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American Journal of  Applied 
Statistics and Economics (AJASE)

Effective Health Care Plan for National Health Insurance Scheme Patients with
Non-Communicable Diseases in Plateau North Senatorial District

Philemon Polycarp Davwar1*

Volume 2 Issue 1, Year 2022
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Article Information ABSTRACT

Received: February 25, 2023

Accepted: May 08, 2023

Published: May 14, 2023

Patients of  non-communicable diseases (NCDs) are usually placed on a life-long prescription 
or procedure. This is sometimes a problem in itself. They could get tired since they are in 
most cases, not sickly, they could get careless as a result of  familiarity or boredom, etc. The 
greatest challenge is that they could decide not to access care or continue to access care 
at a particular location for several reasons which may be culturally, politically, or socially 
influenced. Consequently, their situation could become more complicated. The location of  
access points to healthcare for them becomes a critical issue here. In this research, we looked 
at location of  healthcare access points for NCD patients living in Plateau North Senatorial 
district who are also registered with the National Health Insurance Scheme (NHIS). Data 
on specialist opinions as to the relevance of  each specialist and equipment for the effective 
management of  the associated NCD was collected and analysed to determine relevance 
ratings. These ratings along with data on availability of  specialists and equipment from each 
care provider registered with the NHIS in the study area, was analysed using the Patient-
based Set Covering Location Model (Davwar, Wajiga & Okolo, 2021). The results show 
care providers that can provide healthcare services to such patients at a quality level T, 
the threshold value for patients in each location, below which a service provider is not 
considered. This was done for each NCD (Diabetes and Cancer) under consideration. In the 
analysis, each NCD was considered a scenario. For each patient of  diabetes and or cancer, 
in each location in the study area, this research determines points of  access to quality care.

Keywords

Patient-Based Facility Location, 
Non-Communicable Diseases, 
Diabetes, Cancer, Set Covering 
Location Models

1 Department of  Mathematics and Statistics, Federal Polytechnic Idah, Kogi State, Nigeria
* Corresponding author’s e-mail: ppdavwar@gmail.com

INTRODUCTION
Patients of  chronic non-communicable diseases are usually 
placed on a life-long prescription or procedure. This is 
sometimes a problem in itself. They could get tired since 
they are in most cases, not sickly, they could get careless 
as a result of  familiarity or boredom, etc. The greatest 
challenge is that they could decide not to continue to access 
care at a particular location for a number of  reason which 
may be cultural, political, or social. They are mostly healthy 
looking and so may feel uncomfortable that other people 
know that they are sick. They may prefer to pretend they 
have no problems. 
They most times prefer to access medical care in some 
concealed manner. So this study attempts to locate points 
of  access to healthcare service for them. Since this is 
a medical problem, it is required that a total coverage is 
achieved. Ordinarily, the classical set covering facility 
location model would suffice, except that if  the classical 
model optimizes well, a patient will be assigned to one 
point of  healthcare service only. Therefore, if  this patient 
has other psychological considerations but compelled to 
access care in this one facility prescribed by the model, he 
may do so but suffer from a psychological stress which may 
complicate the management of  his case over time. 
The objective of  this research is to locate points of  access 
to health care services for patients suffering from either 
diabetes or Cancer and who reside in any of  the local 
government areas in Plateau North senatorial district. 
These points of  access provide ‘cover’ for each of  these 
patient locations at a quality level of  at least a threshold 

value as prescribed by the patient-based facility location 
model (Davwar, Wajiga & Okolo, 2021).

