		0.07 (-0.11, 0.25)		0.03 (-0.13, 0.19)		0.01 (-0.19, 0.21)
Clinical Cluster 2	-0.29 (-0.53, -0.05)	*
Clinical Cluster 3	-0.25 (-0.54, 0.04)	+
Clinical Cluster 4	0.23 (-0.02, 0.48)	+
Insurance	S		S		S		S		S
Community Level (Zip Code)
Log(Population)	-0.11 (-0.19, -0.03)	**	-0.21 (-0.46, 0.04)	+	-0.28 (-0.42, -0.14)	***	-0.07 (-0.21, 0.07)		0.13 (-0.07, 0.33)
Percentage White	1.19 (-3.16, 5.54)		-6.62 (-21.99, 8.75)		8.51 (0.63, 16.39)	*	13.39 (6.14, 20.64)	***	-5.42 (-14.69, 3.85)
Percentage African American	0.2 (-2.8, 3.2)		-1.27 (-11.74, 9.2)		-3.43 (-8.88, 2.02)		-6.24 (-11.14, -1.34)	*	6.08 (-0.39, 12.55)	+
Log(Income)	0.21 (0.01, 0.41)	*	0.49 (-0.29, 1.27)		0.07 (-0.3, 0.44)		0.36 (0.01, 0.71)	*	0.29 (-0.12, 0.7)
Percentage High School	3.22 (1.63, 4.81)	***	3.59 (-1.7, 8.88)		3.12 (0.08, 6.16)	*	2.1 (-0.21, 4.41)	+	6.28 (1.91, 10.65)	**
Percentage Graduate	1.85 (1.01, 2.69)	***	0.97 (-1.83, 3.77)		0.95 (-0.6, 2.5)		3.48 (2.15, 4.81)	***	0.08 (-1.94, 2.1)
Number of Patients	2124		526		569		451		578
N-Observations	12533		3104		3357		2661		3411
Theta (Zero Inflation Factor)	1.21		1.17		1.21		2.01		1.24
Log-Likelihood	-2.61E+04		-6.53E+03		-7.16E+03		-6.18E+03		-7.24E+03

Significance Code. 0 <’***’ < = 0.001 < ’**’ < = 0.01 < ’*’ < = 0.05 < ’.’ < = 0.1.

S: Significant at at least 0.05 level.

Parameter estimates with 95% confidence intervals of the parameter estimates are provided.

When the model is fitted within each clinical cluster, the coefficient estimates vary but the general insights remain similar for most ZIP code variables. For clinical Cluster-1 (with lower risk from disease condition) and clinical Cluster-2 (with medium risk from disease condition), the percentage of college graduates (coef = 7.46, p<0.05; coef = 3.13, p<0.01) and log population size (coef = 0.58, p<0.05; coef = 0.35, p<0.001) are both significantly positively related to physical encounters. For clinical Cluster-3 (with medium disease condition), percentage of white (coef = 22.97, p<0.001), and percentage of college graduates (coef = 5.32, p<0.001) are both significantly positively related to physical encounters, while the relationship between the percentage of African American (coef = −11.54, p<0.01) and physical encounters is significant and negative. For clinical Cluster-4 (most severe disease condition), log income (coef = 0.62, p<0.05) and percentage of high-school graduates (coef = 7.9, p<0.05) are the most significant ZIP code factors that correlate to physical encounters, and their effects are both positive. The model estimates show that there exists heterogeneity in physical encounters across ZIP codes with varying sociodemographic characteristics, after adjusting for patients’ clinical and demographic factors. The model suggests healthcare providers need to pay special attention to: (i) patients in clinical Cluster-4 (most severe disease condition) from ZIP codes with low-income and low education level, (ii) patients in clinical Cluster-3 from ZIP codes with low education level, low percentage of white, and high percentage of African American, and (iii) patients in clinical Clusters 1 and 2 from ZIP codes with small population and low education level, since these patients are likely to have fewer encounters, which may be inadequate for their disease control.

