Inter-regional patient mobility and the spatialaccessibility of primary healthcare

Does distance go far enough?

Dieter Pennerstorfer1 and Anna-Theresa Renner2

1 Johannes Kepler University Linz2 Vienna University of Economics and Business

June 27th 2019

eeecon research seminar

University of Innsbruck

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General ObjectiveInter-regional flow data are typically analyzed by gravity-typemodels of the following form form, with distance as a proxy fortransportation costs, driving time or connectivity:

Yi ,j =Mβii ×M

βjj

distβdisti,j

Distance a good proxy? What is the ideal level of regionalaggregation?

I detailed flow data unavailable due to privacy issues(commuting to work or school, patient flows, ...) or becausedata is not recorded (trade, shopping tourism, ...)

I but data on supply and demand often easily accessible!

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General ObjectiveInter-regional flow data are typically analyzed by gravity-typemodels of the following form form, with distance as a proxy fortransportation costs, driving time or connectivity:

Yi ,j =Mβii ×M

βjj

distβdisti,j

Distance a good proxy? What is the ideal level of regionalaggregation?

I detailed flow data unavailable due to privacy issues(commuting to work or school, patient flows, ...) or becausedata is not recorded (trade, shopping tourism, ...)

I but data on supply and demand often easily accessible!

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General ObjectiveInter-regional flow data are typically analyzed by gravity-typemodels of the following form form, with distance as a proxy fortransportation costs, driving time or connectivity:

Yi ,j =Mβii ×M

βjj

distβdisti,j

Distance a good proxy? What is the ideal level of regionalaggregation?

I detailed flow data unavailable due to privacy issues(commuting to work or school, patient flows, ...) or becausedata is not recorded (trade, shopping tourism, ...)

I but data on supply and demand often easily accessible!

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General Objective: Illustration

Note: See Hornak, Struhar and Psenka, 2015, Figure 1

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General Objective: Illustration

Note: See Hornak, Struhar and Psenka, 2015, Figure 1

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Specific Objective

To model inter-regional patient flows using a refined measure ofavailability & spatial accessibility of public outpatient healthcare

I Is district level centroid-to-centroid distance an appropriatemeasure for spatial accessibility?

I How accurately can we predict inter-regional patient flowswithin a healthcare system based on geographic accessibility?

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Relevance

I General: extension to the usually employed gravity model

I Augment gravity model with indicator of accessibility based onregionally disaggregated, but easily available data to improvemodel fit and model predictions

I Method can be applied to other fields of regional science (e.g.consumer flows to commercial centres, work migration versuscommuting)

I Linking of datasets with different levels of aggregationreflecting different levels of sensitivity (privacy concerns)

I Specific: peculiarities of health care

I Expected shortage of general practitioners due to retirement of”baby boomers”

I Rural areas facing depopulation which fuels demographicchange

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Media Attention

Kurier

Welt

Heute

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Institutional background

Austrian outpatient healthcare providers:

I Self-employed private and public outpatient physicians

I Free location choice for private physicians

I Placement plan for public (i.e. contracted) physicians

Healthcare utilization:

I Free provider choice for patients

I No spatial restrictions

I No / negligible co-payments for public physician services

I Out-of-pocket payments for private physician services (partialreimbursement possible)

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Data sources

District pair level data: (115 × 115 observations)

I Patient contacts with public physicians (Main association ofthe Austrian Social Security Funds)

I Distances between districts (ArcData Austria 2016)

I Commuters (Statistik Austria)

Grid / point level data:

I Locations of (4,083) public and (4,684) private physicians(dexhelpp/TU Wien - web-scraping)

I Population grid data at 250m × 250m level (Statistik Austria)

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Inter-regional patient flows

Around 13.7% of patients see GP in another district

Figure 1: Scatterplot of distance and share of first GP contacts if > 1%

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Private and public GPs’ Locations

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Methodological background

Utilization data (i.e. patient flows) available at regional level

Gravity model usually used for analyzing spatial interactions

I Demand at location i is attracted by mass of productionfactors supplied at region j

I Resulting trade flows is reduced by distance between i and j

BUT!

