Title: Reproduction of Spatial Accessibility of COVID-19 Healthcare Resources in Illinois¶

Reproduction of: Rapidly measuring spatial accessibility of COVID-19 healthcare resources: a case study of Illinois, USA

Original study by Kang, J. Y., A. Michels, F. Lyu, Shaohua Wang, N. Agbodo, V. L. Freeman, and Shaowen Wang. 2020. Rapidly measuring spatial accessibility of COVID-19 healthcare resources: a case study of Illinois, USA. International Journal of Health Geographics 19 (1):1–17. DOI:10.1186/s12942-020-00229-x.

Reproduction Authors: Joe Holler, Derrick Burt, and Kufre Udoh With contributions from Peter Kedron, Drew An-Pham, and the Spring 2021 Open Source GIScience class at Middlebury, Isaiah Bennett

Reproduction Materials Available at: github.com/HEGSRR/RPr-Kang-2020

Created: 2021-06-01 Revised: 2023-11-09

Original Study Design¶

The original Kang et al. (2020) is a network analysis that investigates the access to COVID-19 related healthcare resources in the state of Illinois. This network analysis uses hospital point location data with their capacity represented by ICU beds, and ventilators, OSM road networks, population data with the at risk population represented by ages over 50, and COVID19 case data. First they calculate catchment areas for each hospital to show distances for where the hospital is accessible within radii of 10, 20, and 30 minutes assigning them weights of 1, 0.68, and 0.22 respectively. Centroid points are then created for both the at risk population data and COVID-19 cases. They next calculate a weighted service ratio by executing a spatial join with the population centroids and the weighted hospital catchment polygons. The weighted service ratios are then aggregated to a grid of hexagons that is rescaled on a spectrum of 0 to 1 where 1 is the greatest accessibility to healthcare resources. Our original reproduction of Kang et al. (2020) was partially successful in reproducing the results of the Kang et al. (2020) by focusing on only the extent of the city of Chicago instead of all of Illinois to adapt to the storage capacity of Github repositories since the files for all of the state were too large. While our reproduction did have a Spearman's Rho of 0.532 it identified areas for improvement which this reanalysis focuses on. First is fixing the boundary issue by buffering the extent of the road network to expand outside the city to include any roads or populations that might access hospitals within the city boundaries. Second is to improve the uncertainty from generalizing all roads with unknown speed limits to 35mph, by using speed limits by road types from the osmnx package. Lastly, they identified the opportunity to improve accuracy by changing the method of aggregating data into the hexagons to an area weighted reaggregation instead of using the threshold of measuring if the service polygons cover over 50% of the hexagon.

Reanalysis¶

This reanalysis makes three big changes to improve reproducibility and develop scientific discovery:

  1. Expanding the road network 15 miles outside the city to address boundary issues
  2. Replacing missing speed limit values based on OSMNX road type speed limits
  3. Implementing an Area Weighted Reaggregation for the aggregation of data into the hexagonal grid

Original Data¶

To perform the ESFCA method, three types of data are required, as follows: (1) road network, (2) population, and (3) hospital information. The road network can be obtained from the OpenStreetMap Python Library, called OSMNX. The population data is available on the American Community Survey. Lastly, hospital information is also publically available on the Homelanad Infrastructure Foundation-Level Data.

Modules¶

Import necessary libraries to run this model. See environment.yml for the library versions used for this analysis.

In [2]:
# Import modules
import numpy as np
import pandas as pd
import geopandas as gpd
import networkx as nx
import osmnx as ox
import re
from shapely.geometry import Point, LineString, Polygon
import matplotlib.pyplot as plt
from tqdm import tqdm
import multiprocessing as mp
import folium
import itertools
import os
import time
import warnings
import IPython
import requests
from IPython.display import display, clear_output

warnings.filterwarnings("ignore")
print('\n'.join(f'{m.__name__}=={m.__version__}' for m in globals().values() if getattr(m, '__version__', None)))
numpy==1.22.0
pandas==1.3.5
geopandas==0.10.2
networkx==2.6.3
osmnx==1.1.2
re==2.2.1
folium==0.12.1.post1
IPython==8.3.0
requests==2.27.1

Check Directories¶

Because we have restructured the repository for replication, we need to check our working directory and make necessary adjustments.

In [3]:
# Check working directory
os.getcwd()
Out[3]:
'/home/jovyan/work/RPr-Kang-2020/procedure/code'
In [4]:
# Use to set work directory properly
if os.path.basename(os.getcwd()) == 'code':
    os.chdir('../../')
os.getcwd()
Out[4]:
'/home/jovyan/work/RPr-Kang-2020'

Load and Visualize Data¶

Population and COVID-19 Cases Data by County¶

'Cases' column is coming in as 'Unnamed_0' --> easy to rename but this probably should be reportede to the original authors

If you would like to use the data generated from the pre-processing scripts, use the following code:

covid_data = gpd.read_file('./data/raw/public/Pre-Processing/covid_pre-processed.shp')
atrisk_data = gpd.read_file('./data/raw/public/Pre-Processing/atrisk_pre-processed.shp')
In [5]:
# Read in at risk population data
atrisk_data = gpd.read_file('./data/raw/public/PopData/Illinois_Tract.shp')
atrisk_data.head()
Out[5]:
GEOID STATEFP COUNTYFP TRACTCE NAMELSAD Pop Unnamed_ 0 NAME OverFifty TotalPop geometry
0 17091011700 17 091 011700 Census Tract 117 3688 588 Census Tract 117, Kankakee County, Illinois 1135 3688 POLYGON ((-87.88768 41.13594, -87.88764 41.136...
1 17091011800 17 091 011800 Census Tract 118 2623 220 Census Tract 118, Kankakee County, Illinois 950 2623 POLYGON ((-87.89410 41.14388, -87.89400 41.143...
2 17119400951 17 119 400951 Census Tract 4009.51 5005 2285 Census Tract 4009.51, Madison County, Illinois 2481 5005 POLYGON ((-90.11192 38.70281, -90.11128 38.703...
3 17119400952 17 119 400952 Census Tract 4009.52 3014 2299 Census Tract 4009.52, Madison County, Illinois 1221 3014 POLYGON ((-90.09442 38.72031, -90.09360 38.720...
4 17135957500 17 135 957500 Census Tract 9575 2869 1026 Census Tract 9575, Montgomery County, Illinois 1171 2869 POLYGON ((-89.70369 39.34803, -89.69928 39.348...
In [6]:
# Read in covid case data
covid_data = gpd.read_file('./data/raw/public/PopData/Chicago_ZIPCODE.shp')
covid_data['cases'] = covid_data['cases']
covid_data.head()
Out[6]:
ZCTA5CE10 County State Join ZONE ZONENAME FIPS pop cases geometry
0 60660 Cook County IL Cook County IL IL_E Illinois East 1201 43242 78 POLYGON ((-87.65049 41.99735, -87.65029 41.996...
1 60640 Cook County IL Cook County IL IL_E Illinois East 1201 69715 117 POLYGON ((-87.64645 41.97965, -87.64565 41.978...
2 60614 Cook County IL Cook County IL IL_E Illinois East 1201 71308 134 MULTIPOLYGON (((-87.67703 41.91845, -87.67705 ...
3 60712 Cook County IL Cook County IL IL_E Illinois East 1201 12539 42 MULTIPOLYGON (((-87.76181 42.00465, -87.76156 ...
4 60076 Cook County IL Cook County IL IL_E Illinois East 1201 31867 114 MULTIPOLYGON (((-87.74782 42.01540, -87.74526 ...

