Fairness in Healthcare Services for Italian Older People: A Convolution-Based Evaluation to Support Policy Decision Makers

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper describes a methodology for assessing the distribution of healthcare services for the elderly in Italy using convolution matrices and the Gini coefficient. The paper is written in clear technical language. It requires the following improvement.

1. Clarify how a 60 km radius translates to a 121×121 kernel (e.g., resolution of grid tiles: 1 km² implies a 121×121 kernel spans 120 km radially, ensuring coverage).
2. Table 1 shows a 5x5 kernel, but the values don't seem to decrease linearly from the center. The center is 1.0, surrounded by 0.55, then 0.1. This might not be a linear decrease. Clarifying how the kernel values were determined.
3. Provide equations for estimating elderly population density per km², clarifying how municipal age distributions were combined with spatial data.
4. Correct minor errors (e.g., "cumlative" in Table 2).
5. Consistent use of terms (e.g., "elderly" vs. "aged population")
6. Break down the Methodology section into clearer subsections (e.g., "Kernel Design Rationale," "Convolution Implementation," "Gini Coefficient Calculation") to improve readability.

Author Response

[Comments 1] The paper describes a methodology for assessing the distribution of
healthcare services for the elderly in Italy using convolution matrices and the Gini
coefficient. The paper is written in clear technical language. It requires the following
improvement.
[Responses 1] Thanks for your work done revising our paper and for all your considerations
and suggestions. We appreciate your effort. We did our best to answer point
by point all of your comments. We highlighted in blue the most important corrections.

Comments 2 Clarify how a 60 km radius translates to a 121×121 kernel (e.g., resolution of grid
tiles: 1 km² implies a 121×121 kernel spans 120 km radially, ensuring coverage).
[Responses 2] Thanks for the suggestion, we agree that this description
could clarify the kernel definition. Thus, we added the following sentence:
"In particular, since each grid cell represents a 1 × 1 km area, a 60 km radius
from the center requires extending 60 cells in every direction. Consequently, we
have 60 cells to the left, 60 cells to the right, plus the central cell, yielding a
121×121 kernel (i.e., 60+60+1 = 121). This ensures coverage of 60 km in each
direction from the central tile."

Comments 3 Table 1 shows a 5x5 kernel, but the values don’t seem to decrease linearly from
the center. The center is 1.0, surrounded by 0.55, then 0.1. This might not be a
linear decrease. Clarifying how the kernel values were determined.
[Responses 3] Thanks for highlighting the error. We agree that the one proposed
is not a linear decrease. We fixed the sentence and corrected the description
of the kernel example as follows:
"The values within the kernels were defined in the interval [0.1, 1.0]. Once
the kernel size is set, the values in the matrix decrease linearly from the central
highest value (equal to 1) to a minimum at the outermost layer. Consequently,
any layer not included in the kernel is assumed to have a value of 0."

Comments 4 Provide equations for estimating elderly population density per km², clarifying
how municipal age distributions were combined with spatial data.
[Responses 4] Thanks for the suggestion, we agree that this description
could improve the manuscript. To clarify this point, we added the following sentence
in section 2.2.1.
"For this purpose, let Pop be the matrix containing population data per square
kilometre, where popij represents the population residing in tile (i, j). Given M
the set of municipalities where each m ∈ M represents a specific municipality, let
Popm be the total population residing in municipality m ∈ M, and let eP opm be
the number of elderly residents (i.e. those over 65) in m. We define f(i, j) −→ m
a function that, given the coordinate of tile (i, j), returns the municipality to
which the tile belongs. First, we compute the percentage of elderly residents in
municipality m as %eP opm = ePopm Popm× 100. Then, we calculate the number of
elderly residents residing in each tile (i, j) using the formula %eP opm×popij
100 ."

Comments 5 Correct minor errors (e.g., "cumlative" in Table 2).
[Responses 5] We fixed the typo.