The results of the model for telephonic encounters are similar to those for physical encounters, showing that the patients from ZIP codes with a larger population, lower-income, and lower education level are likely to have fewer telephonic encounters. Moreover, log age (coef = 1.15, p<0.001) and indicator for clinical Cluster-2 (coef = −0.29, p<0.05) are significantly related to telephonic encounters. The model is also fitted within each clinical cluster. For clinical Cluster-1 (mildest condition), ZIP code variables do not show significant effects on telephonic encounters. For clinical Cluster-2 (medium condition), significant ZIP-code variables include the percentage of white (coef = 8.51, p<0.05), percentage of high school graduates (coef = 3.12, p<0.05), and log population (coef = −0.28, p<0.001). For clinical Cluster-3 (medium condition), the percentage of white (coef = 13.39, p<0.001), log income (coef = 0.36, p<0.05), and percentage of college graduates (coef = 3.48, p<0.001) all have a significant positive effect, while the percentage of African American (coef = −6.24, p<0.05) has a significant negative effect on telephonic encounters. For clinical Cluster-4 (severe condition), percentage of high-school graduates (coef = 6.28, p<0.01) is the only significant ZIP code variable. Therefore, like physical encounters, we observe similar disparity in telephonic encounters across ZIP codes with varying sociodemographic characteristics, after adjusting for patients’ clinical and demographic factors. In general, the results can help identify ZIP codes that may correlate to insufficient telephonic encounters (e.g., with high population, low percentage of white, high percentage of African American, low income, and low education level).

We also compute the marginal effect of the sociodemographic variables on patient encounters. As an illustration, we divide the patient populations based on the percentage of high school graduates. We find that patients from a ZIP code at the lower quartile of high school education have 1 fewer average encounter than those at the upper quartile. A similar analysis for income reveals that there are 1.3 fewer average encounters of patients in a ZIP code at the lower quartile than those at the upper quartile.

Effect of encounters on glucose transition

Estimates of Model 2 are shown in Table 3. Significance level and 95% confidence interval (CI) are also reported for each estimate. The first column denotes the transition of glucose level between two successive time periods. The three states of glucose level N, P, and D are going from mild to severe. Higher probabilities of transitioning to a milder state (e.g., D to P, D to N, and P to N) and lower probabilities of transitioning to a more severe state (e.g., N to P, N to D, and P to D) are desired by both healthcare providers and patients. According to the estimates, more physical encounters predict a higher probability of transitioning from D to P (coef = 0.01, CI: 0.00, 0.02), N to N (coef = 0.02, CI: 0.00, 0.04), and P to N (coef = 0.01, CI: 0.00, 0.02). The results indicate that more physical encounters, after controlling for sociodemographic factors (ZIP-code level), help patients to transit to a milder state from D to P, or P to N, or maintain a healthy glucose level (N to N). Telephonic encounters have a significant negative effect on transition probabilities of N to P (coef = −0.03, CI: −0.05, −0.01) and P to D (coef = −0.02, CI: −0.04, 0.00). It means that more telephonic encounters can help reduce the chance of transitioning to a higher-risk state (N to P and P to D), after controlling for patients’ sociodemographic factors (at ZIP-code level).

Table 3

Multinomial logistic model estimates for glucose state transition of patients.

