correlation of opioid mortality with prescriptions and social determinants -a cross-sectional study...

ORIGINAL RESEARCH ARTICLE

Correlation of Opioid Mortality with Prescriptions and SocialDeterminants: A Cross-sectional Study of Medicare Enrollees

Christos A. Grigoras1,3 • Styliani Karanika1,2 • Elpida Velmahos1 •

Michail Alevizakos1 • Myrto-Eleni Flokas1 • Christos Kaspiris-Rousellis3 •

Ioannis-Nektarios Evaggelidis3 • Panagiotis Artelaris4 • Constantinos I. Siettos3 •

Eleftherios Mylonakis1

� Springer International Publishing AG, part of Springer Nature 2017

Abstract

Background The opioid epidemic is an escalating health

crisis. We evaluated the impact of opioid prescription rates

and socioeconomic determinants on opioid mortality rates,

and identified potential differences in prescription patterns

by categories of practitioners.

Methods We combined the 2013 and 2014 Medicare Part

D data and quantified the opioid prescription rate in a

county level cross-sectional study with data from 2710

counties, 468,614 unique prescribers and 46,665,037 ben-

eficiaries. We used the CDC WONDER database to obtain

opioid-related mortality data. Socioeconomic characteris-

tics for each county were acquired from the US Census

Bureau.

Results The average national opioid prescription rate was

3.86 claims per beneficiary that received a prescription for

opioids (95% CI 3.86–3.86). At a county level, overall

opioid prescription rates (p\0.001, Coeff = 0.27) and

especially those provided by emergency medicine

(p\0.001, Coeff = 0.21), family medicine physicians

(p = 0.11, Coeff = 0.008), internal medicine (p = 0.018,

Coeff = 0.1) and physician assistants (p = 0.021,

Coeff = 0.08) were associated with opioid-related mor-

tality. Demographic factors, such as proportion of white

(pwhite\0.001, Coeff = 0.22), black (pblack\0.001,

Coeff =- 0.19) and male population (pmale\0.001,

Coeff = 0.13) were associated with opioid prescription

rates, while poverty (p\0.001, Coeff = 0.41) and pro-

portion of white population (pwhite\0.001, Coeff = 0.27)

were risk factors for opioid-related mortality

(pmodel\0.001, R2 = 0.35). Notably, the impact of pre-

scribers in the upper quartile was associated with opioid

mortality (p\0.001, Coeff = 0.14) and was twice that of

the remaining 75% of prescribers together (p\0.001,

Coeff = 0.07) (pmodel = 0.03, R2 = 0.03).

Conclusions The prescription opioid rate, and especially

that by certain categories of prescribers, correlated with

opioid-related mortality. Interventions should prioritize

providers that have a disproportionate impact and those

that care for populations with socioeconomic factors that

place them at higher risk.

Christos A. Grigoras and Styliani Karanika contributed equally to this

work.

Electronic supplementary material The online version of thisarticle (https://doi.org/10.1007/s40265-017-0846-6) contains supple-mentary material, which is available to authorized users.

& Eleftherios Mylonakis

[email protected]

1 Medical Science, Program on Outcomes Research, Infectious

Diseases Division, Rhode Island Hospital, Warren Alpert

Medical School of Brown University, 593 Eddy Street, POB,

3rd Floor, Suite 328/330, Providence, Rhode Island 02903,

USA

2 General Internal Medicine Section, Boston Medical Center,

Boston University School of Medicine, Boston,

Massachussets, USA

3 School of Applied Mathematics and Physical Sciences,

National Technical University of Athens, Athens, Greece

4 Department of Geography, Harokopio University, Athens,

Greece

Drugs

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Key points for Decision Makers

Primary care providers prescribe most opioids.

Opioid prescription rate is associated with opioid-

related deaths (in total, as well as for each category

of opioids and heroin)

Particular specialties’ prescription rate is correlated

with the opioid-related deaths and practitioners that

prescribe more (super-prescribers) are associated

disproportionally with opioid-related deaths

Poverty level in the county strengthened the

correlation between opioid prescriptions and opioid-

related deaths

1 Introduction

More than 650,000 opioid prescriptions are dispensed daily

in the USA [1] and 78 people die daily from an opioid-

related overdose [2]. The mortality associated with the

most commonly prescribed opioids (natural/semisynthetic

opioids) represents more than one-third of total overdose

deaths [3, 4]. Over the last 15 years, opioid prescriptions

and deaths have been moving in parallel, and the experi-

ence from the USA and other countries indicates that

restrictions in the use of opioids can decrease mortality

[5, 6]. However, previous studies reported conflicting data

[7, 8] and the size and the fragmented nature of healthcare

in the USA create the need to develop local strategies and

to prioritize potential interventions to assure significant

impact in decrease of mortality.

The association between the opioid prescription rate by

different specialties and the opioid-related mortality has

not been reported and the impact of different socioeco-

nomic factors has not been documented. The aim of our

study was to co-analyze nationwide opioid prescription

Medicare part D data (down to individual practitioner) with

socioeconomic factors and opioid-related mortality, to

evaluate potential connections at a county level.

2 Methods

2.1 Opioid Prescription Data

To estimate the opioid prescription rate, we extracted

information on the number of claims, generic drug name,

number of Medicare beneficiaries to whom these claims

were prescribed, category and specialty of practitioner and

ZIP code of each healthcare provider, as reported in the

2013 and 2014 Medicare Part D Opioid Prescriber Sum-

mary Files [9]. This database contains annual information

for over 30 million patients (that is approximately 60% of

the beneficiaries enrolled in the Medicare program) [10].

The search results were classified based on drug class. The

first category contained all the claims containing the search

term ‘‘methadone’’, while the second included results

containing the search term ‘‘fentanyl OR meperidin’’. The

final prescription category contained any claim containing

the following search terms: ‘‘levorph OR morphone OR

opium OR oxycodo OR hydromorpho OR butorpha OR

oxymorphone OR codein OR morphine OR buprenorphine

OR nalbuphine OR tramadol OR tapentadol OR codone

OR pentazocine OR alfentanil OR remifentanil OR

sufentanil’’. Both chronic and acute care conditions, as well

as long- and short-acting formulations of opioid prescrip-

tions were included in our analysis. Physicians with less

than 11 opioid claims per class of drugs (667,294 physi-

cians) were excluded from our study.