LITERATURE REVIEW
NCDs results from a mixture of  genetic, physiological, 
environmental and behavioural factors with pronounced 
dangers because of  its chronic nature. Annually, its global 
mortality is 41 million people, which accounts for 70% of  
global deaths. Approximately 40% of  these deaths occur 
among people aged between 30 and 69 years (WHO, 
2018a), while 80% of  these early deaths occur in low and 
middle-income countries (WHO, 2018b). Global Health 
Observatory data in 2018 predicted that deaths from 
NCDs would rise to about 52 million worldwide in the 
year 2030 (WHO, 2020).
Of  all NCDs, cardiovascular disease accounts for about 
40% of  all deaths annually while cancers, respiratory 
diseases and diabetes account for 22%, 10% and 4% 
respectively. These four diseases similarly account for 
over 80% of  all premature deaths (Olukoya, 2017).
In a WHO report, the probability of  dying prematurely 
from NCDs in Nigeria is put at 20% (WHO, 2018c) while 
the projected prevalence estimate of  diabetes in Nigeria 
is 4.04% (IDF, 2011). According to the 2012 Globocan 
data, Nigeria’s top five cancer burdens are breast, cervix 
uteri, liver, prostate and colorectal cancers (Awodele, 
Adeyomoye,  Awodele, Fayankinnu & Dolapo, 2011). 
Workable and evidence-based solutions must be provided 
(Ezzati & Riboli, 2012) to relieve the burden of  NCDs 
in Nigeria which is the aim of  this research. Current, 

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Am. J. Appl. Stat. Econ.1(1) 1-6, 2023

Daskin, & David (2001) maintained among others that 
location decisions are often strategic in nature, frequently 
impose economic externalities and often extremely 
difficult to solve. He further puts it that there does not 
exist a general location model that is appropriate for all 
potential or existing applications.
Therefore, different models are developed for different 
location decisions. The model employed in this study 
Davwar, Wajiga & Okolo (2021) was developed to cater 
for the peculiarities of  patients with NCDs.
It will be recalled that Diabetes and Cancer are both 
NCDs. They are probably the most common chronic 
health challenges in the contemporary society. 
Any research that could lead to an enhanced management 
of  NCDs is very needful because NCDs are an important 
contemporary health issue, and is growing in importance, 
because:

i. A person’s social circumstances affect the chance of  
him/her having a NCD greatly. So, the chances are right 
that more people will come down with one NCD or the 
other.

ii. Some patients have multiple NCDs, which make 
their care particularly complex.

iii. NCDs usually have a mild beginning, a simple social 
habit, or what appears to be a normal life, but gradually 
grow into a life-threatening monster.

iv. There is evidence that NCDs can be better managed 
through increased ease of  access to special medical help.

METHODOLOGY
Data from Plateau North Senatorial district on Diabetes and 
Cancer were collected for this study. Data on availability of  
specialists and equipment/procedures were collected from 
all NHIS service providers in the district and used for the 
analyses. The Microsoft EXCEL solver was used to analyse 
the data. The analyses and results are presented below:
The Patient-Based Set Covering Facility Location model 
developed by Davwar, Wajiga & Okolo (2021) was used 
in this analyses.
Given a set of  NHIS service providers in the study area,
Ni= {J\Qjis≥Ts }, ∀j ∈ J, ∀i ∈ I and for each scenario s, 
s= 1,2
And given that:
Ni is a set of  facilities capable of  offering service to 

patients in location i with scenario s  at a quality level of  
at least Ts 
Where:
Ts= Quality threshold for scenario s.
Qji= 1/dij{Fjs+ Ejs } (1)
Fjs= Rating of  Specialists at service point j for management 
of  scenario s.
Ejs= Rating of  equipment at service point j for 
management of  scenario s.
Qjis= Quality of  service facility j can provide to patient 
location i with scenario s.  
And dij= Distance from patient location i to hospital j
Then the minimum number of  health facilities Zs that 
can provide coverage for patients with chronic condition 

RESULTS AND DISCUSSION
To evaluate equation (1) we require the following:

The Specialists and Equipment/Procedure Ratings 
(Fjs and Ejs) respectively for every specialist and 
equipment/procedure
Using the data collected a score was determined for 
each specialist and equipment/procedure respectively, 
as a measure of  their relevance to the management of  a 
particular condition (scenario). The rating which is from 
a five-point scale is the average rating from the responses 
of  professionals in the field of  health care provision 
(Doctors, Laboratory Scientists, Pharmacists, others) 
on the relevance of  a given specialist or equipment/
procedure in the management of  the particular chronic 
challenge as presented in table 1 below:

