Identifying sociodemographic profiles of veterans at risk for high-dose opioid prescribing using classification and regression trees

Abstract

Objective:

To identify sociodemographic profiles of patients prescribed high-dose opioids.

Design:

Cross-sectional cohort study.

Setting/Patients:

Veterans dually-enrolled in Veterans Health Administration and Medicare Part D, with ≥1 opioid prescription in 2012.

Main Outcome Measures:

We identified five patient-level demographic characteristics and 12 community variables reflective of region, socioeconomic deprivation, safety, and internet connectivity. Our outcome was the proportion of veterans receiving >120 morphine milligram equivalents (MME) for ≥90 consecutive days, a Pharmacy Quality Alliance measure of chronic high-dose opioid prescribing. We used classification and regression tree (CART) methods to identify risk of chronic high-dose opioid prescribing for sociodemographic subgroups.

Results:

Overall, 17,271 (3.3 percent) of 525,716 dually enrolled veterans were prescribed chronic high-dose opioids. CART analyses identified 35 subgroups using four sociodemographic and five community-level measures, with high-dose opioid prescribing ranging from 0.28 percent to 12.1 percent. The subgroup (n = 16,302) with highest frequency of the outcome included veterans who were with disability, age 18–64 years, white or other race, and lived in the Western Census region. The subgroup (n = 14,835) with the lowest frequency of the outcome included veterans who were without disability, did not receive Medicare Part D Low Income Subsidy, were >85 years old, and lived in communities within the second and sixth to tenth deciles of community public assistance.

Conclusions:

Using CART analyses with sociodemographic and community-level variables only, we identified subgroups of veterans with a 43-fold difference in chronic high-dose opioid prescriptions. Interactions among disability, age, race/ethnicity, and region should be considered when identifying high-risk subgroups in large populations.

BACKGROUND

Prescription opioids play an important role in the opioid epidemic in the United States. In 2015, approximately half of opioid overdose deaths involved prescription opioids.¹ From a medication safety perspective, multiple organizations have advised against the prescription of opioids at high doses.^2,3 Although definitions of such prescriptions vary across studies and have changed over time, ample evidence indicates that chronic use of opioids at higher dosages is associated with opioid misuse,⁴ overdose, and death.^5–7 Conversely, analgesia from chronic use of opioids diminishes with prolonged use.⁸ Accordingly, limiting chronic, high-dose prescribing may improve rates of adverse opioid-related outcomes.

Prior studies have examined sociodemographic risk factors associated with opioid use, misuse, and high-dose prescribing. Whereas white race,^9–13 older age,¹⁴ and female sex^10,15,16 have generally been associated with increased opioid prescribing, younger age, and male sex have more frequently been associated with opioid misuse and abuse.^4,17–20 Studies have also examined geographic and regional variation in opioid prescribing rates, with higher rates observed in areas with low socioeconomic status and high income inequality,^21–23 as well as more access to healthcare providers.^14,24 These differences in prescribing rates have prompted investigation into neighborhood characteristics that may explain disparate opioid-related outcomes.^17,25–27

Prior investigations have not examined interactions between individual and community-level sociodemographic determinants of opioid prescribing, at least partially due to difficulty identifying relevant combinations using traditional regression-based techniques. Accordingly, there remains a void in our understanding of how sociodemographic and community factors interact to influence risk. The ability to accurately identify groups at high risk for high-dose opioid prescribing would facilitate policy development and tailored interventions aimed at curbing opioid misuse. This is especially true in situations where clinical data are not available for identifying such high-risk patients.

One technique for examining interactions among variables is the classification and regression tree (CART) analysis. CART is a machine learning technique capable of identifying complex interactions between pertinent risk factors and using these terms to identify patient subgroups with wide ranging risks for the specified patient outcome. Our aim was to use CART to identify combinations of individual sociodemographic and neighborhood characteristics that define distinct subpopulations of patients at highest risk for high-dose opioid prescribing. In defining these subpopulations, our goal was to demonstrate the capability of CART to expand our understanding of sociodemographic and regional risk factors associated with high-dose opioid prescribing.²⁸