We employed the 2010 ZIP Code Tabulation Area

(ZCTA) to County Relationship File [11] to assign the

opioid claims to the county enclosing each census tract. In

case a census tract was contained in more than one county,

we assigned the claims to the county that contained the

largest proportion of the census tract. Physicians with a

unique National Provider Identifier (NPI) were included in

the study. The opioid prescription rate was calculated as

the total number of opioid claims prescribed per the

number of beneficiaries that were prescribed these medi-

cations and 95% Poisson confidence intervals (CIs) were

estimated. Of note is that nurse practitioners and physician

assistants are considered independent prescribers in

Medicare, with their own NPI. The District of Columbia

was considered as a separate state in all analyses and only

data from practitioners with data available from both years

were included (113,233 physicians excluded).

Furthermore, we grouped physicians based on the dif-

ferences both in the mean and variance of prescription rates

across prescribers. In order to include the highest number

of prescribers, we utilized the most current Medicare Part

D dataset of 2014 that includes prescribers who were

excluded from our previous analysis due to lack of

reporting data for 2013. To examine the potential impact of

‘‘super-prescribers’’, we identified the physicians in the

fourth quartile of the opioid prescription rate of each

medical specialty. We then separately calculated the pre-

scription rate of all the super-prescribers and all the

remaining physicians in a county level and fitted a multi-

variable linear regression on the total opioid mortality with

the prescription rates of the two groups as independent

variables. This procedure was repeated for several values

C. A. Grigoras et al.

of the threshold of the classification as super-prescribers,

namely (80, 90, 95, 99%) and the results of the sensitivity

analysis were reported in the Supplementary Material.

2.2 Mortality Data

The opioid-related mortality data for each county and state

were extracted from the Multiple Cause of Death

1999–2014 dataset published by the Centers for Disease

Control and Prevention (CDC) WONDER Online Database

[2]. In the ICD-10 coding system, T40.1 encodes heroin-

related data, T40.2 natural (morphine, codeine, thebaine)

and semi-synthetic (oxycodone, hydrocodone, oxymor-

phone, hydromorphone, buprenorphine) opioid analgesic-

related data (except heroin), T40.3 encodes methadone-

related mortality data, and T40.4 synthetic (fentanyl,

meperidine) opioid analgesics, except methadone.

We also calculated the total opioid mortality rate as the

total opioid-related deaths, summing up all four mortality

ICD-10 codes, occurring during 2010–2014, divided by the

size of population residing in a county or state. We selected

to use aggregate mortality data per county over a 5-year

period in order to maximize the number of counties with

reported mortality rates. Counties with suppressed mor-

tality data were excluded from our analysis. Similarly, the

mortality rate per each opioid class was calculated as the

total deaths attributed to each opioid class occurring in the

2010–2014 time-period, divided by the size of population

residing in a county or state.

2.3 Socioeconomic Data

We obtained socioeconomic characteristics for each county

from the 2010–2014 American Community Survey (ACS)

5-year estimates dataset provided by the US Census Bureau

[12]. This dataset is considered to be the most current and

most reliable dataset containing information for all coun-

ties within the USA [13]. The following explanatory vari-

ables were included in our analysis: (1) percentage of

people living under the poverty line, (2) percentage of

Black, Hispanic or White population, (3) percentage of

males, (4) percentage of population aged C 65 years, (5)

population density, and (6) number of medicare-enrolled

opioid prescribing physicians per county population.

2.4 Statistical Analysis

Multivariable linear regression was implemented to predict

county opioid-related mortality based on the aggregate

opioid prescription rate per county, percentage of people

living under poverty line, gender and race distribution in

each county. Output of the regression analysis included the

p value of the model or variable, value of the coefficient of

a variable (Coeff) and the coefficient of determination (R2),

which indicates the proportion of variance in the dependent

variable that is predictable from the independent variable.

To allow comparisons between the effects of each variable,

each dependent and independent variable was rescaled to

have a mean of zero and standard deviation (SD) of 1. We

employed Belsley’s test to examine collinearity between

independent variables [13, 14]. We performed spatial

regression analyses to identify and control for any spatial

autocorrelation effect between our variables. Data pro-

cessing and statistical analyses were performed using

MATLAB 2016a (The MathWorks Inc., Natick, MA) and

GeoDa (version 1.10). Mortality and prescription rate

mappings were created using the Quantum Geographic

Information System (QGIS) [15].

3 Results

We analyzed 180,285,363 opioid prescriptions, provided

by practitioners with reported data in both 2013 and 2014

Medicare Part D datasets that were prescribed to

46,665,037 beneficiaries. The overall average annual opi-

oid prescription rate was 3.86 claims per beneficiary who

received a prescription for opioids (CI 3.86–3.86). Ver-

mont [6.62 opioid claims per beneficiary (CI 6.6–6.65)],

Montana [5.18 opioid claims per beneficiary (CI

5.17–5.20)] and Wyoming [5.14 opioid claims per benefi-

ciary (CI 5.11–5.16)] were the states with the highest total

opioid prescription rate, while the lowest total opioid pre-

scription rate was noted in New York [3.45 opioid claims

per beneficiary (CI 3.44–3.45)], Texas [3.42 opioid claims

per beneficiary (CI 3.42–3.42)] and Florida [3.37 opioid

claims per beneficiary (CI 3.36–3.37)] (Fig. 1, Table 1 and

eTable 1).

At a county level, 14% of the variance of the total

opioid-related prescription rate was associated with race

(% of white/black population) and gender (pmodel\0.001,

R2 = 0.14) and an increase of 1 SD in % of white, black or

male population resulted in a change of 0.22 SD

(p\0.001), - 0.19 SD (p\0.001) and 0.13 SD (p\0.001),

respectively, in the total opioid prescription rate. Notably,

while poverty was discarded from the stepwise selection

algorithm multivariable model, a single linear regression

yielded that an increase of 1 SD in poverty resulted in a

decrease of - 0.19 SD (p\0.001) in the opioid prescrip-

tion rate (pmodel\0.001, R2 = 0.04).

The CDC WONDER multiple cause of death database

provided the information that in 2010–2014, opioids were

associated with 9.72 deaths per 100,000 individuals (CI

9.53–9.83). Methadone was associated with 1.50 deaths/

100,000 people (CI 1.29–1.68), natural and semi-synthetic

opioid analogues 4.55 deaths/100,000 people (CI

Relation Between Opioid Prescriptions and Opioid Mortality

4.22–4.90), synthetic opioids (except methadone) 1.41

deaths/100,000 people (CI 1.21–1.60) and heroin 2.26

deaths/100,000 people (CI 1.8–2.40). In order to evaluate

for a potential association between opioid-related mortality

and opioid prescription rate, we used multivariable

regression models and took into consideration the effect of

the socioeconomic parameters noted above. At a county

level, mortality rate attributed to each class of opioids was

Fig. 1 Opioid prescription and mortality rates. Choropleth map presenting opioid prescription rates per state (2013 and 2014) in blue color

progression. Concentric circles represent opioid-related mortality rates per state (2010–2014)