Table 1: Showing Specialists and Equipment/Procedure Ratings
Scenario Specialists Fjs Equipment Ejs

1. Diabetes Dietician 5.00 Spectrophometer 4.83
Endocrinologists 4.80 Glucometer 4.80
Pharmacists 4.80 Insulin Infusion Pump 4.08
Lab. Scientists 4.71
Emergency Rm Med 4.50
Dialysis Nurses 3.45

2. Cancer Oncologists 4.97 Radiation Machines 4.66
Pathologists 4.59 Microscopes 4.53
Surgeons 4.46 CT Scan MRI 4.24

s in all patient locations is given as:
Where: Zs= minimum number of  facilities required to offer 
complete coverage to all patient locations with scenario s. 
J= the set of  eligible NHIS facilities (Indexed by j) 
I=  the set of  patients’ locations (Indexed by i)

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Am. J. Appl. Stat. Econ.1(1) 1-6, 2023

Pharmacists 4.44 Immunohistochemistry 4.21
Psychologists 3.47 X-Ray Machine 3.83
Psychotherapists 3.15

*Key to abbreviations in table above: CT Computerized Tomography, MRI Magnetic Resonance Imaging

Determination of  Health Service Centre Potentials 
(Total Scores for Specialists and Equipment/
Procedure Availability (Fjs+ Ejs))
Data on the availability of  specialists and equipment/

procedure at each facility was collected and used 
to determine specialists’ availability score Fjs  and 
equipment/procedure availability score Ejs (ie Potential) 
for each facility as presented in table 2 below:

Table 2: Hospital Potentials (Total Scores for Specialists and Equipment/Procedure Availability (Fjs+ Ejs)
S/N HOSPITAL DIABETES CANCER
1 PL/0057 14.29 14.02
2 PL/0163 14.29 14.02
3 PL/0003 14.29 14.02
4 PL/0172 14.29 14.02
5 PL/0171 14.29 14.02
6 PL/0150 27.21 30.78
7 PL/0014 14.29 14.02
8 PL/0103 14.29 17.86
9 PL/0159 14.29 14.02
10 PL/0116 14.29 14.02
11 PL/0169 14.29 14.02
12 PL/0100 41.13 40.60
13 PL/0168 14.29 14.02
14 PL/0010 14.29 17.86
15 PL/0067 14.29 14.02
16 PL/0079 14.29 14.02
17 PL/0021 14.29 14.02
18 PL/0008 14.29 14.02
19 PL/0075 22.71 26.28
20 PL/0104 14.29 17.86
21 PL/0170 14.29 14.02
22 PL/0009 14.29 17.86
23 PL/0076 14.29 14.02
24 PL/0064 14.29 14.02
25 PL/0120 14.29 14.02
26 PL/0176 14.29 14.02
27 PL/0058 14.29 14.02
28 PL/0019 14.29 14.02
29 PL/0018 14.29 14.02
30 PL/0115 14.29 14.02
31 PL/0111 14.29 14.02
32 PL/0077 14.29 14.02
33 PL/0020 14.29 14.02
34 PL/0066 14.29 17.86
35 PL/0158 28.21 31.94
36 PL/0007 14.29 14.02
37 PL/0057 14.29 14.02

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Am. J. Appl. Stat. Econ.1(1) 1-6, 2023

38 PL/0153 14.29 14.02
39 PL/0023 14.29 14.02
40 PL/0108 14.29 14.02
41 PL/0117 14.29 14.02
42 PL/0080 14.29 14.02
43 PL/0139 14.29 14.02
44 PL/0148 14.29 14.02
45 PL/0161 14.29 14.02
46 PL/0165 14.29 14.02
47 PL/0106 14.29 17.86
48 PL/0122 14.29 14.02
49 PL/0164 14.29 14.02
50 PL/0107 14.29 14.02
51 PL/0167 14.29 14.02
52 PL/0102 23.79 27.36
53 PL/0162 14.29 14.02
54 PL/0141 14.29 17.86
55 PL/0121 17.71 21.28
56 PL/0001 14.29 14.02
57 PL/0071 14.29 14.02

Note: See Appendix III for key to Hospital Codes.