Load Hospital Data¶

Note that 999 is treated as a "NULL"/"NA" so these hospitals are filtered out. This data contains the number of ICU beds and ventilators at each hospital.

In [7]:
# Read in hospital data
hospitals = gpd.read_file('./data/raw/public/HospitalData/Chicago_Hospital_Info.shp')
hospitals.head()
Out[7]:
FID Hospital City ZIP_Code X Y Total_Bed Adult ICU Total Vent geometry
0 2 Methodist Hospital of Chicago Chicago 60640 -87.671079 41.972800 145 36 12 MULTIPOINT (-87.67108 41.97280)
1 4 Advocate Christ Medical Center Oak Lawn 60453 -87.732483 41.720281 785 196 64 MULTIPOINT (-87.73248 41.72028)
2 13 Evanston Hospital Evanston 60201 -87.683288 42.065393 354 89 29 MULTIPOINT (-87.68329 42.06539)
3 24 AMITA Health Adventist Medical Center Hinsdale Hinsdale 60521 -87.920116 41.805613 261 65 21 MULTIPOINT (-87.92012 41.80561)
4 25 Holy Cross Hospital Chicago 60629 -87.690841 41.770001 264 66 21 MULTIPOINT (-87.69084 41.77000)

Generate and Plot Map of Hospitals¶

In [8]:
# Plot hospital data
m = folium.Map(location=[41.85, -87.65], tiles='cartodbpositron', zoom_start=10)
for i in range(0, len(hospitals)):
    folium.CircleMarker(
      location=[hospitals.iloc[i]['Y'], hospitals.iloc[i]['X']],
      popup="{}{}\n{}{}\n{}{}".format('Hospital Name: ',hospitals.iloc[i]['Hospital'],
                                      'ICU Beds: ',hospitals.iloc[i]['Adult ICU'],
                                      'Ventilators: ', hospitals.iloc[i]['Total Vent']),
      radius=5,
      color='blue',
      fill=True,
      fill_opacity=0.6,
      legend_name = 'Hospitals'
    ).add_to(m)
legend_html =   '''<div style="position: fixed; width: 20%; heigh: auto;
                            bottom: 10px; left: 10px;
                            solid grey; z-index:9999; font-size:14px;
                            ">&nbsp; Legend<br>'''

m
Out[8]:
Make this Notebook Trusted to load map: File -> Trust Notebook

Load and Plot Hexagon Grids (500-meter resolution)¶

In [9]:
# Read in and plot grid file for Chicago
grid_file = gpd.read_file('./data/raw/public/GridFile/Chicago_Grid.shp')
grid_file.plot(figsize=(8,8))
Out[9]:
<AxesSubplot:>

Load the Road Network¶

If Chicago_Network_Buffer.graphml does not already exist, this cell will query the road network from OpenStreetMap.

Each of the road network code blocks may take a few mintues to run.

In [10]:
%%time
# To create a new graph from OpenStreetMap, delete or rename data/raw/private/Chicago_Network_Buffer.graphml 
# (if it exists), and set OSM to True 
OSM = False

# if buffered street network is not saved, and OSM is preferred, # generate a new graph from OpenStreetMap and save it
if not os.path.exists("./data/raw/private/Chicago_Network_Buffer.graphml") and OSM:
    print("Loading buffered Chicago road network from OpenStreetMap. Please wait... runtime may exceed 9min...", flush=True)
    G = ox.graph_from_place('Chicago', network_type='drive', buffer_dist=24140.2) 
    print("Saving Chicago road network to raw/private/Chicago_Network_Buffer.graphml. Please wait...", flush=True)
    ox.save_graphml(G, './data/raw/private/Chicago_Network_Buffer.graphml')
    print("Data saved.")

# otherwise, if buffered street network is not saved, download graph from the OSF project
elif not os.path.exists("./data/raw/private/Chicago_Network_Buffer.graphml"):
    print("Downloading buffered Chicago road network from OSF...", flush=True)
    url = 'https://osf.io/download/z8ery/'
    r = requests.get(url, allow_redirects=True)
    print("Saving buffered Chicago road network to file...", flush=True)
    open('./data/raw/private/Chicago_Network_Buffer.graphml', 'wb').write(r.content)

# if the buffered street network is already saved, load it
if os.path.exists("./data/raw/private/Chicago_Network_Buffer.graphml"):
    print("Loading buffered Chicago road network from raw/private/Chicago_Network_Buffer.graphml. Please wait...", flush=True)
    G = ox.load_graphml('./data/raw/private/Chicago_Network_Buffer.graphml') 
    print("Data loaded.") 
else:
    print("Error: could not load the road network from file.")
Loading buffered Chicago road network from raw/private/Chicago_Network_Buffer.graphml. Please wait...
Data loaded.
CPU times: user 39.2 s, sys: 1.67 s, total: 40.9 s
Wall time: 41 s

Plot the Road Network¶

In [11]:
%%time
ox.plot_graph(G, node_size = 1, bgcolor = 'white', node_color = 'black', edge_color = "#333333", node_alpha = 0.5, edge_linewidth = 0.5)
CPU times: user 58.5 s, sys: 373 ms, total: 58.9 s
Wall time: 58.7 s
Out[11]:
(<Figure size 576x576 with 1 Axes>, <AxesSubplot:>)

Check speed limit values¶

Display all the unique speed limit values and count how many network edges (road segments) have each value. We will compare this to our cleaned network later.

In [12]:
%%time
# Turn nodes and edges into geodataframes
nodes, edges = ox.graph_to_gdfs(G, nodes=True, edges=True)

# Get unique counts of road segments for each speed limit
print(edges['maxspeed'].value_counts())
print(str(len(edges)) + " edges in graph")

# can we also visualize highways / roads with higher speed limits to check accuracy?
# the code above converts the graph into an edges geodataframe, which could theoretically be filtered
# by fast road segments and mapped, e.g. in folium
25 mph                        4793
30 mph                        3555
35 mph                        3364
40 mph                        2093
45 mph                        1418
20 mph                        1155
55 mph                         614
60 mph                         279
50 mph                         191
40                              79
15 mph                          76
70 mph                          71
65 mph                          54
10 mph                          38
[40 mph, 45 mph]                27
[30 mph, 35 mph]                26
45,30                           24
[40 mph, 35 mph]                22
70                              21
25                              20
[55 mph, 45 mph]                16
25, east                        14
[45 mph, 35 mph]                13
[30 mph, 25 mph]                10
[45 mph, 50 mph]                 8
50                               8
[40 mph, 30 mph]                 7
[35 mph, 25 mph]                 6
[55 mph, 60 mph]                 5
20                               4
[70 mph, 60 mph]                 3
[65 mph, 60 mph]                 3
[40 mph, 45 mph, 35 mph]         3
[70 mph, 65 mph]                 2
[70 mph, 45 mph, 5 mph]          2
[40, 45 mph]                     2
[35 mph, 50 mph]                 2
35                               2
[55 mph, 65 mph]                 2
[40 mph, 50 mph]                 2
[15 mph, 25 mph]                 2
[40 mph, 35 mph, 25 mph]         2
[15 mph, 40 mph, 30 mph]         2
[20 mph, 25 mph]                 2
[30 mph, 25, east]               2
[65 mph, 55 mph]                 2
[20 mph, 35 mph]                 2
[55 mph, 55]                     2
55                               2
[15 mph, 30 mph]                 2
[45 mph, 30 mph]                 2
[15 mph, 45 mph]                 2
[55 mph, 45, east, 50 mph]       2
[20 mph, 30 mph]                 1
[5 mph, 45 mph, 35 mph]          1
[55 mph, 35 mph]                 1
[5 mph, 35 mph]                  1
[55 mph, 50 mph]                 1
Name: maxspeed, dtype: int64
384240 edges in graph
CPU times: user 36.6 s, sys: 97.9 ms, total: 36.7 s
Wall time: 36.6 s
In [13]:
edges.head()
Out[13]:
osmid highway oneway length name geometry lanes ref bridge maxspeed access service tunnel junction width area
u v key
261095436 261095437 0 24067717 residential False 46.873 NaN LINESTRING (-87.90237 42.10571, -87.90198 42.1... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
261095437 261095439 0 24067717 residential False 46.317 NaN LINESTRING (-87.90198 42.10540, -87.90159 42.1... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
261095436 0 24067717 residential False 46.873 NaN LINESTRING (-87.90198 42.10540, -87.90237 42.1... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
261109275 0 24069424 residential False 34.892 NaN LINESTRING (-87.90198 42.10540, -87.90227 42.1... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
261109274 0 24069424 residential False 47.866 NaN LINESTRING (-87.90198 42.10540, -87.90156 42.1... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