Comments 6 Consistent use of terms (e.g., "elderly" vs. "aged population")
[Responses 6] We thank the reviewer’s feedback. The term "elderly" was
replaced with "aged population".

Comments 7 Break down the Methodology section into clearer subsections (e.g., "Kernel Design
Rationale," "Convolution Implementation," "Gini Coefficient Calculation")
to improve readability.
[Responses 7] We thank the reviewer’s feedback. We broke down the
methodology section into subsections we have renamed as suggested. The term
"elderly" was replaced with "aged population".

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1. The Abstract section of this paper should be straightforward. The author needs to re-condense the abstract as the background information in the current abstract is overly redundant. The abstract should first point out the challenging problems faced, followed by the specific solutions, and finally the experimental results.
2. To demonstrate the depth and breadth of the content of this paper, it is advisable to complete the INTRODUCTION section based on the citation of the latest research papers. For example, citing papers such as "Generate adversarial-driven cross-aware network" and "CATNet: Cascaded attention transformer network" can make your paper more credible.
3. The elaboration of the innovative points in the introduction section of the paper is not clear enough. It is recommended that the author further condense the main contributions of this paper and list them one by one in the form of bullet points in the introduction. This will clearly showcase the core innovative points of the paper in terms of theory, methodology, etc., highlight the differences from existing works, and enable readers to quickly understand the unique features of the paper.
4. The paper only provides an overall flowchart, but for the image convolution method innovatively used in this paper, the corresponding overall structural diagram is not given. To reflect the professionalism and rigor of the paper, it is recommended that the author add the structural diagram of this method and provide detailed explanations and descriptions of it. This will help readers more intuitively understand the specific implementation process and principles of the image convolution method, and enhance the readability and comprehensibility of the paper.
5. In the Method section of this paper, it is stated that population data is required to weight the convolution results. However, the paper does not explain why this weighting is necessary. This makes it difficult for readers to understand the contribution of this operation to the overall research methodology and how this step can improve the accuracy and reliability of the research results. The author should provide a detailed explanation of the theoretical basis for choosing the weighting process to facilitate readers' understanding.
6. The author should add comparative experiments. In this paper, only the overall and average impacts of the proposed method on health services are given, but no similar comparative experiments are added to highlight the effectiveness of the proposed method.

Comments on the Quality of English Language

 This paper needs careful proofread before publication. Many sentences are not clear and need to be rewritten. The manuscript needs to be concise, and improve readability. 

Author Response

Thanks for your work done revising our paper and for all your considerations and
suggestions. We appreciate your effort. We did our best to answer point by point all of
your comments. As the reviewer suggested, we ask for the help of a professional English
Editing Services. All linguistic errors have been fixed according to the suggestions of
the service. We highlighted in blue the most important corrections.

Comments 1 The Abstract section of this paper should be straightforward. The author needs
to re-condense the abstract as the background information in the current abstract
is overly redundant. The abstract should first point out the challenging problems
faced, followed by the specific solutions, and finally the experimental results.
[Responses 1] We thank the reviewer for the suggestion. We revised the
abstract according to the comments provided.

Comments 2 To demonstrate the depth and breadth of the content of this paper, it is advisable
to complete the INTRODUCTION section based on the citation of the latest
research papers. For example, citing papers such as "Generate adversarial-driven
cross-aware network" and "CATNet: Cascaded attention transformer network"
can make your paper more credible.
[Responses 2] We thank the reviewer for the suggestion. We added the
suggested papers in the introduction section as follows: "In this vein, additional
studies are investigating the potential of the convolutional method across several
domains. As an example, [12] present a cascading attention transformation
network for marine image classification, termed CATNet, which incorporates an
efficient channel attention module that uses deep convolution to effectively extract
essential image features. [13], instead, integrate a semi-supervised generative
adversarial network (SSGAN) for data augmentation and a cross-aware attention
network (CAANet) using a combination of 3D and 2D convolutions along with
attention mechanism to improve the identification of different wheat varieties by
focusing on their spectral, spatial, and textual features".