I Does not account for distribution of supply (i.e. doctors) andof population within a region

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An illustrative example with three regions

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An illustrative example with three regions

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Floating catchment areas

Step 1

Rl =1∑

m Pm ∗ f (distl,m)(1)

with∂f (distl,m)

∂distl,m≤ 0 and f (distl,m) = 0 if distl,m > distmax

Step 2

Ak =∑l

Rl ∗ f (distk,l) (2)

with∂f (distk,l )

∂distk,l≤ 0 and f (distk,l) = 0 if distk,l > distmax

k (Potential) patient

l Physician

Pm Population in location m

dist Distance between physician and patient

distmax Size of catchment area

Rl Degree of outpatient physician service provision of physician l

Ak Accessibility level of patiant k

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Accessibility measure: Intuition

I Accessibility measure Ak is calculated for each potentialpatient k

I Accessibility is higher ifI there are more GPs in the patient’s neighborhoodI the GPs are located closer to the patient’s place of residenceI there are fewer patients within the GPs’ catchment areas

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2SFCA - Power 1.85

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2SFCA - Power 0.3

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Floating catchment areas (continued)

Rl =1∑

m Pm ∗ f (distl,m)(1)

Ak =∑l

Rl ∗ f (distk,l) (2)

Note: Ak is individual (patient) specific ⇒ need accessibility measure at a

district × district level!

Ak,v =∑

l∈V Rl ∗ f (distk,l) with Ak =∑

v Ak,v

⇒ Ak,v is individual × district specific

Au,v =∑

k∈U Ak,v

Pu

⇒ Au,v is district × district specific

Au,v measures the average access level of (potential) patientslocated in district u to public physicians of district v

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An illustrative example with three regions

Au,v

Initial situation:

Au,v increases if:

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Regression model

E (yGPu,v |X u,v ) = exp

(β1f (distu,v ) + β2A

pubu,v + β3A

priu,v + β4Cu,v + τu + τv

)

with Au,v =∑k∈U

Pk

∑l∈V

Rl ∗ f (distk,l)

u Region of the patient

v Region of the physician

yGPu,v Number of first contacts of patients from region u with GP in region v

f (distu,v ) Distance decay function between district u and v , with∂f (distu,v∂distu,v≤0

and f (distu,v ) = 0 if distu,v > distmax

Apubu,v Average access level to public physicians of district v for patients located in district u

Apriu,v Average access level to private physicians of district v for patients located in district u

Cu,v Number of commuters from region u to region

τu , τv Patient’s and physician’s region fixed effects

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Empirical strategy

1. Calculate different 2SFCA for each patient location (grid cell)

2. Derive accessibility measure for each district pair

3. Model inter-regional patient flows usingI Model 1: distance function onlyI Model 2: add 2SFCA as measures of accessibilityI Model 3: add commuting flows (full model)I Patient and physician region fixed effects in all models

4. Select model with best fit (adjusted R-squared and BIC)

5. Predict patient flows following changes in physician locations

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Results - Model selection

Model 1 Model 2 Model 3

Adj R-sq BIC Adj R-sq BIC Adj R-sq BIC

Power 1.85 0.03 153,360,310 0.97 11,269,306 0.99 8,979,335

Power 1 0.29 104,254,091 0.94 12,496,035 0.98 8,368,319

Power 0.7 0.47 69,813,302 0.93 12,257,716 0.98 7,310,973

Power 0.3 0.57 38,769,412 0.89 14,102,269 0.97 5,830,060

Gauss 10 0.04 37,264,491 0.96 11,945,747 0.98 8,814,681

Gauss 50 0.19 74,381,001 0.94 12,596,777 0.98 8,441,677

Gauss 200 0.30 124,089,690 0.86 17,056,686 0.97 8,042,767

Gauss 500 0.54 147,308,308 0.79 20,341,865 0.96 8,073,544

Logistic 0.5 0.23 94,642,587 0.91 12,976,540 0.98 7,788,743

Logistic 7.5 0.32 73,781,853 0.88 15,148,331 0.97 7,777,371

Logistic 15 0.41 49,582,090 0.81 19,634,262 0.97 8,127,423

Logistic 25 0.54 32,050,862 0.69 25,252,420 0.95 8,872,462

Notes: All models estimated with Poisson regression and include patient and physician regional fixed effects.R-squared is variance-function-based and adjusted for model size (Zhang, 2016)