network_setting function¶

Cleans the OSMNX network to work better with drive-time analysis.

First, we remove all nodes with 0 outdegree because any hospital assigned to such a node would be unreachable from everywhere. Next, we remove small (under 10 node) strongly connected components to reduce erroneously small ego-centric networks. Lastly, we ensure that the max speed is set and in the correct units before calculating time.

Args:

  • network: OSMNX network for the spatial extent of interest

Returns:

  • OSMNX network: cleaned OSMNX network for the spatial extent
In [14]:
# view all highway types
print(edges['highway'].value_counts())
residential                     296481
secondary                        30909
tertiary                         29216
primary                          19277
motorway_link                     2322
unclassified                      1840
motorway                          1449
trunk                              843
primary_link                       833
secondary_link                     356
living_street                      238
trunk_link                         157
tertiary_link                      121
[residential, unclassified]         69
[tertiary, residential]             66
[secondary, primary]                15
[secondary, tertiary]               10
[motorway, motorway_link]            6
[tertiary, unclassified]             6
[motorway, trunk]                    4
[residential, living_street]         4
[secondary, secondary_link]          3
busway                               2
[motorway, primary]                  2
[tertiary, motorway_link]            2
emergency_bay                        2
[trunk, primary]                     2
[tertiary, tertiary_link]            1
[trunk, motorway]                    1
[primary, motorway_link]             1
[secondary, motorway_link]           1
[primary_link, residential]          1
Name: highway, dtype: int64
In [15]:
# two things about this function:
# 1) the work to remove nodes is hardly worth it now that OSMnx cleans graphs by default
# the function is now only pruning < 300 nodes
# 2) try using the OSMnx speed module for setting speeds, travel times
# https://osmnx.readthedocs.io/en/stable/user-reference.html#module-osmnx.speed
# just be careful about units of speed and time!
# the remainder of this code expects 'time' to be measured in minutes

def network_setting(network):
    _nodes_removed = len([n for (n, deg) in network.out_degree() if deg ==0])
    network.remove_nodes_from([n for (n, deg) in network.out_degree() if deg ==0])
    for component in list(nx.strongly_connected_components(network)):
        if len(component)<10:
            for node in component:
                _nodes_removed+=1
                network.remove_node(node)
    ox.speed.add_edge_speeds(network)
    ox.speed.add_edge_travel_times(network)
    print("Removed {} nodes ({:2.4f}%) from the OSMNX network".format(_nodes_removed, _nodes_removed/float(network.number_of_nodes())))
    print("Number of nodes: {}".format(network.number_of_nodes()))
    print("Number of edges: {}".format(network.number_of_edges()))
    return(network)

Preprocess the Network using network_setting¶

In [16]:
%%time
# G, hospitals, grid_file, pop_data = file_import (population_dropdown.value)
G = network_setting(G)
# Create point geometries for each node in the graph, to make constructing catchment area polygons easier
for node, data in G.nodes(data=True):
    data['geometry']=Point(data['x'], data['y'])
# Modify code to react to processor dropdown (got rid of file_import function)
Removed 274 nodes (0.0019%) from the OSMNX network
Number of nodes: 142044
Number of edges: 383911
CPU times: user 45.9 s, sys: 465 ms, total: 46.4 s
Wall time: 46.3 s

Re-check speed limit values¶

Display all the unique speed limit values and count how many network edges (road segments) have each value. Compare to the previous results.

In [17]:
%%time
## Get unique counts for each road network
# Turn nodes and edges in geodataframes
nodes, edges = ox.graph_to_gdfs(G, nodes=True, edges=True)

# Check that osmnx added speeds and travel times to graph
print(edges['speed_kph'].value_counts())
print(str(len(edges)) + " edges in graph")
print(edges['travel_time'].value_counts())
39.2     291413
48.3      29822
56.7      26353
60.1      14985
40.2       5604
56.3       3364
86.3       2200
64.4       2093
32.2       1872
42.9       1793
72.4       1418
69.8        654
88.5        606
90.1        565
96.6        277
80.5        191
51.0        118
40.0         80
24.1         76
112.7        61
104.6        42
16.1         38
25.0         34
68.0         29
52.0         26
45.3         24
60.0         24
70.0         21
64.0         18
80.0         16
44.0         12
56.0          9
76.0          8
50.0          8
48.0          8
36.0          6
92.0          5
96.0          4
71.0          4
20.0          4
104.0         3
32.0          3
72.0          3
45.0          3
100.0         3
52.4          2
55.0          2
108.0         2
35.0          2
53.0          2
84.0          1
Name: speed_kph, dtype: int64
383911 edges in graph
9.3      14185
9.2      11922
18.6      8012
9.4       7209
18.5      6608
         ...  
199.5        1
115.5        1
145.7        1
122.3        1
136.9        1
Name: travel_time, Length: 1183, dtype: int64
CPU times: user 36.1 s, sys: 143 ms, total: 36.2 s
Wall time: 36.2 s

"Helper" Functions¶

The functions below are needed for our analysis later, let's take a look!

hospital_setting¶

Finds the nearest network node for each hospital.