Comments 3 The elaboration of the innovative points in the introduction section of the paper
is not clear enough. It is recommended that the author further condense the
main contributions of this paper and list them one by one in the form of bullet
points in the introduction. This will clearly showcase the core innovative points
of the paper in terms of theory, methodology, etc., highlight the differences from
existing works, and enable readers to quickly understand the unique features of
the paper.
[Responses 3]We thank the reviewer for the suggestion.We summarized the
main contributions of this paper in the introduction section, by highlighting the
innovative aspects introduced with the study. We added the following paragraph:
"This study specifically aids in developing an advanced and innovative approach
to assist policymakers in their allocation decisions about health services for the
increasing demography of individuals over 65 in Italy. The study offers multiple
contributions:
1 It uses advanced artificial intelligence methods to automate how healthcare
services are distributed in Italy for people over 65, tackling the issue of thoroughly
assessing healthcare resources and checking the fairness of services
in different regions.
2 It provides a new way to evaluate the unfair distribution of health services
by combining image processing technique with geographic analysis, using
weighted convolution matrices as statistical units instead of administrative
boundaries, which improve accuracy of estimating health resources in the
area.
3 It uses a measure of inequality called Gini Index to assess the fairness of
health services distribution, taking into account both how many aged population
live in an area and how the wealth is spread out in that area.
4 It could aid in future practical development of support systems, by incorporating
the proposed methodological model into decision support systems
improved through dashboards with more accessible information for policymakers"
. We hope that this may clarify the content of novelty
of our paper.

Comments 4 The paper only provides an overall flowchart, but for the image convolution
method innovatively used in this paper, the corresponding overall structural diagram
is not given. To reflect the professionalism and rigor of the paper, it is
recommended that the author add the structural diagram of this method and
provide detailed explanations and descriptions of it. This will help readers more
intuitively understand the specific implementation process and principles of the
image convolution method, and enhance the readability and comprehensibility of
the paper.
[Responses 4] Thanks for the suggestion, we agree that a detailed description
of the convolution step could improve the manuscript. To this aim we add
a new figure with the flow chart of the convolution step and add the following
sentence:
"A flowchart detailing the Matrix Convolution step introduced in Figure 2 and
described in this section is shown in Figure 5. It illustrates the logical structure
of the computational process used to obtain the matrix Ct. After determining the
dimensions of the resource matrix Rt, namely W and H, the algorithm iterates
over each tile (i, j) in the matrix and calculates the convolution between Rt and
the corresponding resource kernel, as given by Equation 2. The result of this
convolution is then weighted by the population Pi,j residing in the tile (i, j).
Finally, the algorithm returns the convolved matrix Ct."

Comments 5 In the Method section of this paper, it is stated that population data is required
to weight the convolution results. However, the paper does not explain why this
weighting is necessary. This makes it difficult for readers to understand the con-
tribution of this operation to the overall research methodology and how this
step can improve the accuracy and reliability of the research results. The author
should provide a detailed explanation of the theoretical basis for choosing the
weighting process to facilitate readers’ understanding.
[Responses 5] Thanks for the suggestion, we agree that this description
could improve the manuscript. To clarify this point, we added the following sentence
in section 2.2.1.
"Note that we weight the convolution results with population data to account
for the potential demand for services, rather than just their presence. Without
this weighting, the analysis would focus solely on the supply of services, overlooking
how many people reside in each area and might use them. By incorporating
population data, we address both supply and demand, which are crucial for accurately
assessing service distribution [21 , 22]. This step enhances the validity
and interpretability of our findings by emphasizing the real impact on the population."