METHODS

We obtained approval for this cross-sectional cohort study from the Institutional Review Board at the Veterans Affairs (VA) Pittsburgh Healthcare System. We followed the Strengthening the Reporting of Observational Studies in Epidemiology guideline for reporting cross-sectional studies.²⁹

Study cohort

We utilized data from a previously identified national cohort of 568,514 veterans enrolled in both VA and Medicare Part D in calendar year 2012 who filled at least one opioid prescription from either source in 2012.³⁰ The cohort was created by linking patient-level data from calendar year 2012 from the VA Corporate Data Warehouse (sociodemographic characteristics), VA Pharmacy Benefits Management (dispensed VA outpatient prescriptions), and Centers for Medicare and Medicaid Services Part D event file (Part D prescriptions) and the Master Beneficiary Summary File (enrollment), available from the VA Information Research Center (VIReC).^31,32 We excluded individuals enrolled in hospice (n = 28,667), receiving only injection opioids or opium tinctures (n = 407), with prescriptions for which morphine milligram equivalent (MME) could not be calculated (n = 5,403), and those who received VA health care outside of the 50 states or DC (n = 8,354). Our analytical sample comprised 525,716 veterans.

Baseline patient sociodemographic and community-level variables

We assessed five patient-level sociodemographic variables. These included age (mean years; 18–39, 40–64, 65–85, and 85 + years), sex, and race/ethnicity (Hispanic, non-Hispanic white, non-Hispanic African American, and non-Hispanic other) based on VA data supplemented by the Research Triangle Institute race code from Medicare.³³ We also recorded patient enrollment in Medicare Part D low-income subsidy (LIS) and disability as the original reason for Medicare enrollment.

We assessed 12 community-level variables for each patient based on their geographic residence. We determined each patient’s county-level urban influence code (large metropolitan, small metropolitan, micropolitan, and rural)³⁴ and geographic census region of residence (South, West, Northeast, and Midwest) by matching patient ZIP codes from Medicare to the 2012 Area Health Resource File.³⁵ Six community-level variables were indicators of neighborhood socioeconomic deprivation: median household income, adults age ≥25 years with less than high school education (percent), unemployed males age ≥16 (percent), households below the poverty level (percent), households receiving public assistance (percent), and female-headed households with children (percent). In addition to these measures, we assessed indicators of income inequality (Gini index) and racial segregation (percentage of residents who were non-Hispanic African-American race) using the US Census American Community Survey (2006–2011). As a measure of neighborhood safety, we assessed the community violent crime rate from the Uniform Crime Reporting Program accessed through the Inter-University Consortium for Political and Social Research (2012).³⁶ As a measure of internet connectivity, which is associated with using the internet for health-related information seeking and communication,³⁷ we assessed an indicator of high-speed internet, categorized by rate of households per 1,000 with high speed internet 0, 1–200, >200–400, >400–600, >600–800, and >800) using data from the Federal Communication Commission.³⁸

We constructed the socioeconomic deprivation and internet connectivity community-level variables at the census tract level. Specifically, we obtained patients’ address information at the census tract level from the 2012 Planning System Support Group. A census tract is identified by an 11-digit number; the first two digits identify the state, the next three digits identify the county, and the final six digits identify the census tract. Of the cohort, 67 percent patients had a perfect match with a tract in the American Community Survey. The remainder were matched to the closest matching tract. Violent crime rate was assessed at the county level, merging the violent crime rate to patient-level data by county with exact match.

Socioeconomic and violent crime community-level variables were originally abstracted as continuous variables and converted into categorical variables based on deciles of the national distribution. Conversion to deciles was used to facilitate CART modeling and to create a standardized framework for comparisons across community-level variables.

Study outcome

For each patient, we combined all active opioid prescriptions from VA and Part D and calculated daily MME using the conversion formulae established by the Centers for Disease Control.³⁹ We used daily MME to calculate whether each patient had a total daily dosage of >120 MME for at least 90 consecutive days in 2012, which represented the original measure of chronic, high-dosage opioid prescribing that had been developed by the Pharmacy Quality Alliance.^30,40

Statistical analyses

We described the overall frequencies of all patient and community-level variables and compared these variables for individuals who received and did not receive ≥90 consecutive days of prescription opioids with a daily MME >120, using Chi-square tests for categorical variables and ANOVA for continuous variables. For the community-level variables abstracted as continuous data, we calculated corresponding means standard deviations (SDs). The national decile cut points and cohort frequencies by deciles are shown in Appendix A.