Args:

  • hospital: GeoDataFrame of hospitals
  • G: OSMNX network

Returns:

  • GeoDataFrame of hospitals with info on nearest network node
In [18]:
def hospital_setting(hospitals, G):
    # Create an empty column 
    hospitals['nearest_osm']=None
    # Append the neaerest osm column with each hospitals neaerest osm node
    for i in tqdm(hospitals.index, desc="Find the nearest network node from hospitals", position=0):
        hospitals['nearest_osm'][i] = ox.get_nearest_node(G, [hospitals['Y'][i], hospitals['X'][i]], method='euclidean') # find the nearest node from hospital location
    print ('hospital setting is done')
    return(hospitals)

pop_centroid¶

Converts geodata to centroids

Args:

  • pop_data: a GeodataFrame
  • pop_type: a string, either "pop" for general population or "covid" for COVID-19 case data

Returns:

  • GeoDataFrame of centroids with population data
In [19]:
def pop_centroid (pop_data, pop_type):
    pop_data = pop_data.to_crs({'init': 'epsg:4326'})
    # If pop is selected in dropdown, select at risk pop where population is greater than 0
    if pop_type =="pop":
        pop_data=pop_data[pop_data['OverFifty']>=0]
    # If covid is selected in dropdown, select where covid cases are greater than 0
    if pop_type =="covid":
        pop_data=pop_data[pop_data['cases']>=0]
    pop_cent = pop_data.centroid # it make the polygon to the point without any other information
    # Convert to gdf
    pop_centroid = gpd.GeoDataFrame()
    i = 0
    for point in tqdm(pop_cent, desc='Pop Centroid File Setting', position=0):
        if pop_type== "pop":
            pop = pop_data.iloc[i]['OverFifty']
            code = pop_data.iloc[i]['GEOID']
        if pop_type =="covid":
            pop = pop_data.iloc[i]['cases']
            code = pop_data.iloc[i].ZCTA5CE10
        pop_centroid = pop_centroid.append({'code':code,'pop': pop,'geometry': point}, ignore_index=True)
        i = i+1
    return(pop_centroid)

djikstra_cca_polygons¶

Function written by Joe Holler + Derrick Burt. It is a more efficient way to calculate distance-weighted catchment areas for each hospital. The algorithm runs quicker than the original one ("calculate_catchment_area"). It first creates a dictionary (with a node and its corresponding drive time from the hospital) of all nodes within a 30 minute drive time (using single_cource_dijkstra_path_length function). From here, two more dictionaries are constructed by querying the original one. From this dictionaries, single part convex hulls are created for each drive time interval and appended into a single list (one list with 3 polygon geometries). Within the list, the polygons are differenced from each other to produce three catchment areas.

Args:

  • G: cleaned network graph with node point geometries attached
  • nearest_osm: A unique nearest node ID calculated for a single hospital
  • distances: 3 distances (in drive time) to calculate catchment areas from
  • distance_unit: unit to calculate (time)

Returns:

  • A list of 3 differenced (not-overlapping) catchment area polygons (10 min poly, 20 min poly, 30 min poly)
In [20]:
def dijkstra_cca_polygons(G, nearest_osm, distances, distance_unit = "travel_time"):
    
    '''
    
    Before running: must assign point geometries to street nodes
    
    # create point geometries for the entire graph
    for node, data in G.nodes(data=True):
    data['geometry']=Point(data['x'], data['y'])
    
    '''
    
    ## CREATE DICTIONARIES
    # create dictionary of nearest nodes
    nearest_nodes_30 = nx.single_source_dijkstra_path_length(G, nearest_osm, distances[2], distance_unit) # creating the largest graph from which 10 and 20 minute drive times can be extracted from
    
    # extract values within 20 and 10 (respectively) minutes drive times
    nearest_nodes_20 = dict()
    nearest_nodes_10 = dict()
    for key, value in nearest_nodes_30.items():
        if value <= distances[1]:
            nearest_nodes_20[key] = value
        if value <= distances[0]:
            nearest_nodes_10[key] = value
    
    ## CREATE POLYGONS FOR 3 DISTANCE CATEGORIES (10 min, 20 min, 30 min)
    # 30 MIN
    # If the graph already has a geometry attribute with point data,
    # this line will create a GeoPandas GeoDataFrame from the nearest_nodes_30 dictionary
    points_30 = gpd.GeoDataFrame(gpd.GeoSeries(nx.get_node_attributes(G.subgraph(nearest_nodes_30), 'geometry')))

    # This line converts the nearest_nodes_30 dictionary into a Pandas data frame and joins it to points
    # left_index=True and right_index=True are options for merge() to join on the index values
    points_30 = points_30.merge(pd.Series(nearest_nodes_30).to_frame(), left_index=True, right_index=True)

    # Re-name the columns and set the geodataframe geometry to the geometry column
    points_30 = points_30.rename(columns={'0_x':'geometry','0_y':'z'}).set_geometry('geometry')

    # Create a convex hull polygon from the points
    polygon_30 = gpd.GeoDataFrame(gpd.GeoSeries(points_30.unary_union.convex_hull))
    polygon_30 = polygon_30.rename(columns={0:'geometry'}).set_geometry('geometry')
    
    # 20 MIN
    # Select nodes less than or equal to 20
    points_20 = points_30.query("z <= 1200")
    
    # Create a convex hull polygon from the points
    polygon_20 = gpd.GeoDataFrame(gpd.GeoSeries(points_20.unary_union.convex_hull))
    polygon_20 = polygon_20.rename(columns={0:'geometry'}).set_geometry('geometry')
    
    # 10 MIN
    # Select nodes less than or equal to 10
    points_10 = points_30.query("z <= 600")
    
    # Create a convex hull polygon from the points
    polygon_10 = gpd.GeoDataFrame(gpd.GeoSeries(points_10.unary_union.convex_hull))
    polygon_10 = polygon_10.rename(columns={0:'geometry'}).set_geometry('geometry')
    
    # Create empty list and append polygons
    polygons = []
    
    # Append
    polygons.append(polygon_10)
    polygons.append(polygon_20)
    polygons.append(polygon_30)
    
    # Clip the overlapping distance ploygons (create two donuts + hole)
    for i in reversed(range(1, len(distances))):
        polygons[i] = gpd.overlay(polygons[i], polygons[i-1], how="difference")

    return polygons

hospital_measure_acc (adjusted to incorporate dijkstra_cca_polygons)¶

Measures the effect of a single hospital on the surrounding area. (Uses dijkstra_cca_polygons)

Args:

  • _thread_id: int used to keep track of which thread this is
  • hospital: Geopandas dataframe with information on a hospital
  • pop_data: Geopandas dataframe with population data
  • distances: Distances in time to calculate accessibility for
  • weights: how to weight the different travel distances

Returns:

  • Tuple containing:
    • Int (_thread_id)
    • GeoDataFrame of catchment areas with key stats
In [21]:
def hospital_measure_acc (_thread_id, hospital, pop_data, distances, weights):
    # Create polygons
    polygons = dijkstra_cca_polygons(G, hospital['nearest_osm'], distances)
    
    # Calculate accessibility measurements
    num_pops = []
    for j in pop_data.index:
        point = pop_data['geometry'][j]
        # Multiply polygons by weights
        for k in range(len(polygons)):
            if len(polygons[k]) > 0: # To exclude the weirdo (convex hull is not polygon)
                if (point.within(polygons[k].iloc[0]["geometry"])):
                    num_pops.append(pop_data['pop'][j]*weights[k])  
    total_pop = sum(num_pops)
    for i in range(len(distances)):
        polygons[i]['time']=distances[i]
        polygons[i]['total_pop']=total_pop
        polygons[i]['hospital_icu_beds'] = float(hospital['Adult ICU'])/polygons[i]['total_pop'] # proportion of # of beds over pops in 10 mins
        polygons[i]['hospital_vents'] = float(hospital['Total Vent'])/polygons[i]['total_pop'] # proportion of # of beds over pops in 10 mins
        polygons[i].crs = { 'init' : 'epsg:4326'}
        polygons[i] = polygons[i].to_crs({'init':'epsg:32616'})
    print('{:.0f}'.format(_thread_id), end=" ", flush=True)
    return(_thread_id, [ polygon.copy(deep=True) for polygon in polygons ]) 

measure_acc_par¶

Parallel implementation of accessibility measurement.

