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Research Article
Application of Bayesian Nonparametric Estimation on Cervical Cancer: A Case
Study of University College Hospital, Nigeria
Onatunji Adewale P
1
, Folorunso Serifat A
2
*, Oluwasola Timothy AO
3
, Adesina Oluwaseun A
4
and Uthman Kafayat T
5
1
LAUTECH Int’l College, Ogbomoso, Oyo State, Nigeria
2
University of Ibadan Laboratory for Interdisciplinary Statistical Analysis (UI-LISA), Nigeria
3
Department of Obstetrics and Gynecology, College of Medicine, University of Ibadan, Nigeria
4
Department of Mathematics and Statistics, The Polytechnic, Ibadan, Oyo State, Nigeria
5
National Centre for Genetic Resources and Biotechnology, Ibadan, Oyo State, Nigeria
*Corresponding Author
: Folorunso Serifat A,Department of Statistics, University of Ibadan, Oyo State, Nigeria.
Received: October 28, 2020; Published: February 12, 2021
Abstract
Cervical cancer is the third most common malignancy in women worldwide, and in developing countries, it remains a leading


nd
most prevalent cancer among women in Nigeria and the most prevalent cancer among ages 15 - 44

   
examining the Bayesian estimation of cervical cancer on a woman’s age and survival period of the disease using the application of


the survival period is between stage I-IV. Also, there is an increase in woman’s age and survival period of living with the disease which

Keywords: Bayesian Estimation; Mortality; Risk Factors; Probability; Survival Time
Citation: Folorunso Serifat A., et al. “Application of Bayesian Nonparametric Estimation on Cervical Cancer: A Case Study of University
College Hospital, Nigeria”. EC Nursing and Healthcare 3.3 (2021): 161-167.
Introduction
Globally, approximately 10 million people are diagnosed with cancer annually. The increase of cancer incidence is occurring at a faster
-
zation, 100,000 new cancer cases have been reported in the country each year; and projected that by 2020, cancer incidence for Nige-
rian males and females would rise to 90.7/100,000 and 100.9/100,000, respectively. In Nigeria, with a population of nearly 200 million
people, complex diseases such as cancer are currently emerging as important health care priorities for the future. A report by Stewart.,
et al

-
mies, they will encounter much higher cancer rates, particularly gynecological cancers such as cervical cancer. This disease has continued
Citation: Folorunso Serifat A., et al. “Application of Bayesian Nonparametric Estimation on Cervical Cancer: A Case Study of University
College Hospital, Nigeria”. EC Nursing and Healthcare 3.3 (2021): 161-167.
162
Application of Bayesian Nonparametric Estimation on Cervical Cancer: A Case Study of University College Hospital, Nigeria
to be a threat to women’s health in developing countries. Marc., et al
mortality from it occurred in 2018. In Malawi, 132 (44%) patients in stage 1 cervical cancer and 168 (56%) patients in stage 1 - 4 were
reported for the study periods of 310 patients (Pandaora., et al. 2017). Cervical cancer grows in the cervix (the entrance from the vagina

an extremely contagious virus that is transmitted through sexual contact. Once diagnosed, as long as it is treated early and controlled


According to Human Papillomavirus and Related Cancers, Fact Sheet 2018, it was reported that there are 50.33 million women aged

cervical cancer every year and 10403 dies from the illness. It is estimated that approximately 3.5% of women in the general population in
Nigeria are projected at a given time to have harbor cervical HPV-16/18 infection and 66.9% of invasive cervical cancers are due to HPVs

-
ease and screening methods.
Materials and Methods
University College Hospital (UCH) of the University of Ibadan, Nigeria is a leading tertiary Centre for cancer care in Nigeria and as


extracted from medical records of cervical cancer in this hospital. This study examined 310 patients with cervical cancer from reproduc-
tive-age women and other data with considered variables such as age and survival time which is the period used in admission and this is
measured in a month. The months are categorized as follows: stage I = 12 months, stage II = 24 months, stage III = 36 months, stage IV =
48 months, and stage V = 60 months and above. The ages of the patients are also grouped into 4 as shown in table 1. The mortality by the
disease is a binary event indicator (response) measured alive = 1 and dead = 0 with continuous explanatory variables that are captured
nonparametrically.
The Bayesian nonparametric regression model was applied to estimate cervical cancer women with their age and the survival period
with cervical cancer measured in several months. Age of the woman and this period are modeled by basic functions (
and
ij
ff
) ap-