We used CART analyses to determine the ability of patient and community-level characteristics to discriminate subgroups of veterans with a differential risk of our opioid prescription outcome. CART is a nonlinear, nonparametric, tree-building method that uses binary recursive partitioning to identify optimal cut points for key discriminating variables in the predictor set. CART systematically searches among all possible predictors for cut points that split the sample into increasingly homogenous subgroups with respect to the outcome variable.²⁸ CART modeling was conducted using SAS Enterprise Miner (SAS-EM) version 14.3 (SAS Institute, Inc., Cary, North Carolina). We used the Gini impurity index, a measure of node impurity, to select splits in predictors with each tree grown to its maximal depth. We used k-fold cross-validation based on 10 randomly selected subsamples to “prune” weak predictors from the final tree.⁴¹ We imposed two additional rules to guard against tree instability and increase interpretability: pruning of terminal nodes with less than 1,000 veterans and tree depth restricted to four levels. The overall population regression tree is included to depict the hierarchical order and frequency with which individual variables appear as splitting rules within the model. Variable importance in the final tree structure was determined using SAS-EM’s default metric. Specifically, importance was quantified as the amount of variability in the outcome explained by the corresponding predictor relative to the variance explained by the most important predictor. We conducted sensitivity analyses to test robustness of the final tree structure to different model specifications (eg, minimum terminal node size, tree depth, model splitting method, and number of cross-validation folds).

Missing values were replaced by using the hot-deck procedure in SAS/stat.⁴² Specifically, we used the SAS proc surveyimpute procedure⁴³ to impute missing values based on simple random samples of recipients from stratified donor pools. Donor pools were constructed using the limited number of variables with missing data: race/ethnicity (n = 936); urban influence (n = 36); census region (n = 25); community-level variables (range in n: 1,088–7,945); and households per 1,000 with high-speed internet (n = 4,120).

RESULTS

Characteristics of the study cohort

Our cohort of 525,716 veterans had a mean age (SD) of 71.5 (11.0) years, 96.6 percent were male, and 82.3 percent were non-Hispanic white (Table 1). Overall, 36.6 percent were enrolled in Medicare due to disability, 29.6 percent were eligible for full or partial Medicare Part D LIS, and more than three-quarters resided in large (43.3 percent) or small (35.6 percent) metropolitan areas.

Table 1.

Patient-level and community-level characteristics of the study cohort overall and by prescribing of chronic high-dose opioids