Table 1 Opioid prescription rate in US states

State Opioid claims per beneficiary 95% confidence interval Physicians Beneficiaries Opioid claims

Top 5 opioid prescription states

Vermont 6.62 [6.60, 6.65] 463 41,742 276,439

Montana 5.18 [5.17, 5.20] 1062 114,390 593,024

Wyoming 5.14 [5.11, 5.16] 414 37,577 192,967

Alaska 4.89 [4.86, 4.92] 317 25,788 126,121

West Virginia 4.83 [4.83, 4.84] 1945 413,132 1,997,122

Bottom 5 opioid prescription states

Arizona 3.46 [3.46, 3.47] 5693 987,806 3,421,638

District of Columbia 3.45 [3.43, 3.48] 321 29,810 102,991

New York 3.45 [3.44, 3.45] 12,070 1,464,417 5,045,533

Texas 3.42 [3.42, 3.42] 18,861 3,766,162 12,889,203

Florida 3.37 [3.36, 3.37] 16,549 3,696,917 12,444,407


Table 2 Multivariable regression modelsa

Coeff p value SE t statistic # R2 p value (model)

A. Association of total opioid prescription rate with race, gender, physicians/population, age and spatial

autocorrelation

2710 0.30 \0.001

White 0.11 \0.001 0.02 4.83

Black - 0.11 \0.001 0.02 - 4.79

Male 0.05 0.003 0.02 2.92

Physicians - 0.18 \0.001 0.02 - 11.52

Aged[65 years 0.17 \0.001 0.02 9.48

Spatial lag 0.38 \0.001 0.02 15.94

B. Association of total opioid mortality rate with opioid prescription rate, poverty, physicians/population,

spatial autocorrelation and race

832 0.62 \0.001

Poverty 0.28 \0.001 0.03 9.10

Prescription rate 0.28 \0.001 0.05 5.06

White 0.16 \0.001 0.04 4.23

Physicians - 0.07 0.01 0.03 - 2.49

Spatial lag 0.57 \0.001 0.03 21.75

C. Association of mortality related to synthetic opioids with total opioid prescription rate, poverty, physicians/

population, spatial autocorrelation and race

181 0.81 \0.001

Poverty 0.53 \0.001 0.07 7.86

White 0.41 \0.001 0.07 6.12

Prescription rate 0.32 0.02 0.14 2.37

Physicians - 0.32 \0.001 0.06 - 4.91

Spatial lag 0.57 \0.001 0.04 14.69

D. Association of mortality related to natural and semi-synthetic opioids with total opioid prescription rate,

poverty, physicians/population, spatial autocorrelation and race

179 0.8 \0.001

Poverty 0.37 \0.001 0.06 5.88


White 0.21 0.001 0.07 3.21

Physicians - 0.22 \0.001 0.06 - 3.46

Spatial lag 0.63 \0.001 0.04 16.6

E. Association of mortality related to heroin with total opioid prescription rate, poverty, spatial autocorrelation,

and race

151 0.49 \0.001

Poverty 0.42 \0.001 0.12 8.17

White 0.37 \0.001 0.11 3.32


Spatial lag 0.48 \0.001 0.06 8.17

F. Association of mortality related to methadone with total opioid prescription rate, poverty, spatial

autocorrelation, and race

124 0.35 \0.001

Poverty 0.33 \0.001 0.1 3.3

White 0.26 0.007 0.1 2.7


Spatial error 0.42 \0.001 0.08 5.55

G. Association of mortality related to opioids with total opioid prescription rate per specialty 794 0.1 \0.001

Emergency medicine 0.21 \0.001 0.03 6.13

Family medicine 0.11 0.008 0.04 2.67

Internal medicine 0.1 0.018 0.04 2.37

Physician assistant 0.08 0.021 0.03 2.31


linearly associated with the total opioid prescription rate and

35% of the variance of total opioid-related mortality was

correlated with opioid prescription rate (pmodel\0.001,

R2 = 0.35) (Table 2B). This correlation between opioid

prescription rate, poverty, % of white population and opioid

mortality was consistent with each opioid mortality category

[natural/semi-synthetic opioids (pmodel\0.001, R2 = 0.45)

(Table 2D), synthetic opioids (pmodel\0.001, R2 = 0.52)

(Table 2C), heroin (pmodel\0.001, R2 = 0.18) (Table 2E)

and methadone (pmodel\0.001, R2 = 0.35)] (Table 2F).

The correlation with poverty is particularly interesting,

especially since poverty was negatively correlated with the

opioid prescription rate. To further examine this correlation,

we compared the fitted single linear regression lines of the

total opioid mortality to the prescription rate in counties

above and below the median poverty level and found that

the impact of prescription rate in opioid mortality in

counties with high poverty (p\0.001, Coeff = 0.51) was

higher than in counties with lower poverty (p\0.001,

Coeff = 0.35). This finding indicates that, even though

poverty is negatively correlated with the opioid prescription

rate in areas with high poverty, high prescription rate is

closely correlated with high opioid-related mortality.

Then, we analyzed data on the prescription patterns

among 93 categories of prescribers and found that 10 cat-

egories accounted for 90.22% of all opioid claims.

Breaking down the opioid prescription per category, family

medicine practitioners ranked first, accounting for 31.15%

of all opioid claims reported, prescribing 5.32 opioid

claims per beneficiary who received an opioid prescription.

Internal medicine physicians prescribed 29.04% of all

opioid claims reported, with 5.11 opioid claims per bene-

ficiary, while nurse practitioners and physician assistants

were accountable for 6.64% of all opioid claims, pre-

scribing 3.81 and 2.74 opioid claims per beneficiary who

received an opioid prescription, respectively (Table 3A,

eFig. 1, and eTable 2). Because the top 10 medical cate-

gories accounted for 9 out of 10 of all opioid claims, we

fitted a multivariable linear regression model to examine

the impact of the opioid prescription rate of these cate-

gories in opioid-related mortality at a county level and we

found that overall opioid prescription rates provided by

emergency medicine, family medicine physicians, internal

medicine and physician assistants were positively associ-

ated with opioid-related mortality (Table 2A).