Main Effects Model
	Physical Encounter	Telephonic Encounter	Log(Patient Age)	Percentage White	Percentage African American	Log(Income)	HighSchool	Graduate
D→N	0.00 (-0.02, 0.02)	0.02 (-0.02, 0.06)	-0.24 (-0.61, 0.13)	1.99 (-1.02, 5.00)	-4.68* (-7.14, -2.22)	0.18* (0.04, 0.32)	0.59 (-0.24, 1.42)	-0.42 (-0.99, 0.15)
D→P	0.01* (0.00, 0.02)	-0.01 (-0.03, 0.01)	0.18 (-0.08, 0.44)	3.62* (1.10, 6.14)	-4.16* (-8.16, -0.16)	0.09* (0.05, 0.13)	0.31* (0.09, 0.53)	0.93* (0.52, 1.34)
N→D	-0.01 (-0.03, 0.01)	0.03 (-0.29, 0.35)	0.42* (0.01, 0.83)	-6.31* (-8.83, -3.79)	1.68 (-0.82, 4.18)	0.02 (-0.01, 0.05)	-0.49* (-0.90, -0.08)	-0.74* (-1.41, -0.07)
N→N	0.02* (0.00, 0.04)	0.02 (-0.02, 0.06)	0.54 (-0.19, 1.27)	5.78* (1.13, 10.43)	0.07 (-0.11, 0.25)	0.04* (0.01, 0.07)	4.91* (0.91, 8.91)	0.19* (-0.14, 0.52)
N→P	0.02 (-0.02, 0.06)	-0.03* (-0.05, -0.01)	0.13 (-0.11, 0.37)	-1.41* (-2.67, -0.15)	9.63* (0.98, 18.28)	-0.27* (-0.51, -0.03)	-2.70* (-4.73, -0.67)	-1.56* (-2.47, -0.65)
P→D	0.01* (0.00, 0.02)	-0.02* (-0.04, 0.00)	0.67* (0.04, 1.30)	-2.58* (-4.96, -0.20)	4.12* (0.02, 8.24)	-0.10* (-0.16, -0.04)	-0.17 (-0.39, 0.05)	-0.79* (-1.54, -0.04)
P→N	0.01* (0.00, 0.02)	0.02 (-0.02, 0.06)	-0.13* (-0.23, -0.03)	4.04* (0.08, 8.00)	-2.34* (-4.39, -0.29)	0.10 (-0.16, 0.36)	1.55 (-0.38, 3.48)	1.05* (0.58, 1.52)
P→P	0.02 (-0.02, 0.06)	-0.04 (-0.10, 0.02)	0.30 (-0.19, 0.79)	3.16 (-2.45, 8.77)	0.03* (0.01, 0.05)	-0.21* (-0.37, -0.05)	-1.49* (-2.49, -0.49)	-0.14 (-0.36, 0.08)
Interaction Effects
Interaction with Physical Encounter
D→N			0.08 (-0.04, 0.20)	1.34 (-0.45, 3.13)	2.02 (-1.27, 5.31)	-0.01 (-0.03, 0.01)	0.37* (0.05, 0.69)	0.18 (-0.06, 0.42)
D→P			0.08* (0.02, 0.14)	1.32 (-0.39, 3.03)	2.12* (0.13, 4.11)	-0.02 (-0.05, 0.01)	0.31* (0.05, 0.57)	0.17* (0.05, 0.29)
N→D			-0.07* (-0.13, -0.01)	-0.94 (-2.22, 0.34)	-1.61* (-3.01, -0.21)	-0.06* (-0.10, -0.02)	-0.37* (-0.69, -0.05)	0.02 (-0.01, 0.05)
N→N			0.02* (0.01, 0.03)	1.86* (0.84, 2.88)	1.71* (0.11, 3.31)	0.01* (0.00, 0.02)	0.76* (0.25, 1.27)	0.09* (0.02, 0.16)
N→P			-0.17* (-0.29, -0.05)	-1.57* (-2.97, -0.17)	-2.10* (-4.12, -0.08)	-0.13* (-0.22, -0.04)	-0.46 (-1.00, 0.08)	0.05 (-0.03, 0.13)
P→D			0.06 (-0.02, 0.14)	-1.69* (-2.73, -0.65)	-1.66* (-2.86, -0.46)	-0.04* (-0.07, -0.01)	-0.16 (-0.50, 0.18)	-0.12* (-0.22, -0.02)
P→N			-0.04 (-0.10, 0.02)	1.99* (0.97, 3.01)	1.86* (0.43, 3.29)	0.00 (-0.02, 0.02)	-0.45* (-0.77, -0.13)	0.05 (-0.04, 0.14)
P→P			0.03 (-0.02, 0.08)	2.59 (-1.22, 6.40)	2.49 (-1.50, 6.48)	-0.06 (-0.17, 0.05)	-0.30 (-1.04, 0.44)	0.16 (-0.12, 0.44)
Interaction with Telephonic Encounters
D→N			-0.18 (-0.52, 0.16)	-0.21 (-0.71, 0.29)	0.63* (0.00, 1.26)	0.08 (-0.04, 0.20)	0.29 (-0.05, 0.63)	0.03 (-0.02, 0.08)
D→P			0.10* (0.04, 0.16)	1.67* (0.76, 2.58)	1.90* (0.83, 2.97)	0.00 (-0.02, 0.02)	0.21* (0.07, 0.35)	0.29* (0.09, 0.49)
N→D			-0.13 (-0.26, 0.00)	-0.67 (-2.12, 0.78)	-0.70 (-1.95, 0.55)	-0.01* (-0.02, 0.00)	-0.06 (-0.16, 0.04)	-0.08 (-0.22, 0.06)
N→N			0.00 (-0.03, 0.03)	0.59 (-0.13, 1.31)	1.32* (0.27, 2.37)	0.06* (0.02, 0.10)	0.33* (0.05, 0.61)	0.42* (0.04, 0.80)
N→P			-0.25 (-0.47, -0.03)	-1.03 (-2.85, 0.79)	-1.84* (-3.29, -0.39)	0.03 (-0.02, 0.08)	-0.42* (-0.80, -0.04)	0.18 (-0.08, 0.44)
P→D			-0.10* (-0.19, -0.01)	0.90 (-0.75, 2.55)	-1.22* (-2.35, -0.09)	0.02 (-0.01, 0.05)	-0.10 (-0.24, 0.04)	0.17 (-0.01, 0.35)
P→N			0.15* (0.01, 0.29)	1.14* (0.19, 2.09)	2.33* (0.16, 4.50)	0.03 (-0.01, 0.07)	-0.14 (-0.46, 0.18)	0.32 (-0.06, 0.70)
P→P			0.03 (-0.01, 0.07)	-0.39 (-0.93, 0.15)	0.60 (-0.35, 1.55)	0.14* (0.03, 0.25)	0.69* (0.26, 1.12)	0.31* (0.10, 0.52)