l

i
f
is the seasonal effect
and
j
f
-
proximated by a polynomial spline of degree
l

min 0 1 1 max
...
mm
xx
ζζ ζ ζ
−
= < << < =
. To ensure
-

that assumption of a strictly linear effect on the continuous variables (woman‘s age and length of stay) is not appropriate, non-parametric
modeling of cervical cancer is then developed and compactly written as
( ) ( )
period ' age (1)
ij
mortality f time f woman s= +
The estimated nonlinear functions
depend considerably on the hyperprior assumptions with the choice of hyperparam-
eters
ij
0.001 and 0.001
ij
αβ
= =

the patient status regresses nonparametrically on woman’s age and survival period of the disease in Bayesian approach.
Citation: Folorunso Serifat A., et al. “Application of Bayesian Nonparametric Estimation on Cervical Cancer: A Case Study of University
College Hospital, Nigeria”. EC Nursing and Healthcare 3.3 (2021): 161-167.
163
Statistical analysis
The cases of cervical cancer are denoted as
i
y
is a binary variable (alive=1 and dead=0) associated with the study area conditional

outcome (
i
p
), the probability of mortality caused by cervical cancer given the health Care Centre in the study area.
.;
12
i
.;
12
exp( age+ time period)
: ~ Bin( , ) where p (2)
1+ exp( age+ time period)
i ii
woman s
p y pn
woman s
ββ
ββ
=

( )
i
|p ,
ii
Ly n
=
( )
1
i
1 (3)
i
i
y
y
ii
i
n
pp
y
−

−


Here, the study area is UCH situated in the Ibadan area of Nigeria and
i
n
is the total population of women diagnosed with cervical can-
-
dictor replaced by structured additive predictors such as
( )
log , 1, 2
i ii
it p x i
β
= =
where
x
are the i
th
design matrix (not including
an intercept) of women’s age and period of cervical cancer. The parameters distribution for the continuous variables considered have vari-

in
i
p
. The hyperprior distribution for the variance parameter on the positive real line follows a gamma distribution as against Jeffrey’s


j
and
i
ff
depend on the woman’s age and length of
stay of the disease and prior beliefs about the smoothness
j
and
i
ff
.The vector of function evaluation
( )
j
, '
i
f ff=
as the matrix
product of a design matrix
( )
wowan's age , time period of living with the diseaseX =
.
The non-informative prior for a function
f


( )
( )
( )
2'
2
2
2
11
/ exp (4)
2
rank K
pK
βτ β β
τ
τ

∝−



K
is the penalty matrix, for the
β
is partially improper Gaussian prior that follows
( )
22
/ ~ N 0, K
βτ τ
and variance
parameter
2
τ
to be inverse smoothing parameter in a generalized nonparametric regression model which controls the tradeoff between
-
rior marginal distribution of cervical cancer is then given as
( )
2
,/
i
py
βτ
=
( )
|
i
Ly
β
x
( )
2
/p
βτ
x
( )
2
(5)p
τ
The choice of before estimating the smoothing parameter
2
τ
simultaneously with
β
, a proper hyperprior is assigned to it by choos-
ing
2
~ IG(a=0.001, b=0.001)
τ

for the regression parameters
β

Bayesian logistics regression model


Application of Bayesian Nonparametric Estimation on Cervical Cancer: A Case Study of University College Hospital, Nigeria
Citation: Folorunso Serifat A., et al. “Application of Bayesian Nonparametric Estimation on Cervical Cancer: A Case Study of University
College Hospital, Nigeria”. EC Nursing and Healthcare 3.3 (2021): 161-167.
164
Application of Bayesian Nonparametric Estimation on Cervical Cancer: A Case Study of University College Hospital, Nigeria
Results and Discussion
Variables/ Covariates Alive Dead Total
Patients’ age
20 - 40 31 (10) 16 (5.16) 47 (15.16)
41 - 60 136 (43.87) 36 (11.61) 172 (55.48)
61 - 80 55 (17.74) 30 (9.68) 85 (27.42)
81 - 100 4 (1.29) 2 (0.65) 6 (1.94)
Total 226 (72.90) 84 (27.10) 310 (100)
Period (Months)
Stage I 144 (46.45) 50 (16.13) 194 (62.58)
Stage II 49 (15.81) 13 (4.19) 62 (20)
Stage III 15 (4.84) 9 (2.90) 24 (7.74)
Stage IV 8 (2.58) 7 (2.26) 15 (4.84)
Stage V 10 (3.23) 5 (1.61) 15 (4.84)
Total 226 (72.90) 84 (27.10) 310 (100)
Table 1: Distribution of characteristics of risk factors of mortality.
This table shows the total number of women that died or survived cervical cancer at different age groups and the period of the disease