We included the top 25 opioid-prescribing medical spe-

cialties accounting for more than 98% of all opioid pre-

scriptions and estimated the mean and the variance of the

prescription rate of physicians for each medical specialty

and displayed them graphically (Fig. 2). Based on the dis-

tribution of the prescription rates, we identified five groups

of medical specialties with similar combinations of mean

prescription rates and variances, providing potential groups

of practitioners who, on average, have similar opioid pre-

scription patterns. The first category consisted mostly of

surgical specialties and emergency-medicine physicians,

while the second included advanced practice providers

(nurse practitioners and physician assistants). The third

group included mostly internal and family-medicine prac-

titioners and oncologists. Interestingly, in the last two

groups, that were considerably smaller with respect to the

number of specialties, we observed both higher variance and

mean prescription rates. More specifically, the fourth group

consisted of neurologists and infectious diseases practi-

tioners. This difference from the previous groups could be

attributed to the variability of clinical practice among the

specialists in the same field which reflects the patients’

characteristics. Even higher variability was detected in the

fifth category, which included the psychiatrists. These

findings indicate that regarding opioid policies, educational

tools and metrics, one size does not ‘‘fit all’’ and, while some

prescribers could be grouped, others should be highly dif-

ferentiated based on practice characteristics.

Interestingly, we found that a minority of prescribers

contributed most prescriptions, and that was particularly

characteristic of specific categories of practitioners. For

example, the top 25% of physician assistants prescribed

more than 55% of the opioids prescribed in this category,

while in other categories that are more closely associated

with the use of opioid agents (such as hematologists/on-

cologists) the contribution of these prescribers was more

proportionate (Table 3B).The impact of prescribers in the

upper quartile on the opioid mortality was associated with

opioid-related mortality (p\0.001, Coeff = 0.14) and was

Table 2 continued

Coeff p value SE t statistic # R2 p value (model)

H. Association of mortality related to opioids with total opioid prescription rate of prescribers in the 4th quartile

(super-prescribers) vs the remaining prescribers

919 0.03 \0.001

Super-prescribers 0.14 \0.001 0.03 4.3

Remaining 0.07 \0.001 0.03 2.16

SE standard error, Coeff coefficient, # number of countiesaThe complete regression analyses are presented in Supplementary File 1. The increase in the dependent variable in standard deviations (SD) due

to an increase of 1 SD in the respective independent variable


twice that of the remaining 75% of practitioners (p\0.001,

Coeff = 0.07) (pmodel = 0.03, R2 = 0.03) (Table 3B).

4 Discussion

The USA faces an opioid overdose epidemic [16, 17].

Using the Medicare Part D nationwide database, we found

that opioid prescription rates varied widely, and at a county

level, the opioid prescription rate was associated with

opioid-related mortality (in total, as well as for each cate-

gory of opioids and heroin). Most opioid prescriptions were

provided in the primary/general-care setting and were

related to the percent of white and male population in the

county. Moreover, opioid-related deaths were correlated

with the opioid prescription rate of specific categories of

practitioners and they were disproportionally associated

with prescribers who belonged to the upper quartile of

Table 3 Opioid prescription rate per medical specialty

A.

Specialty # of counties Opioid beneficiaries Opioid claims Claims per beneficiary Proportion of total

opioid claims (%)

Family practice 2826 10,549,952 56,158,035 5.32 31.15

Internal medicine 2238 10,237,738 52,354,379 5.11 29.04

Nurse practitioner 2418 3,146,818 11,976,790 3.81 6.64

Physician assistant 1954 3,333,374 9,136,242 2.74 5.07

Orthopedic surgery 1423 3,951,371 9,023,800 2.28 5.01

Interventional pain management 474 1,234,933 5,747,668 4.65 3.19

Anesthesiology 582 1,215,039 5,730,458 4.72 3.18

Emergency medicine 1814 3,847,040 5,132,330 1.33 2.85

Rheumatology 626 785,773 3,957,165 5.04 2.19

Pain management 399 723,269 3,435,111 4.75 1.91

General surgery 1659 1,333,230 2,052,799 1.54 1.14

Neurology 632 345,828 2,034,899 5.88 1.13

Dentist 2011 1,264,041 1,668,344 1.32 0.93

Hematology/oncology 708 286,779 1,436,653 5.01 0.8

Geriatric medicine 309 239,845 1,310,961 5.47 0.73

Urology 979 653,803 960,123 1.47 0.53

Neurosurgery 490 366,319 956,279 2.61 0.53

Oral surgery (dentists only) 754 676,883 814,350 1.2 0.45

Cardiology 448 160,787 622,956 3.87 0.35

Podiatry 934 276,597 605,814 2.19 0.34

B.

Specialty Proportion of total prescriptions

due to physicians in the

upper quartile (%)

Proportion of total prescriptions

due to physicians in the

lower quartile (%)

Mean of prescription

rate (claims/beneficiary)

Standard deviation

of prescription rate

Physician assistant 55.58 8.03 1.67 0.85

Cardiology 50.00 6.49 2.77 1.42

Nurse practitioner 48.03 5.31 2.79 1.50

Emergency medicine 42.27 8.53 0.99 0.01

Internal medicine 40.23 5.26 3.61 1.53

Family practice 38.56 7.71 3.88 1.47

Anesthesiology 38.52 10.03 3.73 1.34

Geriatric medicine 37.28 12.07 3.80 1.12

Pain management 35.76 13.59 3.88 1.22

Podiatry 35.19 12.69 1.68 0.45

The list contains the top 20 prescribing medical specialties, accountable for 97.16% of all opioid prescriptions. Combined data from Medicare

Part D datasets for 2013 and 2014


prescribers in their category. Interestingly, most categories

of practitioners could be assigned in one of three groups

based on similar prescription profiles, while the poverty

level in the county was negatively associated with opioid

prescriptions, but opioid-related deaths were positively

associated with poverty.

In our analysis, most opioid prescriptions were provided

by general and primary-care prescribers (family medicine,

internal medicine, nurse practitioners and physician assis-

tants). Pain constitutes one of the most prevalent com-

plaints in primary- and emergency-care settings [7] and in a

study involving physicians who faced criminal prosecution

or charges by medical boards for inappropriate opioid

prescribing practices between 1998 and 2006, they found

that 39% were either general practitioners or family

physicians [18]. Interestingly, prescription behavior has an

effect at a county level, as, increased prescription rates by

these prescribers was associated with increased opioid-re-

lated mortality. The suggested mechanism seems to be

multi-factorial. Our working hypothesis is that when pro-

viders prescribe more opioids, they become a significant

source of diverted opioids [19]. The availability of pre-

scribed opioids inevitably increases not only among direct

beneficiaries but also their social environment (diversion)

leading to misuse, abuse, overdose and accidental deaths.

Of note, 37% of the 44,000 drug-overdose deaths in 2013

was attributable to pharmaceutical opioids, while heroin

accounted for an additional 19%, implying that widespread

‘‘legal’’ availability can drive the mortality [20].