Notes. 1. D: high glucose, P: medium glucose, N: low glucose.

2. The class transitions likelihoods are estimated using a Multinomial logistic model.

3. The numbers signify multinomial slope estimates.

4. * indicates significant at 0.05 level.

The interaction coefficient (inter coef) estimates (in Table 3) show how patients’ sociodemographic characteristics at the ZIP-code level interact with encounters to influence glucose state transitions. For example, physical encounters have significantly stronger effects on older patients in terms of improving patients’ state from D to P (inter coef = 0.08, CI: 0.02, 0.14), keeping patients in state N (inter coef = 0.02, CI: 0.01, 0.03), and preventing transitions from N to D (inter coef = −0.07, CI: −0.13, −0.01) and from N to P (inter coef = −0.17, CI: −0.29, −0.05). While we observe significant racial disparity in encounter usage, the interaction effects on transition probabilities are similar across races in terms of sign, magnitude, and significance level. Other ZIP-code level variables such as income and percentage of college graduates also have significant interactions with physical encounters on some of the transition types. In general, the significant interactions between physical encounters and the ZIP-code variables indicate that increasing encounters would have higher benefits for patients who are older, reside in a ZIP-code with a higher percentage of white, a higher percentage of African American, higher income, or higher education level. The only counterintuitive exception is the interaction effect between physical encounters and percentage of high-school graduates on the transition from P to N, which is significantly negative (inter coef = −0.45, CI: −0.77, −0.13), indicating that for patients in ZIP codes with a higher percentage of high school graduates, the effect of physical encounters is smaller in helping the transition from P to N. This is surprising since in general education should be positively associated with lower risk from diabetes. However, we feel that the causal chain is through the nature of patients’ occupations, which may be generally less physical for high-school graduates than for non-high-school graduates, and higher levels of physical activity are associated with lower diabetic risks [37]. The current data does not include occupational information of patients.

