J. Nig. Soc. Phys. Sci. 4 (2022) 99–104

Journal of the
Nigerian Society

of Physical
Sciences

Juxtaposing Vertically Transmitted Infections (VTIs) and the
Spread of HIV/AIDS in a Typically Infection Prevalent Region

in Nigeria

Matthew Iseh, Anthony Usoro, Nsisong Ekong∗, Idara Ukpe

aDepartment of Statistics, Akwa Ibom State University, Ikot Akpaden, Nigeria

Abstract

In this paper, we investigate by putting side by side the rate at which Human Immuno-deficiency Virus/ Acquired Immune Deficiency Syndrome
HIV/AIDS spreads through Vertical Transmission (VT) in a typically infection prevalent region. Also, we model this relationship and present
the enormity and the likelihood of mother-to-child infections given Age, Weight, and Dosage of Drugs taken by the pregnant women. Binary
logistics regression is the approach employed in the analysis of this work. The method is necessary given the dichotomous nature of the variable
under investigation, in this case, the status of the newborns. The result from the Binary logistic regression shows that the probability that a child
will be infected given that the mother is positive is 0.098235 ≈ 0.1, and this is unlikely to happen given the small probability. This result is in
line with the proportion of Event count which is ≈ 0.1. Other complimentary test results also agree that given the biomarkers (Age, weight and
drug doses of the mothers) used in the study, the possibility of a newborn acquiring the deadly disease is very minimal. The study revealed that,
given these biomarkers, the chances of newborns being infected with HIV/AIDS through VT is very minimal. Hence, there is need for donors and
interventionists agencies to redirect attention and interventions to other modes of transmissions.

DOI:10.46481/jnsps.2022.418

Keywords: Human Immunodeficiency Virus (HIV), Acquired Immune Deficiency Syndrome (AIDS), Vertically Transmitted Infections (VTIs),
Akwa Ibom State.

Article History :
Received: 20 September 2021
Received in revised form: 26 November 2021
Accepted for publication: 02 January 2022
Published: 28 February 2022

c©2022 Journal of the Nigerian Society of Physical Sciences. All rights reserved.
Communicated by: W. A. Yahya

1. Introduction

The speedy upsurge of certain diseases notwithstanding the
myriads of precautionary and preventive measures taken glob-
ally by different quarters to evade the prevalence of such dis-
eases is a thing of great concern. One of such diseases is the Hu-
man Immuno-deficiency Virus/ Acquired Immune Deficiency
Syndrome HIV/AIDS - a disease that is still considered a ma-
jor global public health issue. So far, it has been with us for

∗Corresponding author tel. no: +2347069150513
Email address: nsisongekong@aksu.edu.ng (Nsisong Ekong)

the past six decades and has so far claimed not less than 33
million lives globally [9]. According to the same report, it is
estimated that 38 million people were living with this disease
at the end of 2019 across the globe. Upon an establishment
that the disease is one of the numerous Vertically Transmitted
Infections (VTIs), that is, the transmission of from a mother
to her child during pregnancy, labour, delivery or breastfeed-
ing, different approaches have been set in motion to curb the
mother-to-child transmission and so far, about 85% of either
pregnant women or breastfeeding mothers living with the dis-
ease have received Anti-Retroviral Therapy (ART) which apart

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Iseh et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 99–104 100

from reducing the possibilities of transmitting this disease to
their newborns, has made the disease manageable thereby en-
abling the carriers to lead long and healthy lives. Unlike other
forms of infection, preventing vertical transmission of HIV is
more complex, requiring intervention from preconception to the
end of breastfeeding. This includes primary prevention of HIV
before, during, and after pregnancy; prevention of unwanted
or unplanned pregnancies; early initiation of ART; retention on
ART for women with HIV; and retesting women without HIV
to detect new infections early. Early antenatal care is also im-
portant to optimise general care, monitoring of maternal viral
load, safe delivery practices, and infant postexposure prophy-
laxis [10]. Though a good number of women within this sub-
group have had good access to these therapies and interven-
tions, others are getting it difficult, or at worst, not able to access
it at all. Several factors may contribute to this vulnerability. It
could be legal, religious, illiteracy, biological, social, or socio-
cultural ([1]; [8]). In the absence of any intervention, transmis-
sion rates range from 15% to 45% ([4]; [3]). This rate can be
reduced to below 5% with effective interventions during the pe-
riods of pregnancy, labour, delivery and breastfeeding. These
interventions primarily involve antiretroviral treatment for the
mother and a short course of antiretroviral drugs for the baby.
They also include measures to prevent HIV acquisition in the
pregnant woman and appropriate breastfeeding practices.