Furthermore, we demonstrated patterns in the variability

of prescription rates across different medical specialties

which could be attributed to the variability of clinical

practice. The CDC recently published guidelines on opioid

prescribing for primary care providers [19, 20]. Given the

direct association between opioid prescription rates by

general practitioners and opioid mortality, these guidelines

should be expanded and implemented among practitioners

(such as internists and rheumatologists) that have similar

opioid prescription patterns. However, guidelines, metrics

and educational tools for the selection of appropriate

treatment should be adjusted for other groups of practi-

tioners that have different prescription patterns, while for

some categories of prescribers (such as infectious diseases

specialists, neurologists and psychiatrists), there is such

variability that the focus should be on sub-groups and

should be adjusted based on the clinical practice setting.

Importantly, opioid deaths were associated with physi-

cians at the upper quartile of the opioid prescription rate for

their category, suggesting that this subgroup of practi-

tioners should be seen as a separate group and be the pri-

mary focus of policies and interventions, as they are

associated with a disproportionate part of opioid deaths

(twice that of the remaining 75% of practitioners). Notably,

previous efforts have focused on interventions targeting

super-prescribers [21, 22] but these efforts defined the

threshold for intervention arbitrarily. By evaluating dif-

ferent thresholds to define ‘‘super-prescribers’’ (1, 5, 10, 20

and 25%), we found that the impact of this sub-group of

Fig. 2 Mean and variance of opioid prescriptions per specialty.

Scatterplot of mean and variance of opioid prescriptions rates of

physicians across medical specialties. Data reporting opioid claims

per beneficiaries were aggregated for physicians included in the 2014

Medicare Part D dataset


prescribers becomes considerably more significant at the

25% threshold. Taken together, these findings support the

hypothesis that interventions should prioritize prescribers

at the upper end of prescription rate in the category.

However, to make a difference, these interventions should

take place in real-time and include all prescribers in the

upper quartile and prioritize specific categories of pre-

scribers that are disproportionally impacted by super-

prescribers.

In addition to categories of prescribers, we identified

populations with higher prescription rates, as well as areas

where increased prescription rates are more closely corre-

lated with opioid-related deaths. Rural areas appeared to

have higher prescription rates along with people aged

C 65 years. Also, areas with high opioid prescription rates

have increased percentage of white and male population

and indeed, previous studies have documented that physi-

cians seem to be more reluctant to prescribe opioids to

black patients [23–26]. Poverty was negatively correlated

with high opioid prescription rates, but high poverty level

in the county strengthened the correlation between high

opioid prescription rates and opioid-related deaths. This

negative/positive correlation could be attributed to the

unavailability of substance use treatment services, inade-

quate or even lack of access to mental health providers,

naloxone restrictions and emergency medical services

challenges [26–28].

Regarding study limitations, the method of correlating

aggregate mortality data with aggregate opioid prescription

data across counties could provide inferior certainty in our

conclusions, compared to sampling data from actual cases.

Moreover, the Medicare Part D Opioid dataset only

includes opioid claims for approximately 60% of the ben-

eficiaries enrolled in the Medicare program and the detailed

data are limited to the years 2013–2014, and thus may not

accurately represent the whole of Medicare beneficiaries.

However, given the convergence of our findings regarding

socioeconomic characteristics to previous known results

and the necessity of an immediate response to the opioid

crisis, this study provides useful directions. Also, we per-

formed all analyses with each data year (2013 and 2014)

separately and yielded similar results to the combined

database. Notably, the beneficiaries of Medicare (the usual

age of eligibility is 65 years) account for approximately

15% of the total US population so the differences may be

attributable to differences in insurance coverage and it is

unknown if similar deviations in prescription patterns of

physicians exist in private insurance programs. In terms of

disabled patients who may be included in Medicare pop-

ulation and could have skewed our conclusions, although it

could be a limitation of our study since we did not have

raw data to stratify per comorbidities and disability, based

on published data, they have accounted for less than 10%

of Medicare population in 2013 and 2014 [29]. Finally, the

variability of the model with super-prescribers has been

partially explained with the included predictors. Although

it still indicates a true association between the opioid-re-

lated mortality and opioid prescription rate by the super-

prescribers, more variables should be included to optimize

the explanatory power of this model.

5 Conclusion

The opioid epidemic is a complex health crisis demanding

immediate action. The rate of opioid prescriptions is

associated with opioid deaths, at least among Medicare

enrollees, and, as new policies controlling opioid pre-

scriptions are debated and enacted, the initial focus should

be on specific categories of prescribers and especially on

those at the upper quartile of prescription rates. For most

categories of prescribers, policies and educational tools can

be grouped based on prescription patterns. Monitoring at a

county level can be effective and resources should priori-

tize to areas where socioeconomic parameters, such as

poverty, facilitate the connection between high prescription

rates and opioid-related deaths.

Author Contributions Guarantor of the article: CAG and EM

accept full responsibility for the conduct of the study, have access to

the data and have control of the decision to publish.

CAG and EM had full access to all of the data in the study and take

responsibility for the integrity of the data and the accuracy of the data

analysis. CAG: conceptualized and designed the study, performed the

literature search, participated in data collection, extraction and

interpretation, prepared tables and figures, performed the statistical

analysis, drafted the initial manuscript, approved the final manuscript

as submitted and agreed to be accountable for all aspects of the work

in ensuring that questions related to the accuracy or integrity of any

part of the work are appropriately investigated and resolved. SK:

conceptualized and designed the study, performed the literature

search, participated in data collection, extraction and interpretation,

prepared tables and figures, performed the statistical analysis, wrote

and drafted the initial manuscript, approved the final manuscript as

submitted and agreed to be accountable for all aspects of the work in

ensuring that questions related to the accuracy or integrity of any part

of the work are appropriately investigated and resolved. EV: partic-

ipated in literature search, participated in data collection, extraction

and interpretation, reviewed and revised the manuscript, approved the

final manuscript as submitted and agreed to be accountable for all

aspects of the work in ensuring that questions related to the accuracy

or integrity of any part of the work are appropriately investigated and

resolved. MA: participated in literature search, reviewed and revised

the manuscript, approved the final manuscript as submitted, and

agreed to be accountable for all aspects of the work in ensuring that

questions related to the accuracy or integrity of any part of the work

are appropriately investigated and resolved. MEF: participated in

literature search, reviewed and revised the manuscript, approved the

final manuscript as submitted, and agreed to be accountable for all




resolved. CKR: assisted in designing parts of the study, performed the


interpretation, reviewed and revised the manuscript, approved the




resolved. INE: assisted in designing parts of the study, performed the


interpretation, reviewed and revised the manuscript, approved the




resolved. PA: assisted in designing parts of the study, interpreted the

data, prepared tables and figures, performed the statistical analysis,

reviewed and revised the manuscript, approved the final manuscript as

submitted and agreed to be accountable for all aspects of the work in


of the work are appropriately investigated and resolved. CIS: con-

ceptualized and designed the study, interpreted the data, reviewed and

revised the manuscript, approved the final manuscript as submitted

and agreed to be accountable for all aspects of the work in ensuring

that questions related to the accuracy or integrity of any part of the

work are appropriately investigated and resolved. EM: Mylonakis

conceptualized and designed the study, interpreted the data, reviewed

and revised the manuscript, approved the final manuscript as sub-

mitted and agreed to be accountable for all aspects of the work in


of the work are appropriately investigated and resolved.