Comments 6 The author should add comparative experiments. In this paper, only the overall
and average impacts of the proposed method on health services are given, but no
similar comparative experiments are added to highlight the effectiveness of the
proposed method.
[Responses 6] Thanks for the suggestion, we agree that a comparison with
the state of the art could improve the manuscript. To this aim we introduced the
following analisys:
"To further validate our convolution-based evaluation, we conducted a comparative
analysis with traditional spatial accessibility methods, such as the Enhanced
Two-Step Floating Catchment Area (E2SFCA) model [23, 35-37]. While E2SFCA effectively assesses
healthcare accessibility by integrating travel times and demand-supply ratios,
our approach leverages convolution techniques to provide a more detailed representation
of fine-scale spatial disparities. The results indicate that our method
enhances the precision of localized healthcare distribution assessments, which is
crucial for identifying underserved areas and informing targeted policy interventions"

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper addresses the problem of healthcare service distribution in Italy. The Authors proposed a methodology that enables the analysis of fairness in healthcare service availability across the country. Specifically, the research focuses on citizens aged over 65, whose gradually increasing numbers are becoming a significant challenge for Italy's social support system, requiring thoughtful actions from policymakers. The proposed methodology, combining both governmental and open-source data, visualizes it for further analytical purposes. The Authors also evaluated the fairness of healthcare service coverage using the Gini coefficient, highlighting the need for such services and superimposing it with geographical possibilities. In general, the topic is both scientifically interesting and has a significant importance from the social perspective, however, the presented research has several notable weaknesses that make it unsuitable for publication in the current form in a high-quality JCR-listed journal like Mathematics.

Major remarks:

• Section 2 - The Authors briefly listed previous works that inspired them to formulate their methodological framework, however, a more comprehensive description of these pieces of the past research, including visualizations, would help the casual reader to understand how this work contributes to the state-of-the-art.
• Section 2.2.1 - The step of discarding non-aligned resources requires more explanation. How exactly was the map-matching process performed? How many points in total were discarded? These factors could significant impact the further insights and conclusions.
• Section 2.2.2:
  • The authors indicated that kernel sizes were determined based on their experience - this statement should be expanded with additional comments on how this experience informs their decisions, what factors are considered, and examples, if possible.
  • The assumption that an average speed of 50 km/h enables one to cover almost 60 km in an hour is mathematically incorrect - it changes the actual result by 20%.
  • Assumptions regarding walking speed were not mentioned at all. Given that the research concerns people aged 65+, was their walking speed or average assumed? This assumption, like the previous one, could significantly affect later calculations and should be supported by appropriate literature.

Minor remarks:

• Section 2.1 - Although the process of input data preparation is explained step-by-step, providing examples of data gathered from particular sources would be more informative. Detailing file extensions does not add value to the manuscript and may confuse readers unfamiliar with geospatial data.
• Section 2.2.3 - Providing a convolution example is unnecessary; the work should assume the reader either knows the fundamentals or can find them in a provided reference. However, an example of the conversion between a shapefile and a TIFF file would add significant value, highlight the paper's contribution, and prove the authors' expertise in conducting and presenting their research.
• Future works involving data visualization, such as the development of dashboards and user-friendly interfaces, should not be categorized as research.

Nevertheless, despite a few critical remarks that, in my opinion, significantly affect the quality of this manuscript, I would like to appreciate the research conducted and presented by the Authors. The performed calculations and geospatial data analysis, followed by a discussion of the real implications for society, are important and highlight the interdisciplinary nature of this work. I believe that supporting this research with a solid and clearly stated methodology assumptions will lead to many real benefits.

Author Response

[Comments 1] The paper addresses the problem of healthcare service distribution in
Italy. The Authors proposed a methodology that enables the analysis of fairness in
healthcare service availability across the country. Specifically, the research focuses on
citizens aged over 65, whose gradually increasing numbers are becoming a significant
challenge for Italy’s social support system, requiring thoughtful actions from policymakers.
The proposed methodology, combining both governmental and open-source
data, visualizes it for further analytical purposes. The Authors also evaluated the fairness
of healthcare service coverage using the Gini coefficient, highlighting the need
for such services and superimposing it with geographical possibilities. In general, the
topic is both scientifically interesting and has a significant importance from the social
perspective, however, the presented research has several notable weaknesses that make
it unsuitable for publication in the current form in a high-quality JCR-listed journal
like Mathematics.
[Responses 1] Thanks for your work done revising our paper and for all your considerations
and suggestions. We appreciate your effort. We did our best to answer point
by point all of your comments. We highlighted in blue the most important corrections.