Args:

  • hospitals: Geodataframe of hospitals
  • pop_data: Geodataframe containing population data
  • network: OSMNX street network
  • distances: list of distances to calculate catchments for
  • weights: list of floats to apply to different catchments
  • num_proc: number of processors to use.

Returns:

  • Geodataframe of catchments with accessibility statistics calculated
In [22]:
def hospital_acc_unpacker(args):
    return hospital_measure_acc(*args)

# WHERE THE RESULTS ARE POOLED AND THEN REAGGREGATED
def measure_acc_par (hospitals, pop_data, network, distances, weights, num_proc = 4):
    catchments = []
    for distance in distances:
        catchments.append(gpd.GeoDataFrame())
    pool = mp.Pool(processes = num_proc)
    hospital_list = [ hospitals.iloc[i] for i in range(len(hospitals)) ]
    print("Calculating", len(hospital_list), "hospital catchments...\ncompleted number:", end=" ")
    results = pool.map(hospital_acc_unpacker, zip(range(len(hospital_list)), hospital_list, itertools.repeat(pop_data), itertools.repeat(distances), itertools.repeat(weights)))
    pool.close()
    results.sort()
    results = [ r[1] for r in results ]
    for i in range(len(results)):
        for j in range(len(distances)):
            catchments[j] = catchments[j].append(results[i][j], sort=False)
    return catchments

overlap_calc¶

Calculates and aggregates accessibility statistics for one catchment on our grid file.

Args:

  • _id: thread ID
  • poly: GeoDataFrame representing a catchment area
  • grid_file: a GeoDataFrame representing our grids
  • weight: the weight to applied for a given catchment
  • service_type: the service we are calculating for: ICU beds or ventilators

Returns:

  • Tuple containing:
    • thread ID
    • Counter object (dictionary for numbers) with aggregated stats by grid ID number
In [23]:
from collections import Counter
def overlap_calc(_id, poly, grid_file, weight, service_type):
    value_dict = Counter()
    if type(poly.iloc[0][service_type])!=type(None):           
        value = float(poly[service_type])*weight
        intersect = gpd.overlay(grid_file, poly, how='intersection')
        intersect['overlapped']= intersect.area
        intersect['percent'] = intersect['overlapped']/intersect['area']
        intersect=intersect[intersect['percent']>=0.5]
        intersect_region = intersect['id']
        for intersect_id in intersect_region:
            try:
                value_dict[intersect_id] +=value
            except:
                value_dict[intersect_id] = value
    return(_id, value_dict)

def overlap_calc_unpacker(args):
    return overlap_calc(*args)

overlapping_function¶

Calculates how all catchment areas overlap with and affect the accessibility of each grid in our grid file.

Args:

  • grid_file: GeoDataFrame of our grid
  • catchments: GeoDataFrame of our catchments
  • service_type: the kind of care being provided (ICU beds vs. ventilators)
  • weights: the weight to apply to each service type
  • num_proc: the number of processors

Returns:

  • Geodataframe - grid_file with calculated stats
In [24]:
def overlapping_function (grid_file, catchments, service_type, weights, num_proc = 4):
    grid_file[service_type]=0
    pool = mp.Pool(processes = num_proc)
    acc_list = []
    for i in range(len(catchments)):
        acc_list.extend([ catchments[i][j:j+1] for j in range(len(catchments[i])) ])
    acc_weights = []
    for i in range(len(catchments)):
        acc_weights.extend( [weights[i]]*len(catchments[i]) )
    results = pool.map(overlap_calc_unpacker, zip(range(len(acc_list)), acc_list, itertools.repeat(grid_file), acc_weights, itertools.repeat(service_type)))
    pool.close()
    results.sort()
    results = [ r[1] for r in results ]
    service_values = results[0]
    for result in results[1:]:
        service_values+=result
    for intersect_id, value in service_values.items():
        grid_file.loc[grid_file['id']==intersect_id, service_type] += value
    return(grid_file) 

normalization¶

Normalizes our result (Geodataframe) for a given resource (res).

In [25]:
def normalization (result, res):
    result[res]=(result[res]-min(result[res]))/(max(result[res])-min(result[res]))
    return result

file_import¶

Imports all files we need to run our code and pulls the Illinois network from OSMNX if it is not present (will take a while).

NOTE: even if we calculate accessibility for just Chicago, we want to use the Illinois network (or at least we should not use the Chicago network) because using the Chicago network will result in hospitals near but outside of Chicago having an infinite distance (unreachable because roads do not extend past Chicago).

Args:

  • pop_type: population type, either "pop" for general population or "covid" for COVID-19 cases
  • region: the region to use for our hospital and grid file ("Chicago" or "Illinois")

Returns:

  • G: OSMNX network
  • hospitals: Geodataframe of hospitals
  • grid_file: Geodataframe of grids
  • pop_data: Geodataframe of population
In [26]:
def output_map(output_grid, base_map, hospitals, resource):
    ax=output_grid.plot(column=resource, cmap='PuBuGn',figsize=(18,12), legend=True, zorder=1)
    # Next two lines set bounds for our x- and y-axes because it looks like there's a weird 
    # Point at the bottom left of the map that's messing up our frame (Maja)
    ax.set_xlim([314000, 370000])
    ax.set_ylim([540000, 616000])
    base_map.plot(ax=ax, facecolor="none", edgecolor='gray', lw=0.1)
    hospitals.plot(ax=ax, markersize=10, zorder=1, c='blue')

Run the model¶

Below you can customize the input of the model:

  • Processor - the number of processors to use
  • Region - the spatial extent of the measure
  • Population - the population to calculate the measure for
  • Resource - the hospital resource of interest
  • Hospital - all hospitals or subset to check code
In [27]:
import ipywidgets
from IPython.display import display

processor_dropdown = ipywidgets.Dropdown( options=[("1", 1), ("2", 2), ("3", 3), ("4", 4)],
    value = 4, description = "Processor: ")

population_dropdown = ipywidgets.Dropdown( options=[("Population at Risk", "pop"), ("COVID-19 Patients", "covid") ],
    value = "pop", description = "Population: ")

resource_dropdown = ipywidgets.Dropdown( options=[("ICU Beds", "hospital_icu_beds"), ("Ventilators", "hospital_vents") ],
    value = "hospital_icu_beds", description = "Resource: ")

hospital_dropdown =  ipywidgets.Dropdown( options=[("All hospitals", "hospitals"), ("Subset", "hospital_subset") ],
    value = "hospitals", description = "Hospital:")

display(processor_dropdown,population_dropdown,resource_dropdown,hospital_dropdown)
Dropdown(description='Processor: ', index=3, options=(('1', 1), ('2', 2), ('3', 3), ('4', 4)), value=4)
Dropdown(description='Population: ', options=(('Population at Risk', 'pop'), ('COVID-19 Patients', 'covid')), …
Dropdown(description='Resource: ', options=(('ICU Beds', 'hospital_icu_beds'), ('Ventilators', 'hospital_vents…
Dropdown(description='Hospital:', options=(('All hospitals', 'hospitals'), ('Subset', 'hospital_subset')), val…

Process population data¶

In [28]:
if population_dropdown.value == "pop":
    pop_data = pop_centroid(atrisk_data, population_dropdown.value)
elif population_dropdown.value == "covid":
    pop_data = pop_centroid(covid_data, population_dropdown.value)
distances=[600, 1200, 1800] # Distances in travel time
weights=[1.0, 0.68, 0.22] # Weights where weights[0] is applied to distances[0]
# Other weighting options representing different distance decays
# weights1, weights2, weights3 = [1.0, 0.42, 0.09], [1.0, 0.75, 0.5], [1.0, 0.5, 0.1]
# it is surprising how long this function takes just to calculate centroids.
# why not do it with the geopandas/pandas functions rather than iterating through every item?
Pop Centroid File Setting: 100%|██████████| 3121/3121 [03:54<00:00, 13.31it/s]

Process hospital data¶

If you have already run this code and changed the Hospital selection, rerun the Load Hospital Data block.