Compliance with Ethical Standards

Conflict of interest All authors [CAG, SK, EV, MA, MEF, CKR,

INE, PA, EM] declare no competing interests

Funding None.

Ethical approval and informed consent N/A.

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Supplementary Material

Sensitivity Analysis of opioid mortality association with prescription rates of super-prescribers

Physicians identified as “super-prescribers” if they belonged in the 75th

percentile of prescription

rates and “remaining” otherwise.

Estimate

SE

tStat

pValue

(Intercept) -1.820e-16 0.032 -5.598e-15 0.999

Remaining 0.071 0.033 2.162 0.030

Super-Prescribers 0.143 0.033 4.301 1.877e-05

Number of observations: 919, Error degrees of freedom: 916, Root Mean Squared Error: 0.99, R-

squared: 0.03, Adjusted R-Squared: 0.03, F-statistic vs. constant model: 14.17, p-value = 0.

Physicians identified as super-prescribers if they belonged in the 80th


rates

Estimate

SE

tStat

pValue

(Intercept) 1.733e-15 0.032 5.283e-14 0.999

Remaining 0.068 0.033 2.037 0.041






rates

Estimate

SE

tStat

pValue

(Intercept) 7.028e-16 0.033 2.116e-14 0.999

Remaining 0.081 0.033 2.429 0.015






rates

Estimate

SE

tStat

pValue

(Intercept) 3.965e-16 0.034 1.154e-14 0.999

Remaining 0.121 0.034 3.517 0.000

Super-Prescribers 0.103 0.034 3.000 0.002





rates

Estimate

SE

tStat

pValue

(Intercept) -1.060e-15 0.041 -2.526e-14 0.999

Remaining 0.231 0.042 5.498 5.975e-08

Super-Prescribers 0.139 0.042 3.322 0.000



Spatial Regression Analyses

REGRESSION

----------

SUMMARY OF OUTPUT: SPATIAL ERROR MODEL - MAXIMUM LIKELIHOOD

ESTIMATION

Data set : DS_v_2

Spatial Weight : DS_v_2

Dependent Variable : Methadone Number of Observations: 124

Mean dependent var : -0.177 Number of Variables : 9

S.D. dependent var : 0.691 Degrees of Freedom : 115

Lag coeff. (Lambda) : 0.427

R-squared : 0.389 R-squared (BUSE) : -

Sq. Correlation : - Log likelihood : -104.454

Sigma-square : 0.292 Akaike info criterion : 226.908

S.E of regression : 0.540 Schwarz criterion : 252.291

-----------------------------------------------------------------------------

Variable Coefficient Std.Error z-value Probability

-----------------------------------------------------------------------------

CONSTANT 0.668 0.192 3.471 0.000

Poverty 0.329 0.100 3.297 0.000

Male 0.291 0.191 1.518 0.128

White 0.258 0.095 2.7027 0.006

Black 0.074 0.093 0.802 0.422

Physicians -0.030 0.101 -0.300 0.763

popDensity 0.005 0.015 0.351 0.725

over65 0.145 0.084 1.726 0.084

Prescripti 0.435 0.221 1.967 0.049

LAMBDA 0.427 0.077 5.548 0.000

-----------------------------------------------------------------------------

REGRESSION DIAGNOSTICS

DIAGNOSTICS FOR HETEROSKEDASTICITY

RANDOM COEFFICIENTS

TEST DF VALUE PROB

Breusch-Pagan test 8 108.5154 0.000

DIAGNOSTICS FOR SPATIAL DEPENDENCE

SPATIAL ERROR DEPENDENCE FOR WEIGHT MATRIX : DS_v_2

TEST DF VALUE PROB

Likelihood Ratio Test 1 22.1881 0.000

============================== END OF REPORT

================================

REGRESSION

----------

SUMMARY OF OUTPUT: SPATIAL LAG MODEL - MAXIMUM LIKELIHOOD

ESTIMATION

Data set : DS_v_2





Lag coeff. (Rho) : 0.349

R-squared : 0.348 Log likelihood : -106.708

Sq. Correlation : - Akaike info criterion : 233.416

Sigma-square : 0.311 Schwarz criterion : 261.619

S.E of regression : 0.557

-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

W_Methadone 0.349 0.078 4.473 0.000

CONSTANT 0.639 0.186 3.433 0.000

Poverty 0.261 0.109 2.391 0.016

Male 0.273 0.194 1.409 0.158

White 0.229 0.099 2.301 0.021

Black 0.139 0.092 1.495 0.134

Physicians -0.058 0.106 -0.553 0.580

popDensity 0.008 0.014 0.609 0.542

over65 0.179 0.078 2.2883 0.022

Prescripti 0.387 0.217 1.782 0.074

-----------------------------------------------------------------------------



RANDOM COEFFICIENTS

TEST DF VALUE PROB



SPATIAL LAG DEPENDENCE FOR WEIGHT MATRIX : DS_v_2

TEST DF VALUE PROB


============================== END OF REPORT

================================

REGRESSION

----------

SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION

Data set : DS_v_2




R-squared : 0.210 F-statistic : 3.832

Adjusted R-squared : 0.155 Prob(F-statistic) : 0.000

Sum squared residual: 46.8095 Log likelihood : -115.548


S.E. of regression : 0.637 Schwarz criterion : 274.479

Sigma-square ML : 0.377

S.E of regression ML: 0.614

-----------------------------------------------------------------------------

Variable Coefficient Std.Error t-Statistic Probability

-----------------------------------------------------------------------------

CONSTANT 0.631 0.212 2.974 0.003

Poverty 0.231 0.124 1.856 0.065

Male 0.341 0.221 1.538 0.126

White 0.228 0.113 2.007 0.047

Black 0.170 0.106 1.608 0.110

Physicians 0.035 0.121 0.289 0.772

popDensity 0.009 0.016 0.563 0.574

over65 0.230 0.089 2.571 0.011

Prescripti 0.407 0.247 1.644 0.102

-----------------------------------------------------------------------------


MULTICOLLINEARITY CONDITION NUMBER 9.672

TEST ON NORMALITY OF ERRORS

TEST DF VALUE PROB

Jarque-Bera 2 263.8651 0.000


RANDOM COEFFICIENTS

TEST DF VALUE PROB


Koenker-Bassett test 8 23.7926 0.002


FOR WEIGHT MATRIX : DS_v_2

(row-standardized weights)