Patient and community level characteristics	Overall	Chronic High-Dose Opioids*
		No	Yes	P value
	(n = 525,716)	(n = 508,445)	(n = 17,271)
Patient-level
Age in years, mean (SD)	71.5(11.0)	71.8 (10.9)	61.1 (10.1)	<0.001
Age in years, percent				<0.001
18–39	0.6	0.6	2.0
40–64	24.0	22.6	63.7
65–84	62.6	63.7	32.4
85+	12.8	13.1	1.9
Male sex, percent	96.6	96.7	94.6	<0.001
Race/Ethnicity, percent				<0.001
Hispanic	3.5	3.6	2.7
Non-Hispanic white, single race	82.3	82.3	82.5
Non-Hispanic African American, single race	12.1	12.1	12.3
Non-Hispanic Other	2.1	2.1	2.5
Disability Insurance Benefits, percent	36.6	35.0	82.3	<0.001
LIS, percent				<0.001
Not eligible	70.5	71.2	49.9
Fully eligible	24.6	24.0	40.2
Partially eligible	5.0	4.8	9.9
Community-level†				<0.001
Urban Influence, percent
Large metropolitan	43.3	43.4	40.2
Small metropolitan	35.6	35.5	38
Micropolitan	11.9	11.9	12.8
Noncore Rural	9.3	9.3	9.1
Census region (percent)				<0.001
South	41.8	41.8	42.9
West	21.0	20.9	23.3
Northeast	15.3	15.4	14.3
Midwest	21.9	22.0	19.5
Income Inequality (Gini Index), mean (sd)	41.6 (5.8)	41.6 (5.8)	41.6 (5.7)	0.95
Percent households receiving public assistance, mean (sd)	13.5 (10.5)	13.5 (10.5)	14.9 (10.5)	<0.001
Percent households with female head of house, mean (sd)	26.8 (18.1)	26.8 (18.1)	27.8 (18.0)	<0.001
Percent adult male (age 16+) actively looking for work, mean (sd)	10.1 (7.1)	10.1 (7.1)	10.9 (7.3)	<0.001
Percent families under poverty line, mean (sd)	12.2 (10.3)	12.1 (10.3)	13.3 (10.4)	<0.001
Median household income, mean $ (sd)	51,911 (22,612)	52,019 (22,683)	48,683 (20,197)	<0.001
Percent adults (age 25+) without high school degree, mean (sd)	14.9 (10.0)	14.8 (10.0)	15.8 (9.9)	<0.001
Racial segregation (percent non-Hispanic African American), mean (sd)	12.2 (20.8)	12.2 (20.8)	12.1 (20.3)	0.59
Violent crime rate/100 K, mean (sd)	374.4 (236.6)	374.3 (236.7)	378.7 (232.5)	0.02
Households per 1,000 with high-speed internet, percent				<0.001
0	0.4	0.4	0.4
1–200	1.8	1.8	1.8
>200–400	10.1	10.1	10.7
>400–600	27.0	27.0	29.2
>600–800	40.1	40.1	40.3
>800	20.6	20.7	17.6

^*Defined as ≥90 consecutive days of MME >120.

^†Numbers represent Mean (Standard Deviation) unless otherwise noted.

Missing data: race/ethnicity (936); urban influence (36); census region (25); community-level variables (1,088–7,945); Households per 1,000 with high-speed internet (4,120).

P-value from Chi-square test for categorical variables and from ANOVA for continuous variables. Both ANOVA and Wilcoxon tests had similar p-values.

Overall, 17,271 (3.3 percent) veterans were prescribed chronic high-dose opioids. Compared to veterans who did not receive chronic high-dose opioid prescriptions, these individuals were younger, more often female and non-Hispanic white, more frequently eligible for Medicare due to disability and for Medicare Part D LIS, and more likely to live in small metropolitan or micropolitan communities and in the Western or Southern United States (Table 1). These individuals were statistically significantly more likely to live in communities with higher levels of socioeconomic deprivation, higher violent crime rates, and lower rates of high-speed internet access, although these differences were small in magnitude (Table 1). Income inequality and racial segregation of communities did not significantly differ for veterans prescribed versus not prescribed chronic high-dose opioids.

CART analyses

Using four splitting rules and nine of 17 candidate variables, CART analysis identified 35 unique subgroups at different levels of risk for chronic high-dose opioid prescribing (Figure 1; Appendix B). The predictor variables in the final tree consisted of four patient-level variables (disability, age, Medicare Part D LIS, and race/ethnicity) and five community-level variables (census region, percentage of households receiving public assistance, income inequality, percent adults without high school degree, and racial segregation).

Figure 1.

Prevalence of chronic high-dose opioid prescribing across veteran subgroups. Each of the 35 unique subgroups of veterans identified by CART modeling is represented by a dot. The unique combination of four risk factors defining each subgroup is listed on the vertical axis (see Legend), arranged from least to greatest population incidence of chronic high-dose opioid prescribing. Overall population prescribing rate is represented by the vertical blue line (3.29 percent) with subgroups of greater incidence of outcome in red and lesser incidence in yellow. The size of each circle is proportional to the number of veterans included in the subpopulation. The groups with the highest incidence (DIB+/18–64/WH, OTH/W with 12.05 percent incidence) and the largest (DIB−/LIS-/40–84/NE with 0.72 percent incidence) are identified.