cancer while 84 of them could not survive it. In this study patients between 41 and 60 years of age have the highest number, 172 (55.48
percent) women that suffered from cervical cancer from which 36 (11.61 percent) of them could not survive the disease. However, those
between 81 and 100 years have the smallest number, 6 (1.94 percent) women from which 2 (0.65 percent) suffering the disease died of
it. From the length of stay of the disease, stage I contains the highest number, 194 (62.58 percent) women that stayed in the disease mea-
sured in months, but 50 (16.13 percent) women died of the disease in stage I. Stage IV and V have the same total number, 15 (4.84) women
that stayed in the disease but stage 4 has 7 (2.26 percent) and stage 5 has 5 (1.61 percent) women that died.
Covariates Mean Std. Dev. Odds Ratio NSE 95%Cred.Interval
 -0.0054687 0.0041589 0.9945462 0.000772 -.0198049 .0004026
Time period of Disease -0.0072252 0.0040295 0.9928008 0.000634 -.0140168 .0062294
Table 2: Bayesian estimation of the logistic regression model.
Table 2 contains the posterior mean and standard deviation of women and period of living with the disease in the study. It is important




Citation: Folorunso Serifat A., et al. “Application of Bayesian Nonparametric Estimation on Cervical Cancer: A Case Study of University
College Hospital, Nigeria”. EC Nursing and Healthcare 3.3 (2021): 161-167.
165


Application of Bayesian Nonparametric Estimation on Cervical Cancer: A Case Study of University College Hospital, Nigeria
Figure 1: Result of the nonparametric effect of woman’s age with hyperparameters a = b = 0.001.
Figure 2: Result of nonparametric effect of survival time period (months) with cervical cancer with hyperparameters a = b = 0.001.



Citation: Folorunso Serifat A., et al. “Application of Bayesian Nonparametric Estimation on Cervical Cancer: A Case Study of University
College Hospital, Nigeria”. EC Nursing and Healthcare 3.3 (2021): 161-167.
Bibliography
1. Annals of Oncology 17 (2006): 15-23.
2. 
3. 
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Application of Bayesian Nonparametric Estimation on Cervical Cancer: A Case Study of University College Hospital, Nigeria
Conclusion


table 1, it is revealed that more economically active women (41 - 60) as against economically inactive ones (e.g. 61 - 80) are involved in this

mortality caused by cervical cancer by 0.55% and 0.72% respectively. Figure 1 and 2 reveal that age and period of living with the disease
increase the probability of women surviving cervical cancer as the age and period increase. As the westernized lifestyle (with its associ-
ated reproductive patterns and dietary patterns) is continuously adapted, cancer incidents will also rise. Unless medical care and screen-



Appendix
Figure
Citation: Folorunso Serifat A., et al. “Application of Bayesian Nonparametric Estimation on Cervical Cancer: A Case Study of University
College Hospital, Nigeria”. EC Nursing and Healthcare 3.3 (2021): 161-167.
4. Marc A., et al.
5. 
6. 

7. Statistical
Science 11 (1996): 89-121.
8. Holmes C and Held L. “Bayesian auxiliary variable models for binary and multinomial regression”. Bayesian Analysis 1 (2006): 145-
168.
9. Lawson A. “Bayesian disease mapping: Hierarchical modeling in spatial Epidemiology”. Andrew B. Lawson. P; Cm. -- (Chapman and
Hall/CRC Interdisciplinary Statistics Series) includes Bibliographical References and Index (2008).
10. Journal
of the Royal Statistical Society C 50 (2001): 201-220.
11. Bray F., et al. “Global cancer statistics 2018: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 coun-
tries”. CA: A Cancer Journal for Clinicians 68 (2018): 394-424.
12. Brezger A and Lang S. “Generalized Structured Additive Regression Based on Bayesian P-Splines”. Computational Statistics and Data
Analysis 50 (2006): 947-991.
13. et al.
14. Siegel RL., et al. “Cancer statistics, 2015”. CA: A Cancer Journal for Clinicians 65 (2015): 5-29.
15. 
16. 
17. https://emedicine.medscape.com/article/253513-overview
18. https://www.hpvcentre.net/statistics/reports/NGA_FS.pdf
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