Determination of  the Quality of  Facility j to Handle 
Patients In Location i With Scenario s. (Qjis)
We required the distances from the patient location to 
the various potential facilities (Appendix II) and the 
potentials (∑(Ejs+Fjs)) of  these facilities to handle each of  
the chronic conditions.  The potentials were appropriately 
combined with the distance factors (dij) to form the 
quality level of  facility j to handle patients in location i, 

with scenario s. This quality level of  facility j to handle 
patients in location i, with scenario s is computed as 
distance weighted. This is because of  the negative effect 
distance has on the quality of  service. It is computed for 
the two scenarios (Diabetes and Cancer) therefore as:
Qjis=  1/( dij ) {Ejs+ Fjs }
And presented in 3A (for Diabetes) and 3B (for Cancer) 
below:

Table 3: Quality level of  Facility j to Handle Patients in Location i With Scenario s. (Qjis)
Diabetes Cancer

Hospital

B
as

sa

Jo
s 

N
th

Jo
s 

E
st

Jo
s 

St
h

B
/L

ad
i

R
iy

om

B
as

sa

Jo
s 

N
th

Jo
s 

E
st

Jo
s 

St
h

B
/L

ad
i

R
iy

om

PL/0057 4.76 0.41 0.19 0.27 0.18 0.17 4.67 0.40 0.19 0.27 0.18 0.17
PL/0163 4.76 0.41 0.19 0.27 0.18 0.17 4.67 0.40 0.19 0.27 0.18 0.17
PL/0003 4.76 0.41 0.19 0.27 0.18 0.17 4.67 0.40 0.19 0.27 0.18 0.17
PL/0172 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0171 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0150 0.78 9.07 0.70 1.60 0.60 0.58 0.88 10.26 0.79 1.81 0.68 0.65
PL/0014 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0103 0.41 4.76 0.37 0.84 0.32 0.30 0.51 5.95 0.46 1.05 0.40 0.38
PL/0159 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0116 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0169 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0100 1.18 13.71 1.05 2.42 0.91 0.88 1.16 13.53 1.04 2.39 0.90 0.86
PL/0168 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0010 0.41 4.76 0.37 0.84 0.32 0.30 0.51 5.95 0.46 1.05 0.40 0.38

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PL/0067 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0079 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0021 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0008 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0075 0.65 7.57 0.58 1.34 0.50 0.48 0.75 8.76 0.67 1.55 0.58 0.56
PL/0104 0.41 4.76 0.37 0.84 0.32 0.30 0.51 5.95 0.46 1.05 0.40 0.38
PL/0170 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0009 0.41 4.76 0.37 0.84 0.32 0.30 0.51 5.95 0.46 1.05 0.40 0.38
PL/0076 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0064 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0120 0.41 4.76 0.37 0.84 0.32 0.30 0.40 4.67 0.36 0.82 0.31 0.30
PL/0176 0.19 0.37 4.76 0.30 0.19 0.17 0.19 0.36 4.67 0.29 0.19 0.17
PL/0058 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0019 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0018 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0115 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0111 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0077 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0020 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0066 0.27 0.84 0.30 4.76 0.51 0.38 0.34 1.05 0.37 5.95 0.64 0.47
PL/0158 0.54 1.66 0.59 9.40 1.01 0.74 0.61 1.88 0.67 10.65 1.14 0.84
PL/0007 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0057 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0153 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0023 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0108 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0117 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0080 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0139 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0148 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0161 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0165 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0106 0.27 0.84 0.30 4.76 0.51 0.38 0.34 1.05 0.37 5.95 0.64 0.47
PL/0122 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0164 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0107 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0167 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0102 0.46 1.40 0.50 7.93 0.85 0.63 0.53 1.61 0.57 9.12 0.98 0.72
PL/0162 0.27 0.84 0.30 4.76 0.51 0.38 0.27 0.82 0.29 4.67 0.50 0.37
PL/0141 0.27 0.84 0.30 4.76 0.51 0.38 0.34 1.05 0.37 5.95 0.64 0.47
PL/0121 0.34 1.04 0.37 5.90 0.63 0.47 0.41 1.25 0.44 7.09 0.76 0.56
PL/0001 0.18 0.32 0.19 0.51 4.76 0.30 0.18 0.31 0.19 0.50 4.67 0.30
PL/0071 0.18 0.32 0.19 0.51 4.76 0.30 0.18 0.31 0.19 0.50 4.67 0.30