The frequency of being prescribed chronic, high-dose opioids was 43-fold higher for veterans in the highest subgroup compared to veterans in the lowest CART risk subgroups (Figure 1). The frequency of this outcome was 12.05 percent among the 16,302 (3.1 percent of the total sample) veterans who were with disability, under 65 years old, white/other race, and living in the Western region of the United States. In contrast, the frequency was 0.28 percent among the 14,835 (2.8 percent of the total sample) veterans who were not with disability, not eligible for LIS, older than 85 years, and lived in neighborhoods in the second and sixth to tenth deciles of public assistance. The three patient subgroups with the highest concentration of chronic high-dose opioid prescribing (ie, with disability, <65-years old, white/other race, living in the West, Northeast, and South), represented only 12 percent of the overall population (Figure 1). In contrast, 64.7 percent of the study population belonged to subgroups with a frequency of high-dose prescribing below 3.3 percent, the overall frequency observed in the sample, and 52.7 percent belonged to subgroups with a frequency under 1 percent.

The sequence and frequency with which individual variables appeared as splitting rules within the model reflects the magnitude of their predictive power for identifying chronic high-dose opioid prescribing (Table 2). The presence (versus absence) of the first splitting variable, disability status, demonstrated an eightfold increase in the outcome (7.39 percent versus 0.92 percent). In subsequent splits, younger age was associated with a higher incidence of the outcome for both veterans with and without disability. Census region was involved in the fourth-level splits for a variety of population segments, with segments in the Western region being at highest risk of all regions in five out of six splits involving census region (Appendix B). The associations of remaining variables were not consistent. Among veterans with disability, white or other race predicted a greater incidence of the outcome than African American and Hispanic race. Among veterans without disability, LIS predicted a higher incidence of the outcome. Finally, income inequality, neighborhood segregation (percent African American race), and neighborhood public assistance were present as fourth-level splitting rules, but none of these community-level variables demonstrated a consistent directional association with the outcome.

Table 2.

Relative importance of variables used as splitting variables in the final classification tree^*

Variable	Splitting rules1	Relative importance2
Disability insurance benefits	1	1 (reference)
Age	4	0.55
Race/ethnicity	2	0.37
Census region	4	0.17
LIS	1	0.14
Racial segregation	1	0.02
Income inequality	1	0.01
Percent adults (age 24+) without high school degree	1	0.01
Percent households receiving public assistance	1	0.01

^*The following variables were not involved in a splitting decision in the CART model, and therefore had no importance in defining subgroups: Sex, violent crime rate, percent of families under poverty line, percent households with female head of house, households per 1,000 with high-speed internet, percent adult males (age 16+) actively looking for work, median income, and urban influence.

¹Indicates number of splits in tree associated with a variable.

²Based on Gini index of reduction of node impurity. The most important variable was disability status. All subsequent values of importance are relative to Disability Status.

Sensitivity analyses of varying model specification had little effect on the final tree structure, tree misclassification rate, and predictive accuracy (Appendix C).

DISCUSSION

Among veterans dually enrolled in Medicare Part D and VA receiving prescription opioids in 2012, combinations of four patient- and five community-level variables identified 35 unique patient subgroups whose prevalence of chronic high-dose opioid prescribing varied up to 43-fold. We demonstrated that certain combinations of these characteristics identified individual subgroups at higher risk for receiving chronic high-dose opioid prescriptions. In particular, Medicare disability enrollment, white/other race, and younger age were consistently associated with high-dose opioid prescribing, especially when considered in combination. These multidimensional interactions should be considered when evaluating the association of sociodemographic characteristics with opioid prescribing outcomes. CART techniques are particularly useful for identifying these interactions.

In this cohort from 2012, four patient-level variables were associated with chronic high-dose prescribing, either alone or in combination: disability, younger age, white race, and Medicare Part D LIS. Furthermore, we demonstrated that the risk-imparting effects of a single factor can be context-dependent. Race, for example, was a relevant predictor for veterans with disability but not those without disability, whereas the opposite was true for LIS. Living in the South was also associated with lower rates of high-dose opioid prescribing among African American and Hispanic veterans, but not for veterans of white or other race. These findings demonstrate that focusing on sociodemographic factors in isolation may lead to an incomplete or inaccurate description of their importance. The landscape of opioid use in the United States has changed substantially since 2012, most notably due to the proliferation of non-prescription opioids, but also with persistent concerns related to prescription opioids.^44,45 Scrutiny of opioid use has focused on specific demographic traits, often white race and male sex. The interplay between disability, race, and region found in the present study suggests the importance of examining how multiple demographic factors intersect to determine groups at higher risk and in greater need of targeted opioid-safety interventions in more contemporary data.