TEST MI/DF VALUE PROB

Moran's I (error) 0.3673 4.7648 0.000

Lagrange Multiplier (lag) 1 18.5596 0.000

Robust LM (lag) 1 0.0683 0.793

Lagrange Multiplier (error) 1 19.9929 0.000

Robust LM (error) 1 1.5016 0.220

Lagrange Multiplier (SARMA) 2 20.0612 0.000

============================== END OF REPORT

================================

REGRESSION

----------


ESTIMATION

Data set : DS_v_2


Dependent Variable : HeroinMor Number of Observations: 151

Mean dependent var : 0.035 Number of Variables : 9







-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

CONSTANT 0.547 0.206 2.651 0.008

Poverty 0.390 0.123 3.162 0.001

Male -0.002 0.218 -0.010 0.991

White 0.380 0.117 3.235 0.001

Black 0.108 0.118 0.910 0.362

Physicians -0.005 0.117 -0.043 0.965

popDensity -0.007 0.020 -0.339 0.734

over65 -0.028 0.102 -0.276 0.782

Prescripti 0.337 0.243 1.387 0.165

LAMBDA 0.488 0.062 7.800 0.000

-----------------------------------------------------------------------------



RANDOM COEFFICIENTS

TEST DF VALUE PROB




TEST DF VALUE PROB


============================== END OF REPORT

================================

REGRESSION

----------


ESTIMATION

Data set : DS_v_2










-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

W_HeroinMor 0.481 0.058 8.166 0.000

CONSTANT 0.701 0.199 3.515 0.000

Poverty 0.420 0.124 3.369 0.000

Male -0.010 0.210 -0.049 0.960

White 0.367 0.110 3.316 0.000

Black 0.175 0.110 1.589 0.111

Physicians -0.105 0.118 -0.893 0.371

popDensity -0.001 0.017 -0.110 0.912

over65 -0.003 0.090 -0.036 0.970

Prescripti 0.489 0.228 2.139 0.032

-----------------------------------------------------------------------------



RANDOM COEFFICIENTS

TEST DF VALUE PROB




TEST DF VALUE PROB


============================== END OF REPORT

================================

REGRESSION

----------


Data set : DS_v_2





Adjusted R-squared : 0.211 Prob(F-statistic) :1.187e-006






-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

CONSTANT 0.819 0.247 3.316 0.001

Poverty 0.545 0.154 3.536 0.000

Male -0.095 0.260 -0.364 0.715

White 0.594 0.135 4.373 0.000

Black 0.209 0.137 1.528 0.128

Physicians -0.186 0.146 -1.270 0.206

popDensity -0.009 0.022 -0.416 0.677

over65 -0.051 0.112 -0.457 0.648

Prescripti 0.451 0.283 1.590 0.114

-----------------------------------------------------------------------------




TEST DF VALUE PROB

Jarque-Bera 2 159.9630 0.000


RANDOM COEFFICIENTS

TEST DF VALUE PROB







Moran's I (error) 0.3874 5.3280 0.000


Robust LM (lag) 1 8.4345 0.003




============================== END OF REPORT

================================

REGRESSION

----------


ESTIMATION

Data set : DS_v_2


Dependent Variable : OtherOpMo Number of Observations: 179








-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

CONSTANT 0.264 0.110 2.390 0.016

Poverty 0.287 0.070 4.091 0.000

Male 0.042 0.114 0.368 0.712

White 0.206 0.072 2.869 0.004

Black -0.046 0.072 -0.637 0.523

Physicians -0.086 0.066 -1.298 0.194

popDensity -0.013 0.014 -0.953 0.340

over65 0.031 0.059 0.528 0.597

Prescripti 0.209 0.144 1.443 0.148

LAMBDA 0.700 0.037 18.7312 0.000

-----------------------------------------------------------------------------



RANDOM COEFFICIENTS

TEST DF VALUE PROB




TEST DF VALUE PROB


============================== END OF REPORT

================================

REGRESSION

----------


ESTIMATION

Data set : DS_v_2










-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

W_OtherOpMo 0.638 0.038 16.6045 0.000

CONSTANT 0.486 0.096 5.045 0.000

Poverty 0.379 0.064 5.882 0.000

Male 0.025 0.110 0.232 0.816

White 0.209 0.065 3.205 0.001

Black -0.028 0.066 -0.431 0.665

Physicians -0.219 0.063 -3.462 0.000

popDensity -0.011 0.011 -1.029 0.303

over65 0.055 0.048 1.155 0.247

Prescripti 0.258 0.132 1.946 0.051

-----------------------------------------------------------------------------



RANDOM COEFFICIENTS

TEST DF VALUE PROB




TEST DF VALUE PROB


============================== END OF REPORT

================================

REGRESSION

----------


Data set : DS_v_2











-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

CONSTANT 0.977 0.162 6.008 0.000

Poverty 0.835 0.106 7.878 0.000

Male -0.005 0.187 -0.026 0.978

White 0.337 0.110 3.044 0.002

Black -0.154 0.112 -1.371 0.171

Physicians -0.319 0.108 -2.951 0.003

popDensity -0.031 0.018 -1.696 0.091

over65 0.094 0.082 1.150 0.251

Prescripti 0.589 0.225 2.611 0.009

-----------------------------------------------------------------------------




TEST DF VALUE PROB

Jarque-Bera 2 3704.5592 0.000


RANDOM COEFFICIENTS

TEST DF VALUE PROB







Moran's I (error) 0.5609 8.2952 0.000


Robust LM (lag) 1 47.3559 0.000




============================== END OF REPORT

================================

REGRESSION

----------


ESTIMATION

Data set : DS_v_2


Dependent Variable : SynthMor Number of Observations: 181








-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

CONSTANT 0.745 0.112 6.606 0.000

Poverty 0.484 0.073 6.600 0.000

Male 0.039 0.110 0.359 0.719

White 0.427 0.074 5.707 0.000

Black -0.010 0.075 -0.145 0.884

Physicians -0.211 0.069 -3.062 0.002

popDensity -0.018 0.014 -1.283 0.199

over65 0.051 0.061 0.846 0.397

Prescripti 0.301 0.151 1.993 0.046

LAMBDA 0.655 0.042 15.5363 0.000

-----------------------------------------------------------------------------



RANDOM COEFFICIENTS

TEST DF VALUE PROB




TEST DF VALUE PROB


============================== END OF REPORT

================================

REGRESSION

----------


ESTIMATION

Data set : DS_v_2










-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

W_SynthMor 0.574 0.039 14.6933 0.000

CONSTANT 0.847 0.097 8.649 0.000

Poverty 0.526 0.067 7.855 0.000

Male 0.095 0.103 0.923 0.355

White 0.413 0.067 6.119 0.000