In [29]:
# Set hospitals according to hospital dropdown
if hospital_dropdown.value == "hospital_subset":
    hospitals = hospital_setting(hospitals[:1], G)
else: 
    hospitals = hospital_setting(hospitals, G)
resources = ["hospital_icu_beds", "hospital_vents"] # resources
# this is also slower than it needs to be; if network nodes and hospitals are both
# geopandas data frames, it should be possible to do a much faster spatial join rather than iterating through every hospital
Find the nearest network node from hospitals: 100%|██████████| 66/66 [01:25<00:00,  1.29s/it]
hospital setting is done

Visualize catchment areas for first hospital¶

In [30]:
# Create point geometries for entire graph
# what is the pupose of the following two lines? Can this be deleted?
# for node, data in G.nodes(data=True):
#     data['geometry']=Point(data['x'], data['y'])

# which hospital to visualize? 
fighosp = 7

# Create catchment for hospital 0
poly = dijkstra_cca_polygons(G, hospitals['nearest_osm'][fighosp], distances)

# Reproject polygons
for i in range(len(poly)):
    poly[i].crs = { 'init' : 'epsg:4326'}
    poly[i] = poly[i].to_crs({'init':'epsg:32616'})

# Reproject hospitals 
# Possible to map from the hospitals data rather than creating hospital_subset?
hospital_subset = hospitals.iloc[[fighosp]].to_crs(epsg=32616)

fig, ax = plt.subplots(figsize=(12,8))

min_10 = poly[0].plot(ax=ax, color="royalblue", label="10 min drive")
min_20 = poly[1].plot(ax=ax, color="cornflowerblue", label="20 min drive")
min_30 = poly[2].plot(ax=ax, color="lightsteelblue", label="30 min drive")

hospital_subset.plot(ax=ax, color="red", legend=True, label = "hospital")

# Add legend
ax.legend()
Out[30]:
<matplotlib.legend.Legend at 0x7f722bf49340>
In [31]:
poly
Out[31]:
[                                            geometry
 0  POLYGON ((443456.283 4609874.589, 441585.172 4...,
                                             geometry
 0  POLYGON ((433443.581 4600237.316, 427780.923 4...,
                                             geometry
 0  POLYGON ((438932.445 4588484.312, 431706.358 4...]

Calculate hospital catchment areas¶

In [32]:
%%time
catchments = measure_acc_par(hospitals, pop_data, G, distances, weights, num_proc=processor_dropdown.value)
Calculating 66 hospital catchments...
completed number: 5 15 0 10 6 1 16 11 2 7 17 12 3 8 18 13 4 9 19 14 20 25 30 35 21 31 26 36 22 27 32 37 28 23 33 38 29 24 34 39 40 45 50 55 41 46 51 56 42 47 52 57 43 48 58 53 44 49 59 54 60 65 61 62 63 64 CPU times: user 2.23 s, sys: 535 ms, total: 2.76 s
Wall time: 2min 12s

Calculate accessibility¶

In [33]:
%%time
for j in range(len(catchments)):
    catchments[j] = catchments[j][catchments[j][resource_dropdown.value]!=float('inf')]
result=overlapping_function(grid_file, catchments, resource_dropdown.value, weights, num_proc=processor_dropdown.value)
CPU times: user 6.42 s, sys: 460 ms, total: 6.88 s
Wall time: 17.9 s

Area Weighted Reaggregation¶

Instead of aggregating the accesibility results by the 50% threshold, multiply by the weights for their catchment area and reaggregate by hexagon id

In [34]:
# add weight field to each catchment polygon
for i in range(len(weights)):
    catchments[i]['weight'] = weights[i]
# combine the three sets of catchment polygons into one geodataframe
geocatchments = pd.concat([catchments[0], catchments[1], catchments[2]])
geocatchments
Out[34]:
geometry time total_pop hospital_icu_beds hospital_vents weight
0 POLYGON ((446359.955 4637144.048, 444654.345 4... 600 789023.74 0.000046 0.000015 1.00
0 POLYGON ((438353.601 4609853.779, 432065.727 4... 600 717916.38 0.000273 0.000089 1.00
0 POLYGON ((442878.135 4648745.067, 441056.875 4... 600 469346.52 0.000190 0.000062 1.00
0 POLYGON ((423900.989 4621140.151, 421031.920 4... 600 732753.60 0.000089 0.000029 1.00
0 POLYGON ((443322.063 4615428.578, 438387.446 4... 600 716375.12 0.000092 0.000029 1.00
... ... ... ... ... ... ...
0 POLYGON ((440431.675 4605335.203, 415910.447 4... 1800 1015836.64 0.000027 0.000009 0.22
0 MULTIPOLYGON (((418680.569 4620247.323, 411754... 1800 754080.60 0.000060 0.000019 0.22
0 POLYGON ((421589.871 4617483.974, 415910.447 4... 1800 973822.96 0.000086 0.000028 0.22
0 POLYGON ((438852.888 4603453.515, 415910.447 4... 1800 936876.30 0.000065 0.000021 0.22
0 POLYGON ((416049.771 4606193.128, 411127.822 4... 1800 815589.78 0.000115 0.000037 0.22

198 rows × 6 columns

In [63]:
%%time
# set weighted to False for original 50% threshold method
# switch to True for area-weighted overlay
weighted = True 

# if the value to be calculated is already in the hegaxon grid, delete it
# otherwise, the field name gets a suffix _1 in the overlay step
if resource_dropdown.value in list(grid_file.columns.values):
    grid_file = grid_file.drop(resource_dropdown.value, axis = 1)
    
# calculate hexagon 'target' areas
grid_file['area'] = grid_file.area
    
# Intersection overlay of hospital catchments and hexagon grid
print("Intersecting hospital catchments with hexagon grid...")
fragments = gpd.overlay(grid_file, geocatchments, how='intersection')

# Calculate percent coverage of the hexagon by the hospital catchment as
# fragment area / target(hexagon) area
fragments['percent'] = fragments.area / fragments['area']

# if using weighted aggregation... 
if weighted:
    print("Calculating area-weighted value...")
    # multiply the service/population ratio by the distance weight and the percent coverage
    fragments['value'] = fragments[resource_dropdown.value] * fragments['weight'] * fragments['percent']

# if using the 50% coverage rule for unweighted aggregation...
else:
    print("Calculating value for hexagons with >=50% overlap...")
    # filter for only the fragments with > 50% coverage by hospital catchment
    fragments = fragments[fragments['percent']>=0.5]
    # multiply the service/population ration by the distance weight
    fragments['value'] = fragments[resource_dropdown.value] * fragments['weight']

# select just the hexagon id and value from the fragments,
# group the fragments by the (hexagon) id,
# and sum the values
print("Summarizing results by hexagon id...")
sum_results = fragments[['id', 'value']].groupby(by = ['id']).sum()