Community-level variables were not as important as we had anticipated. As in prior studies examining the association between community context and chronic opioid prescriptions,⁴⁶ we found that the population of veterans prescribed chronic, high-dose opioids were more likely to reside in communities with lower overall socioeconomic wellbeing (Table 1). However, only five of 12 community-level variables were relevant predictors in the final analysis. Of these variables, census region was the only community-level factor that displayed a consistent association with chronic high-dose prescription of opioids, with higher prevalence occurring in the Western region. Other community-level variables, percentage of households receiving public assistance, income inequality, and racial segregation, were present as fourth-level splitting rules and did not exhibit a clear, directional relationship with the outcome, suggesting limited practical significance. Although modest but meaningful community-level variation has been found in chronic opioid use, substance use, and other health risks,^46–48 our findings suggest that individual sociodemographic characteristics play a more important role in identifying dually enrolled veterans at risk for high-dose opioid prescribing than the social environments in which they live.

In the present study, utilization of CART identified disability status as the most powerful sociodemographic predictor of chronic high-dose opioid prescribing. While the association between disability and opioid prescribing has been previously described,⁴⁹ it has been relatively understudied compared to factors such as race, gender, and age. While young age, white race, and residence in the Western US have been previously identified as risk factors for opioid prescribing and adverse outcomes, as was the case in the present study, our analysis sheds light on the relative importance of these traits when assessing one’s risk for high-dose opioid prescribing. Several of our findings, including intersections between white race and disability, Western region and nonwhite race are likely to be explained by the use of classification tree analysis, which allows for identification of combinations of risk factors that may be difficult to identify using traditional regression-based techniques. Overall, CART has been recognized as a powerful tool for identifying high-risk subpopulations and combinations of important risk factors in the public health setting,^50–52 and the results of this study suggest an important role for classification tree analysis in epidemiologic investigations of opioid prescribing in more contemporary cohorts.

LIMITATIONS

Our study has limitations. Findings from our cohort of veterans dually enrolled in Medicare Part D and the VA may not be generalizable to nonveterans or veterans receiving care outside of the VA or Medicare Part D. Second, our opioid safety outcome was based on opioids prescribed in VA or Medicare Part D. Further, this outcome did not consider prescription opioids purchased with cash or paid for by other forms of health insurance. Third, our outcome metric of daily MME is but one way to quantify opioid use. While MME is correlated with patient-centered outcomes, other contributing factors such as medical comorbidities and use of other substances are absent from these calculations, thus incompletely describing risk of adverse events. Further, MME calculation is itself limited by variability in opioid potency conversion and a lacking consensus for dosing safety thresholds.⁵³ However, we used MME calculations and dosing guidelines that were endorsed by the CDC and PQA in 2012 in an effort to align our characterization of opioid prescribing in our cohort with definitions that were widely accepted and utilized at that time. Finally, our decision to focus solely on sociodemographic factors precludes assessing the relative importance of these variables compared to patient clinical characteristics; however, this decision was purposeful.

CONCLUSION

In this study of dually enrolled VA and Medicare Part D beneficiaries, we identified a 43-fold variability in chronic high-dose opioid prescribing based on combinations of eight nonclinical sociodemographic characteristics. Interactions among disability, age, race/ethnicity, and region should be considered when attempting to identify high-risk subgroups of a large population. With respect to opioid prescribing, CART is effective at identifying significant combinations of sociodemographic risk factors and should be considered as a tool in studies aimed at characterizing patients at risk for potentially unsafe prescribing in more contemporary cohorts.

Appendix A: Table of decile cut points for and distribution of continuous community-level variables.