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Results - RegressionsPower 0.3 distance decay function Model 1 Model 2 Model 3

Distance decay 29.67*** 11.43*** 8.78***(1.46) (0.72) (0.34)

Accessibility of public GPs - 107.68*** 22.09***(7.03) (2.20)

Accessibility of private GPs - -0.76 -6.46***(3.51) (0.60)

Commuters - - 18.43***(0.71)

Adjusted R2 0.57 0.89 0.97BIC 38,769,412 14,102,269 5,830,060

Power 1.85 distance decay function Model 1 Model 2 Model 3

Distance decay 13.29*** 0.84*** 1.5 ***(2.66) (0.19) (0.16)

Accessibility of public GPs - 16.15*** 8.86***(0.63) (0.53)

Accessibility of private GPs - 1.18 -0.67(0.82) (0.40)

Commuters - - 16.04***(1.17 )

Adjusted R2 0.03 0.97 0.99BIC 153,360,310 11,269,306 8,979,335

∗∗∗p < 0.001, ∗∗p < 0.01, ∗p < 0.05. All models estimated with a Poisson regression and included patient andphysician regional fixed effects. Standard errors in parenthesis are based on sandwich covariance matrix estimator.

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Summary of results

I Accessibility of public physicians consistently positivelyassociated with share of patient flows in public sector

I Accessibility of private physicians sign. associated with lowershare of public patient flows in public sector → substitutioneffect?

I Commuting as a proxy for social and economic ties explainspart of variation in patient flows between two regions

I Adding 2SFCA considerably improves model fit

I Direction and significance of coefficients robust to changes off (dist)

I For predictions, results of full model do not depend so muchon choice of f (dist)

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Limitations and outlook

I Better foundation of distance decay function

I Simulations

I Subsample analysis for gender and age groups

I Analyze utilization of specialists

I Include accessibility of hospitals

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Thank you!

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Distance decay functions

Power function:dist−β (3)

β = 1.85 (‘Power 1.85’), 1 (‘Power 1’), 0.7 (‘Power 0.7’), 0.5 (‘Power 0.5’), and 0.3 (‘Power 0.3’).

Gaussian function:

e−dist2

β (4)

β = 500 (‘Gauss 500’), 200 (‘Gauss 200’), 50 (‘Gauss 50’) and 10 (‘Gauss 10’).

Logistic function:

1 + e− βπ

10√

3

1 + e(dist−β)π

10√

3

(5)

β = 25 (‘Logistic 25’) , 15 (‘Logistic 15’), 7.5 (‘Logistic 7.5’), 2.5 (‘Logistic 2.5’), and 0.5 (‘Logistic 0.5’).

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Distance decay functions

(a) Power 1.85 (b) Power 1 (c) Power 0.3

(d) Gauss 500 (e) Gauss 200 (f) Gauss 50

(g) Logistic 25 (h) Logistic 7.5 (i) Logistic 0.5

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Summary statistics

Variable Mean (SD)

Patient flows from district u to v 1,608.00 (16,978.59)

Share of patients from u to v on total patients from u (%) 0.87 (0.08)

Share of commuters from district u to v per 1,000 population 4.1 (26.16)

2SFCA for public physicians per 1,000 population

Power 1.85 4.30E-03 (3.96E-02)

Power 0.3 4.04E-03 (1.41E-02)

Gauss 10 4.35E-03 (4.07E-02)

Gauss 500 4.11E-03 (2.02E-02)

Logistic 0.5 4.25E-03 (2.79E-02)

Logistic 25 4.10E-03 (1.90E-02)

2SFCA for private physicians per 1,000 population

Power 1.85 5.07E-03 (5.33E-02)

Power 0.3 4.66E-03 (2.15E-02)

Gauss 10 4.92E-03 (5.12E-02)

Gauss 500 4.60E-03 (2.70E-02)

Logistic 0.5 4.69E-03 (3.61E-02)

Logistic 25 4.61E-03 (2.59E-02)

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