 

Major remarks:

Comments 2 Section 2 - The Authors briefly listed previous works that inspired them to formulate
their methodological framework, however, a more comprehensive description
of these pieces of the past research, including visualizations, would help the casual
reader to understand how this work contributes to the state-of-the-art.
[Responses 2] We thank the reviewer for the suggestion. We agree that an
more comprehensive description of the previous works can improve the understanding
of the state-of-art. We added the following paragraphs in section 2: "In
their work, the authors employed a geographic grid to develop a grid partition
model of the study area at 5 km by 5 km intervals, systematically searching
each grid for 30 designated keywords pertinent to healthcare and community resources,
such as hospitals, to produce a vector quantifying hot words for each
grid. They utilised a maximum likelihood estimation method to assess the grid
population using the hot words quantity vector, and contrasted the actual distribution
density of per capita hospital resources by examining the population
inside each grid along with the number of hospitals available". "In
their study [11], a convolutional technique was employed to evaluate the impact
of Nature-Based Solutions (NBSs), such as parks, on the urban grid, with the
kernel matrix delineating the neighbourhood effect of the NBS. They assessed
the cumulative impact of an NBS at each point on the grid by convolving this
kernel with the array of possible locations, and they utilised a mixed-integer linear
programming (MILP) model to determine the ideal places for the installation
of NBSs from a selection of candidate locations".

Comments 3 Section 2.2.1 - The step of discarding non-aligned resources requires more explanation.
How exactly was the map-matching process performed? How many
points in total were discarded? These factors could significant impact the further
insights and conclusions.
[Responses 3] Thanks for the suggestion, we agree that these factors could
significantly impact the results and that a detailed description could improve the
manuscript. For these reasons we substituted the sentence: "Resources for which
no location data were available were discarded." with the following one:
"For each tuple in the services dataset, we checked whether there was a corresponding
reference in OSM by sequentially verifying: the complete address
provided in the dataset (i.e. Name and street), only the service name, only the
street, and only the city. If no coordinates were found during this process, we
removed the entry from the dataset. Through this filtering step, only one entry
was removed from the hospital dataset. We then further filtered the dataset
to remove all duplicate entries. Specifically, if two services had the same name
or street, only one was retained. By removing these duplicates, we eliminated
42.8% of the hospital entries, 28.7% of the parapharmacy entries, and 38.4% of
the pharmacy entries."

Comments 4 Section 2.2.2: The authors indicated that kernel sizes were determined based on
their experience - this statement should be expanded with additional comments
on how this experience informs their decisions, what factors are considered, and
examples, if possible.
[Responses 4] We thank the reviewer for the comment. We defined the
spatial units for territorial analysis based on our prior experience concerning
the phenomenon under investigation and the effects in terms of data resolution.
However, the assumptions were also influenced by previous studies, such as the
ones on the average walking speed of people aged 65 and over and on the ones
assumed as the methodological basis for this study. This allowed us to set certain
kernel dimensions, as they proved to being more effective in representing spatial
units for the target of our interest. We discussed this point in section 2.2.2. We hope that this may clarify the
point.

Comments 5 Section 2.2.2: The assumption that an average speed of 50 km/h enables one to
cover almost 60 km in an hour is mathematically incorrect - it changes the actual
result by 20%.
[Responses 5] Thanks for highlighting the error. We agree that there is
an error. We corrected the sentence by modifying it with the correct speed of
60 km/h.