	N	1	2	3	4	5	6	7	8	9	10
Income inequality (gini)	519,374
Decile cut points		1.2–34.0	34.1–36.3	36.3–38.0	38.0–39.4	39.5–40.9	40.9–42.4	42.4–44.1	44.1–46.4	46.4–49.7	49.8–92.0
Percent of cohort		7.4	9.3	10.5	11.0	11.0	11.0	10.9	10.6	10.0	8.5
Percent households receiving public assistance	519,442
Decile cut points		0–2.0	2.0–3.8	3.8–5.7	5.7–7.8	7.8–10.1	10.1–12.9	12.9–16.4	16.4–21.4	21.4–30.1	30.1–100.0
Percent of cohort		6.9	8.4	9.8	10.2	11.0	11.2	12.2	11.7	10.9	7.9
Percent households female head of house	517,771
Decile cut points		0–6.5	6.5–10.7	10.7–14.5	14.5–18.3	18.3–22.5	22.5–27.2	27.2–33.2	33.2–40.9	40.9–54.0	54.0–100
Percent of cohort		7.7	9.1	10.2	11.0	11.2	10.8	10.9	10.6	9.7	8.7
Percent adult male unemployment	519,467
Decile cut points		0–2.5	2.6–4.1	4.2–5.5	5.6–6.8	6.9–8.2	8.3–9.8	9.9–11.7	11.8–14.3	14.4–18.8	18.9–100.
percent of cohort		8.0	9.1	10.0	9.9	10.4	10.5	10.4	10.7	10.9	10.1
Percent families under poverty line	519,326
Decile cut points		0–1.5	1.6–3.2	3.3–4.9	5.0–6.7	6.8–8.9	9.0–11.6	11.7–15.1	15.2–20.4	20.5–29.3	29.4–100
Percent of cohort		6.8	9.1	10.2	10.4	11.4	11.6	11.6	11.5	10.3	7.0
Median household income, $	519,346
Decile cut points		2,874–27,517	27,518–34,438	34,439–39,874	39,875–44,790	44,792–50,317	50,318–56,155	56,156–63,811	63,813–74,655	74,657–92,564	92,572–247,064
Percent of cohort		8.4	11.5	12.3	12.3	11.8	11.0	10.1	9.1	7.9	5.7
Percent adults without high school degree	519,570
Decile cut points		0–3.2	3.3–5.4	5.5–7.5	7.6–9.6	9.6–12.0	12.1–14.9	14.9–18.6	18.6–23.5	23.6–31.3	31.4–83.3
Percent of cohort		6.1	8.7	9.9	11.1	11.6	12.1	11.8	11.5	10.3	6.9
Percent Non- Hispanic African American, racial segregation/1,000	519,603
Decile cut points		0–0.3	0.3–4.7	4.7–11.4	11.4–22.2	22.3–39.3	39.3–65.7	65.8–112.4	112.4–202.4	202.4–438.5	438.5–1,000
Percent of cohort		10.3	11.8	10.8	10.5	9.9	9.8	9.7	9.7	8.9	8.7
Violent crime rate/lOOK	524,537
Decile cut points		0–38	38–77	77–114	114–148	149–187	187–237	237–291	291–366	366–501	501–1,791
Percent of cohort		1.6	3.5	5.1	5.3	7.8	8.5	8.9	13.2	23.3	22.8

Missing data: between 1,088 and 7,945.

APPENDIX B. Overall Population Regression Tree of Chronic High-Dose Opioid Prescribing.

Panel (a) contains all veterans enrolled in Medicare via disability, whereas veterans without disability are demonstrated in panel (b). Color coded, where darker shades of blue represent greater within-group incidence of chronic high-dose opioid prescribing. Thickness of the line is proportional to number of veterans contained within each subset from the above node.

DIB+, with disability; DIB−, without disability; numbers, age range; WH,OTH, white or other race/ethnicity; BL,HISP, African American or Hispanic; NE, Northeast Census region; MW, Midwest; S, South; W, West; Gini, income inequality index, decile; assistance, percent households receiving public assistance, decile; segregation, percent non-Hispanic African American, decile. (See online edition for more detail.)

APPENDIX C. Results of sensitivity analyses testing robustness of final tree structure.

Dataset was analyzed using CART methods with alternative splitting approaches (gini impurity, information gain entropy) and differing constraints on final node size, resulting in trees of varying depths (numerically represented above, with lettering distinguishing multiple trees of same depth). Gini 4a (green), the simplest top-performing model, was used in this study.