# join the results to the hexagon grid_file based on hexagon id
print("Joining results to hexagons...")
result_new = pd.merge(grid_file, sum_results, how="left", on = "id")

# rename value column name to the resource name
result_new.rename(columns = {'value' : resource_dropdown.value})
Intersecting hospital catchments with hexagon grid...
Calculating area-weighted value...
Summarizing results by hexagon id...
Joining results to hexagons...
CPU times: user 12.8 s, sys: 24.2 ms, total: 12.8 s
Wall time: 12.8 s
Out[63]:
left top right bottom id area geometry hospital_icu_beds
0 440843.416087 4.638515e+06 441420.766356 4.638015e+06 4158 216506.350946 POLYGON ((440843.416 4638265.403, 440987.754 4... 0.003564
1 440843.416087 4.638015e+06 441420.766356 4.637515e+06 4159 216506.350946 POLYGON ((440843.416 4637765.403, 440987.754 4... 0.003617
2 440843.416087 4.639515e+06 441420.766356 4.639015e+06 4156 216506.350946 POLYGON ((440843.416 4639265.403, 440987.754 4... 0.003626
3 440843.416087 4.639015e+06 441420.766356 4.638515e+06 4157 216506.350946 POLYGON ((440843.416 4638765.403, 440987.754 4... 0.003567
4 440843.416087 4.640515e+06 441420.766356 4.640015e+06 4154 216506.350946 POLYGON ((440843.416 4640265.403, 440987.754 4... 0.003676
... ... ... ... ... ... ... ... ...
3274 440843.416087 4.643015e+06 441420.766356 4.642515e+06 4149 216506.350946 POLYGON ((440843.416 4642765.403, 440987.754 4... 0.003583
3275 440843.416087 4.644515e+06 441420.766356 4.644015e+06 4146 216506.350946 POLYGON ((440843.416 4644265.403, 440987.754 4... 0.003473
3276 440843.416087 4.644015e+06 441420.766356 4.643515e+06 4147 216506.350946 POLYGON ((440843.416 4643765.403, 440987.754 4... 0.003499
3277 440843.416087 4.645515e+06 441420.766356 4.645015e+06 4144 216506.350946 POLYGON ((440843.416 4645265.403, 440987.754 4... 0.003427
3278 440843.416087 4.645015e+06 441420.766356 4.644515e+06 4145 216506.350946 POLYGON ((440843.416 4644765.403, 440987.754 4... 0.003445

3279 rows × 8 columns

In [64]:
%%time
result = normalization (result, resource_dropdown.value)
CPU times: user 2.59 ms, sys: 0 ns, total: 2.59 ms
Wall time: 2.38 ms
In [65]:
result.head()
Out[65]:
left top right bottom id area geometry hospital_icu_beds
0 440843.416087 4.638515e+06 441420.766356 4.638015e+06 4158 216661.173 POLYGON ((351469.371 580527.566, 351609.858 58... 0.903274
1 440843.416087 4.638015e+06 441420.766356 4.637515e+06 4159 216661.168 POLYGON ((351477.143 580027.445, 351617.630 58... 0.929614
2 440843.416087 4.639515e+06 441420.766356 4.639015e+06 4156 216661.169 POLYGON ((351453.825 581527.810, 351594.311 58... 0.929785
3 440843.416087 4.639015e+06 441420.766356 4.638515e+06 4157 216661.171 POLYGON ((351461.598 581027.688, 351602.085 58... 0.911208
4 440843.416087 4.640515e+06 441420.766356 4.640015e+06 4154 216661.171 POLYGON ((351438.276 582528.054, 351578.761 58... 0.953645

Results¶

Unclassified Accessibility Map¶

Plot accessibility scores and hospital points over hexagon grid.

In [66]:
%%time
hospitals = hospitals.to_crs({'init': 'epsg:26971'})
result = result.to_crs({'init': 'epsg:26971'})
output_map(result, pop_data, hospitals, resource_dropdown.value)
CPU times: user 1.77 s, sys: 129 ms, total: 1.9 s
Wall time: 1.7 s

Classified Accessibility Map¶

Plot accessibility scores with equal breaks classification and hospital points over hexagon grid.

In [67]:
def output_map_classified(output_grid, hospitals, resource):
    ax=output_grid.plot(column=resource,
                        scheme='Equal_Interval',
                        k=5,
                        linewidth=0,
                        cmap='Blues',
                        figsize=(18,12),
                        legend=True,
                        label="Acc Measure",
                        zorder=1)
    # Next two lines set bounds for our x- and y-axes because it looks like there's a weird
    # Point at the bottom left of the map that's messing up our frame (Maja)
    ax.set_xlim([325000, 370000])
    ax.set_ylim([550000, 600000])
    hospitals.plot(ax=ax,
                   markersize=10,
                   zorder=2,
                   c='black',
                   legend=True,
                   label="Hospital"
                   )
    # ax.legend(loc="upper right")  # add hospital legend
In [68]:
output_map_classified(result, hospitals, resource_dropdown.value)
# save as image with file name including the resource value, population value, and buffered / not buffered
plt.savefig('./results/figures/reproduction/{}_{}_buff_classified_spdLimit.png'.format(population_dropdown.value, resource_dropdown.value))

Compare Reproduction with Original Results¶

Load results provided with the original research compendium from shapefile data/derived/public/Chicago_ACC.shp. The file contains fields hospital_i for "ICU Beds" and hospital_v for "Ventilators". It is not known exactly which version of code was used to create this set of results, although it appears that a more complete road network was used (probably the full state of Illinois) than was provided with the compendium (Chicago only, without a buffer). It is not known whether the population was population at risk (>50 years old) or COVID patients (cases). However, the statistical and geographic distributions of each are extremly similar once the data has been normalized.

In [69]:
# Import study results to compare
# hospital_i assumed to be for ICU and hospital_v assumed to be for ventilator
# however it's unknown whether the population is the COVID-19 population or the AT RISK population
fp = 'data/derived/public/Chicago_ACC.shp'
og_result = gpd.read_file(fp)
og_result.set_index("id")
og_result.head()
Out[69]:
id hospital_i hospital_v geometry
0 4158 0.844249 0.843439 POLYGON ((-87.71312 41.89411, -87.71140 41.896...
1 4159 0.843600 0.843031 POLYGON ((-87.71307 41.88961, -87.71135 41.891...
2 4156 0.906094 0.904699 POLYGON ((-87.71322 41.90312, -87.71150 41.905...
3 4157 0.877197 0.876503 POLYGON ((-87.71317 41.89861, -87.71145 41.900...
4 4154 0.911424 0.910002 POLYGON ((-87.71332 41.91212, -87.71160 41.914...

Join original results to current results¶

Here, we join the current results from the reanalysis to the results of the original so that they have a consistent ordering so that the Spearmans Rho can be calculated.