Comments 6 Section 2.2.2: Assumptions regarding walking speed were not mentioned at all.
Given that the research concerns people aged 65+, was their walking speed or
average assumed? This assumption, like the previous one, could significantly
affect later calculations and should be supported by appropriate literature.
[Responses 6] We thank the reviewer for the comment. In our paper, we
assumed that the average walking speed of people aged 65 and older is 0.8 m/s, as
discussed in literature. We discussed this assumption and its effect in the design
method in the subsection 2.2.2.

 

Minor remarks:

Comments 7 Section 2.1 - Although the process of input data preparation is explained stepby-
step, providing examples of data gathered from particular sources would be
more informative. Detailing file extensions does not add value to the manuscript
and may confuse readers unfamiliar with geospatial data.
[Responses 7] We agree that examples of the dataset could improve the
quality of the manuscript. To this aim, we added an example for services data,
and an example for the population data.
Furthermore, detailing file extensions may confuse readers unfamiliar with
geospatial data. For this reason we removed the details about the format of
the data in section 2.1. Therefore, to answer the question of another reviewer,
we explained better the usage of the geospatial libraries.

Comments 8 Section 2.2.3 - Providing a convolution example is unnecessary; the work should
assume the reader either knows the fundamentals or can find them in a provided
reference. However, an example of the conversion between a shapefile and a TIFF
file would add significant value, highlight the paper’s contribution, and prove the
authors’ expertise in conducting and presenting their research.
[Responses 8] We appreciate the suggestion to include a shapefile to TIFF
conversion example. However, we note that it is not easy to find scientific articles
or sections specifically dedicated to the shapefile to raster conversion function.
We propose citing some articles that mention the conversion function in a general
context, as well as official GIS software documentation that provides a technical
explanation of this process, which we believe will be the most useful for understanding
the procedure. We add the following sentence:
"To ensure accurate spatial data processing, we also converted shapefiles to
TIFF format using standard GIS libraries (e.g., GDAL), preserving spatial metadata
and projection integrity. This step enhances the adaptability and reproducibility
of our methodology, aligning with best practices in geospatial analysis [27-31]"

Comments 9 Future works involving data visualization, such as the development of dashboards
and user-friendly interfaces, should not be categorized as research.
[Responses 9] We thank the reviewer for the suggestion. We modified the
sentence as follows: "this study opens door for creating better technologies that
use the proposed methodological model in decision support systems, enhancing
the dashboard of accessible information, and developing an effective and userfriendly
interface design".
Nevertheless, despite a few critical remarks that, in my opinion, significantly affect
the quality of this manuscript, I would like to appreciate the research conducted and
presented by the Authors. The performed calculations and geospatial data analysis,
followed by a discussion of the real implications for society, are important and highlight
the interdisciplinary nature of this work. I believe that supporting this research with
a solid and clearly stated methodology assumptions will lead to many real benefits.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

It can published. Revisions are appropriate. 

Reviewer 2 Report

Comments and Suggestions for Authors

 All my concerns have been well addressed. The manuscript can be recommended for publication. 

Reviewer 3 Report

Comments and Suggestions for Authors

The Authors have effectively addressed most of the remarks, both major and minor, provided in the initial review.

Firstly, the literature review has been expanded to include the significance of previous works in the research area under consideration. The Authors clearly highlighted how their research contributes to the advancement of the state-of-the-art and provided essential visualizations, which, while perhaps obvious to the Authors, are crucial for readers to follow the work accurately.

Secondly, the methodology section has also undergone significant improvement. The Authors included essential details regarding the data pre-processing operations, justified by metrics for eliminated duplicates, which enhances the understanding of the consistency of the conflated real-life inputs. Also, the Authors refined the kernel design, providing the necessary details required to understand the entire methodology.

I appreciate the Authors' efforts in addressing all the provided remarks, one-by-one, and enhancing the manuscript notably. Although the literature review could be further extended with additional works and the methodology section still contains some content that may be deemed unnecessary, in my opinion at least, such as a convolution example, I agree that the overall quality of the manuscript has been elevated. It is currently well-suited for publication in a JCR-listed journal such as Mathematics.