Telephonic encounters also interact with patients’ age and ZIP-code level sociodemographic variables to affect glucose transitions. For example, for older patients, the effect of telephonic encounters is significantly stronger on improving patients’ states from D to P (inter coef = 0.1, CI: 0.04, 0.16) and from P to N (inter coef = 0.15, CI: 0.01, 0.29), and preventing state worsening from N to D (inter coef = −0.13, CI: −0.26, 0.00), N to P (inter coef = −0.25, CI: −0.47, −0.03), and P to D (inter coef = −0.1, CI: −0.19, −0.01). For the race variables at the ZIP code level, the interaction between percentage of white and telephonic encounters is significant for two transitions (positive inter coef for D to P and P to N), while the interaction between percentage of African American and telephonic encounters is significant for six transitions (positive inter coef for D to N, D to P, N to N, and P to N; negative inter coef for N to P and P to D). This shows that increased telephonic encounters benefit more in the ZIP codes with higher percentage of either white or African American. In addition, the ZIP codes with high percentage of African American benefits from increased telephonic encounters for more transition types, compared to the ZIP codes with high percentage of white. In summary of the interaction effects, increasing telephonic encounters lead to more benefits among patients who are older, or live in a ZIP code with higher percentage of white, higher percentage of African American, higher income, higher percentage of high-school graduates, or higher percentage of college graduates.

We further interpret the results by computing the average marginal effects of the encounters and sociodemographic variables by computing the marginal effects at each observation in the sample, and averaging the marginal effects for all observations. As an illustration, consider the logistic regression model

$$ p_J=\frac{1}{1+{\sum }_{j^{\prime }=1}^{J-1}{e}^{X{\beta }_{j^{\prime }}}},$$ where j = 1,…,J, denote the transitions, X = (x₁,…,x_K) are the values of the K independent variables, and $$ {\beta }_j=({\beta }_{j_1},\dots ,{\beta }_{jK})$$ are the coefficients of the K independent variables for transition category j. For a variable x_k, its marginal effect for transition category j is given by

Then, the average marginal effect of variable x_k on transition j is $$ \frac{1}{N}\sum _{n=1}^N{\left[\frac{\partial p_j}{\partial x_k}\right]}_{X=X_n}$$, where X_n = (x_n1,…,x_nK) denotes the n^th individual in the data. We used the R package margins (https://cran.r-project.org/web/packages/margins/) to compute the average marginal effects of the multinomial transition models. The average marginal effect of physical encounters for all patients for the transition from diabetic to the pre-diabetic stage is 4.3%. This indicates that one additional encounter on average would increase the likelihood of patients’ transition D to P by 4.3%. Similarly, the average marginal effect of one additional physical encounter for the transition P to N is 3.2%. This indicates that encounters with doctors, and nurses increase the likelihood of transition from a higher risk level to a lower risk level. To interpret the effect of encounters for different characteristics of patient populations we compute the average marginal effects for different quartiles of patients. The average marginal effect of one additional physical encounter on the transition from diabetic to pre-diabetic for patient groups falling in the upper quartile of the percentage of high school education is 1.1%, while the corresponding average marginal effect for patient groups falling in the lower quartile of the percentage of high school education is 7.9%. This indicates that the effect of encounters for patients with lower levels of high school education is higher than for patients with higher levels. A similar observation is made for the median income and percentage of college graduates.

These results not only identify significant variation in the effect of physical and telephonic encounters on the health risks from diabetes across patient groups, but also indicate that physical encounters work better for improving disease states (such as increasing chances of the good transitions: D to P, N to N, and P to N), while telephonic encounters work better for preventing disease state worsening (such as reducing chances of the bad transitions: N to P, and P to D). These results, therefore, indicate the prevalence of complementarities between the two types of encounters, which can be used by providers to focus strategically on specific encounter types.

We also combine the results of the two models to interpret the effects of sociodemographic factors on encounters, and the effect of the encounters on the final diabetes outcome. As an illustrative example, we observe that for ZIP-codes which are in the lower quartile of the distribution on the variable percentage of high school graduates, there is a marginal Poisson rate of 1 fewer encounter (from zero-inflated Poisson models) compared to the ZIP-codes at the upper quartile of percentage of high school graduates, which when plugged into the multinomial regression model gives an 5.4% average increase in the probability of transitioning from pre-diabetic to diabetic. The corresponding estimates for median zip code income are 1.3 and 7.3%, respectively.