In [70]:
result.set_index("id")
result_compare = result.join(og_result[["hospital_i","hospital_v"]])
result_compare.head()
Out[70]:
left top right bottom id area geometry hospital_icu_beds hospital_i hospital_v
0 440843.416087 4.638515e+06 441420.766356 4.638015e+06 4158 216661.173 POLYGON ((351469.371 580527.566, 351609.858 58... 0.903274 0.844249 0.843439
1 440843.416087 4.638015e+06 441420.766356 4.637515e+06 4159 216661.168 POLYGON ((351477.143 580027.445, 351617.630 58... 0.929614 0.843600 0.843031
2 440843.416087 4.639515e+06 441420.766356 4.639015e+06 4156 216661.169 POLYGON ((351453.825 581527.810, 351594.311 58... 0.929785 0.906094 0.904699
3 440843.416087 4.639015e+06 441420.766356 4.638515e+06 4157 216661.171 POLYGON ((351461.598 581027.688, 351602.085 58... 0.911208 0.877197 0.876503
4 440843.416087 4.640515e+06 441420.766356 4.640015e+06 4154 216661.171 POLYGON ((351438.276 582528.054, 351578.761 58... 0.953645 0.911424 0.910002

Calculate Spearman's Rank Correlation¶

With the new implementations from this reanalysis the correlation is calculated between the results from this reanalysis and the original to see how much the implementations have infuenced the relationship between the two.

In [71]:
# set original_resource variable to the name of original results column matching the modeling choice
from scipy import stats
if resource_dropdown.value == "icu_beds":
    original_resource = "hospital_i"
else:
    original_resource = "hospital_v"

# calculate spearman's rho
rho = stats.spearmanr(result_compare[[original_resource, resource_dropdown.value]])

print(correlationmsg)
rho_result = "Rho = " + str(round(rho.correlation,3)) + ", pvalue = " + str(round(rho.pvalue,3))
print(rho_result)
Comparing: 
Original resource: hospital_icu_beds and population: unknown
Reproduction resource: hospital_icu_beds and population: pop
Rho = 0.747, pvalue = 0.0

Create Scatterplot¶

The scatterplot helps visualize the correlation.

In [72]:
plt.scatter(result_compare[[original_resource]], result_compare[[resource_dropdown.value]], s=1)
plt.xlabel("Original", labelpad=5)
plt.ylabel("Reproduction", labelpad=5)
plt.text(.45, .08, rho_result, fontsize=8)
# save plot as image with file name including icu/ventilators and buffered or not
plt.savefig("./results/figures/reproduction/compare_{}_buffer_{}.png")

Results¶

The changes made in this reanalysis have influenced the results in important ways.

Looking at the Classified Accessibility Map with the default settings of (buffered, pop50 and icu beds, and all hospitals), when compared to its earlier rendition in our initial reproduction study, the zone of highest accessibility has expanded to show that more healthcare resources can be accessed by more people than was assumed to be possible in the reproduction. It extends outwards in all directions but it especially extends further into the Northwest and Southwest regions of the city. Changing the settings to ventilators did not influence the map significantly, however, when "pop50" was changed to "covid patients" the map did not change much from the original reproduction.

Overall, with the default settings, the Spearman's Rho calculation of the results from this reanalysis to the original Kang et al. (2020) study shows a correlation coefficient of 0.747 compared to 0.532 from our initial reproduction. This indicates that the reproduction overall was significantly more successful at accurately reproducing the original results. Since expanding the road network was the only implementation intended to improve the reproducibility, this better correlation to the original study should not be attributed to the additional reanalysis implementations of OSMNX road-type speed limits and area weighted reaggregation. This is a great increase toward positive 1 which represents a perfect positive correlation or complete identicality to the original study.

Discussion¶

Expanding the road network of Chicago to include a 15 mile buffer outside the city led to a road network map with a larger extent and drastically increased the number of road edges to 384,240 from 75,895 in the original reproduction. The expansion of the road network is likely to have influenced these larger zones of accessibility by accounting for people living outside the city who might access hospitals inside.

Improving the road network speed dataset also played a role in the larger accessibility zones; however, the relationship was not as direct. Initially, in the first reproduction, missing speed limit values were replaced with a generalization of 35mph. This reanalysis however, replaced these generalizations with more accurate speed limit values based on the actual road type. The road speed limit data set from the original reproduction had the most segments with a speed limit of 30 mph while it was 25 mph in this reanalysis with the newly replaced OSMNX speed limits by road type and larger network (Refer to the Check Speed Limits sections). What this means is that there was an overall estimation of how fast one could access hospital resources in the original reproduction which seems to contradict the the results of larger accessibility zones. In addition to there being more segments with speed limits of 25 mph, however, this reanalysis also had more segments with higher speed limits such as those in the 60 - 70 mph range whereas the original version included no segments of with a 70 mph speed limit. Due to more segments with speed limits both on the lower and the higher side of the original, more so than directly influencing the size of the accessibility zones in a certain direction, the improved speed limit data resulted in enhanced content validity simply improving the accuracy of the results.

The map not changing upon switching the settings from hospital beds to ventilators validates the original assumption that hospital beds and ventilators are highly correlated in their influence to accessibility. The lack of change from the original map when the settings were changed from "pop50" to "covid patients" indicates that none of our changes to this study influenced accessibility for covid patients. A possible explanation for this result could be attributed to the expansion of the road network. Seeing how it showed higher accessibility for populations at risk (over 50) but not covid patients, further internal validity tests could examine the relationships between the expansion of the road network and how it impacted covid patient data.

The larger accessibility zones could also be attributed to our implementation of a new Area Weighted Aggregation (AWR) to replace the initial 50% threshold from the original study and our initial reproduction. The initial method of aggregating the data into the hexagonal grid by checking to see if 50% or more of the hospital catchment area was intersecting with the hexagon likely generalized the results by an underrepresentation of data in the hexagons. By weighting all intersecting slices of the catchment areas in the hexagons, not only did we improve on that area of uncertainty but increasing the representation of data in the hexagonal grid could have led to the final results of increased accessibility.

Conclusion¶

Ultimately, this reanalysis of our original reproduction of Kang et al. 2020 was successful both in improving the reproducibility of the study and also improving the study itself by implementing changes that tackle critical areas of uncertainty. While these implementations made strides in this body of scientific knowledge there remains threats to validity that could be expanded on in future work.

The first most tangible step is approaching the threat of partition distortion. Partition distortion describes how decreasing partitions in a dataset inversely increases distortion due to increasing complexities in how the data is aggregated. This applies here with how the study area is represented by a hexagonal grid with the partitions being each edge of each hexagon. The size of the hexagons representing the number of hexagons and partitions, seems to have been arbitrarily chosen. Further validity tests could be beneficial to determine whether decresing the size of the hexagons (increasing partitions) would decrease the distortion of the results producing a more accurate representation of spatial accessibility to healthcare resources.

To expand the study even further, an additional approach is to understand more about the limitations of only using a transportation network based on the use of personal vehicles. Assuming that the accessibility to healthcare resources of everyone in the city of Chicago is determined by the use of personal vehicles is a gross generalization that ignores vast populations that might rely on public transportation, walking, or biking to access their essential needs. Implementing a multi-modal transportation network would be an incredible step toward improving the power of this study especially in the ways that it would highlight accessibility more accurately based on modes of transportation that typical underserved low-income populations rely on that do not involve a personal vehicle.

Lastly, the time-space threat to validity of traffic congestion could be addressed to investigate how different times of day influence the capability to access healthcare resources by implementing traffic data to get a more accurate estimate of how fast cars are able to travel along certain busier road segments.

Overall, this study has made great steps in the develop of Kang et al. 2020 by improving reproducibility and addressing areas of uncertainty and threats to validity, yet there remains great opportunity for future improvement.

References¶

Luo, W., & Qi, Y. (2009). An enhanced two-step floating catchment area (E2SFCA) method for measuring spatial accessibility to primary care physicians. Health & place, 15(4), 1100-1107.