Black 0.041 0.067 0.617 0.537

Physicians -0.317 0.064 -4.900 0.000

popDensity -0.012 0.011 -1.104 0.269

over65 0.081 0.048 1.6712 0.094

Prescripti 0.323 0.136 2.369 0.017

-----------------------------------------------------------------------------



RANDOM COEFFICIENTS

TEST DF VALUE PROB




TEST DF VALUE PROB


============================== END OF REPORT

================================

REGRESSION

----------


Data set : DS_v_2











-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

CONSTANT 1.287 0.142 9.007 0.000

Poverty 0.907 0.096 9.4173 0.000

Male -0.087 0.155 -0.564 0.572

White 0.616 0.100 6.145 0.000

Black -0.040 0.100 -0.397 0.691

Physicians -0.425 0.098 -4.340 0.000

popDensity -0.034 0.016 -2.045 0.042

over65 0.097 0.074 1.3201 0.188

Prescripti 0.591 0.205 2.8823 0.004

-----------------------------------------------------------------------------




TEST DF VALUE PROB

Jarque-Bera 2 974.7218 0.000


RANDOM COEFFICIENTS

TEST DF VALUE PROB







Moran's I (error) 0.4572 6.8760 0.000


Robust LM (lag) 1 39.0484 0.000




============================== END OF REPORT

================================

REGRESSION

----------


ESTIMATION

Data set : DS_v_2


Dependent Variable : AllOpiMor Number of Observations: 832








-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

CONSTANT 0.088 0.057 1.546 0.121

Poverty 0.339 0.037 9.006 0.000

Male -0.002 0.050 -0.050 0.959

White 0.227 0.053 4.261 0.000

Black -0.049 0.055 -0.880 0.378

Physicians -0.008 0.028 -0.292 0.769

popDensity 0.001 0.017 0.101 0.919

over65 0.041 0.035 1.159 0.246

Prescripti 0.277 0.059 4.646 0.000

LAMBDA 0.617 0.025 23.89 0.000

-----------------------------------------------------------------------------



RANDOM COEFFICIENTS

TEST DF VALUE PROB




TEST DF VALUE PROB


============================== END OF REPORT

================================

REGRESSION

----------


ESTIMATION

Data set : DS_v_2










-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

W_AllOpiMor 0.566 0.026 21.7461 0.000

CONSTANT 0.188 0.034 5.394 0.000

Poverty 0.283 0.031 9.103 0.000

Male -0.036 0.050 -0.726 0.467

White 0.160 0.037 4.225 0.000

Black 0.003 0.042 0.092 0.926

Physicians -0.070 0.028 -2.491 0.012

popDensity 0.007 0.012 0.549 0.582

over65 0.026 0.029 0.892 0.371

Prescripti 0.276 0.054 5.058 0.000

-----------------------------------------------------------------------------



RANDOM COEFFICIENTS

TEST DF VALUE PROB




TEST DF VALUE PROB


============================== END OF REPORT

================================

REGRESSION

----------


Data set : DS_v_2





Adjusted R-squared : 0.348 Prob(F-statistic) : 0






-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

CONSTANT 0.326 0.045 7.192 0.000

Poverty 0.542 0.038 14.0568 0.000

Male -0.120 0.066 -1.820 0.068

White 0.272 0.048 5.620 0.000

Black -0.083 0.054 -1.519 0.129

Physicians -0.068 0.036 -1.856 0.063

popDensity -0.000 0.016 -0.015 0.987

over65 -0.006 0.037 -0.182 0.854

Prescripti 0.484 0.070 6.834 0.000

-----------------------------------------------------------------------------




TEST DF VALUE PROB

Jarque-Bera 2 15062.8995 0.000


RANDOM COEFFICIENTS

TEST DF VALUE PROB







Moran's I (error) 0.4756 17.3304 0.000


Robust LM (lag) 1 51.8084 0.000




============================== END OF REPORT

================================

REGRESSION

----------


ESTIMATION

Data set : DS_v_2


Dependent Variable : Prescripti Number of Observations: 2710





Sq. Correlation : - Log likelihood :-3370.126



-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

CONSTANT 0.003 0.026 0.143 0.885

Poverty 0.034 0.024 1.407 0.159

Male 0.049 0.017 2.795 0.005

White 0.118 0.032 3.600 0.000

Black -0.175 0.031 -5.525 0.000

Physicians -0.182 0.015 -11.4965 0.000

popDensity -0.015 0.019 -0.807 0.419

over65 0.186 0.020 9.010 0.000

LAMBDA 0.398 0.025 15.6241 0.000

-----------------------------------------------------------------------------



RANDOM COEFFICIENTS

TEST DF VALUE PROB




TEST DF VALUE PROB


============================== END OF REPORT

================================

REGRESSION

----------


ESTIMATION

Data set : DS_v_2










-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

W_Prescripti 0.388 0.024 15.9371 0.000

CONSTANT -0.002 0.015 -0.1374 0.890

Poverty 0.001 0.019 0.053 0.957

Male 0.050 0.017 2.929 0.003

White 0.114 0.023 4.830 0.000

Black -0.111 0.023 -4.797 0.000

Physicians -0.184 0.016 -11.5218 0.000

popDensity -0.015 0.015 -1.001 0.316

over65 0.167 0.017 9.483 0.000

-----------------------------------------------------------------------------



RANDOM COEFFICIENTS

TEST DF VALUE PROB




TEST DF VALUE PROB


============================== END OF REPORT

================================

REGRESSION

----------


Data set : DS_v_2





Adjusted R-squared : 0.212 Prob(F-statistic) : 0






-----------------------------------------------------------------------------


-----------------------------------------------------------------------------

CONSTANT -0.007 0.016 -0.460 0.645

Poverty -0.011 0.020 -0.567 0.570

Male 0.082 0.018 4.544 0.000

White 0.158 0.025 6.290 0.000

Black -0.189 0.024 -7.846 0.000

Physicians -0.154 0.017 -9.052 0.000

popDensity -0.026 0.016 -1.567 0.117

over65 0.192 0.018 10.3202 0.000

-----------------------------------------------------------------------------




TEST DF VALUE PROB

Jarque-Bera 2 76925.9510 0.000


RANDOM COEFFICIENTS

TEST DF VALUE PROB







Moran's I (error) 0.1907 16.5474 0.000


Robust LM (lag) 1 51.1279 0.000




============================== END OF REPORT

================================

correlation of opioid mortality with prescriptions and social determinants -a cross-sectional study...

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