Determination of  the Quality Threshold (T)
The threshold value T is determined as the lowest quality 
level a service point can offer a demand point to qualify 
that service point for consideration as a candidate in the 

analysis for the scenario under consideration. It therefore 
varies from scenario to scenario and is set by experiment 
as the smallest quality value for which the model has a 
feasible solution.

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Results from Model Analyses
The results from the model analyses shows the hospitals 
selected and the patient location that can enjoy service 
from them for each of  the two scenarios (Diabetes and 

Cancer respectively) at a quality level of  at least T (the 
quality threshold for that scenario). These results are here 
presented on the table below.
The results shown below are identical. This is a pure 

Table 4: Showing results of  the Model Analyses
Diabetes Cancer

Facility

Patient Location

Facility

Patient Location

Jo
s 

N
or

th

Jo
s 

So
ut

h

Jo
s 

E
as

t

B
/L

ad
i

B
as

sa

R
yo

m

Jo
s 

N
or

th

Jo
s 

So
ut

h

Jo
s 

E
as

t

B
/L

ad
i

B
as

sa

R
yo

m

PL/0150 ok ok ok ok ok ok PL/0150 ok ok ok ok ok ok
PL/0100 ok ok ok ok ok ok PL/0100 ok ok ok ok ok ok
PL/0075 ok ok ok ok ok ok PL/0075 ok ok ok ok ok ok
PL/0158 ok ok ok ok ok ok PL/0158 ok ok ok ok ok ok
PL/0102 ok ok ok ok ok ok PL/0102 ok ok ok ok ok ok

*Key: OK Means Covered by the Corresponding Facility

coincidence and does not mean that other scenarios will 
have identical results. From the above results, a patient in 
any of  the six patient locations (i = 1,2,…6)  can access 
service from any of  the five hospitals (j = 1,2,…5) chosen 
by the model with a quality level of  at least T (T= 0.2 for 
Diabetes and T=0.24 for Cancer).

CONCLUSION 
This study therefore concludes that the five hospitals 
(Bingham University Teaching Hospital, Jos University 
Teaching Hospital, Our Lady of  Apostles Hospital, Dee 
Medical Centre and Plateau Specialist Hospital) shown in 
the results provide adequate coverage (makes accessible) 
to patients with any of  the chronic conditions (Diabetes 
or Cancer) who reside in any part of  the Plateau North 
Senatorial District and who are NHIS subscribers.

RECOMMENDATION
The study recommends any of  the five identified 
hospitals to NHIS subscribers (patients) having Diabetes 
or Cancer and who reside in any part of  the Plateau north 
senatorial district. Policies that allow the establishment 
of  community parks, sidewalks, bike lanes, playgrounds 
or village square areas with beautiful landscapes where 
people can gather, jog, meet and play during leisure 
encourages people to participate in physical activity.

Acknowledgements
I would like to acknowledgement the advice and 
encouragement received from Professor G. Wajiga and 
Professor. H. G. Muazu all of  Modibbo Adama University 
Yola, Adamawa State, Nigeria. 

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