However, a concerted global effort against this disease has
steadily increased the HIV services coverage. Apart from the
administration of 68% adults and 53% of children living with
HIV globally, one of such efforts is the move to eradicate mother
to child transmission of the disease. This genuine interest to
curb further spread in the West African region also gave birth
to Nigerian HIV/AIDS Indicator and Impact Survey (NAIIS) in
2018 - a collaborative project by Federal Ministry of Health,
Nigeria, University of Baltimore, Maryland, etc. in attempt to
ascertain the prevalence of the disease in the country. The re-
port of this survey as published on NAIIS website and other
media houses showed that Akwa Ibom State, the major oil-
producing state in the country, has the highest number of peo-
ple living with this virus. Though the survey and data collec-
tion approach used was best known to the investigators, the re-
port, however, raises some sort of panic amongst the residents
of the state. Nevertheless, this panic is neither peculiar to Akwa
Ibom State nor Nigeria, but to other African sub-region and the
world at large. To understand the prevalence trend and other
infection dynamics of the disease in this state, a good number
of researches have been carried out on this topic. To proffer
ways of reducing the Mother-to Child-Transmission (MTCT),
[2] carried out some findings from an early infant diagnosis
program in the south-south region of Nigeria (with Akwa Ibom
state inclusive) and concluded that reduction of MTCT of HIV
is possible with effective Prevention of Mother-to-Child Trans-
mision (PMTCT) interventions, including improved access to
ARVs for PMTCT and appropriate infant feeding practices. On
the same vein, [5] investigated knowledge and practice of pre-
vention of Mother-To-Child-Transmission of HIV among tra-
ditional birth attendants practising in the state, and they dis-
covered that the knowledge and practice of PMTCT of HIV

by the TBAs practising in Akwa Ibom is less than adequate
thus increasing the risk of vertical transmission of HIV. The au-
thors suggested an urgent need for the education and training of
TBAs to improve their knowledge and enhance their practice.
On the global scene, many pieces of research are carried out on
this topic and they could be found in the literature ([7]; [6]; and
others).

Different from these researches which entirely focus on the
preventive measures on tackling mother-to-child-transmission,
this paper will employ the technique of logistic regression to
give an insight into the proportion of HIV/AIDS infections at-
tributed to VT in Akwa Ibom State. Based on the data available,
the paper will predict the status of newborns given the chosen
biomarkers in the pregnant and breastfeeding women. This pa-
per is organised as follows; in section 1, a general introduction
is given, section 2 gives an overview of the methodology em-
ployed in the data analysis, and section 3 presents the results of
the analyses. Finally, section 4 concludes with a summary.

2. Methodology

In the analysis of data related to this research, we will em-
ploy the Binary Logistic Regression technique.

2.1. Logistic Regression Analysis

Regression methods have become an integral component of
any data analysis when it comes to deciphering the relation-
ship between a response variable and explanatory variable(s)
given that the dataset are discrete in nature. Logistic Regres-
sion Model has become the standard of analysis in many fields
of studies specifically the Medical field. At this point it is per-
tinent to note that the goal of Logistic Regression is to find the
best fitting and closest, yet reasonable model to describe the
affinity or relationship between an outcome that is dependent
or response variable and a set of independent otherwise known
as predictor or explanatory variables. In Statistics, Logistic Re-
gression, or Logit Regression, or Logit Model is a regression
model where the dependent variables are categorical. Unlike
the Linear Regression Analysis which is continuous, it is bi-
nary or dichotomous in nature, also the choice of a parametric
model and assumptions differs, thus, these features distinguish
it from others. It could be noted that once this difference has
been accounted for, the procedures employed in an analysis of
logistic regression follows the same general principle of that of
the linear regression.

2.1.1. The Odds
Consider the Linear Regression for n-independent variables

as follows

Y = β0 + β1 X1 + β2 X2 + ... + βn Xn + ε (1)

where Y is the response variable, X1, X2, ...,Xn are the predictor
variables with associated parameters β1 β2, ..., βn respectively.
ε is the error term associated with the model.

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Iseh et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 99–104 101

The above equation could be considered as Binomial case
with n-trials concerning the response variable. Also, consider
the Linear Regression with three independent variables we have;

Ŷ = β̂0 + β̂1 X1 + β̂2 X2 + β̂3 X3 + ε (2)

In the above equation, X1, X2, and X3 are the biomark-
ers representing the Age of the infected pregnant women, the
Weight of the pregnant women infected, and the drug dosage
taken by the pregnant women infected respectively..

Eq (2) is the Bernoulli distribution with n = 1 with respect
to the dependent variable Y , which represent the Binary Lo-
gistic Regression with n = 1 trials, where Success is ”1” and
failure is ”0” Also, recall that the probability of Success in a
Bernoulli Distribution is p and failure q is given as follows:

q = 1 − p

Recall that, the Expectation of a Bernoulli Distribution, given
as E(X) is

E(X) =
p
q

(3)

For q = 1 − p, Eq. (3) becomes

E(X) =
p

1 − p
(4)

Eq. (3) is called the odds, which is the expected value of
a random variable having a Bernuoulli distribution. In logis-
tic regression, we estimate an unknown p for any given linear
combination of the independent variables, thus, linking the in-
dependent variables to the Bernoulli distribution gives us the
Logit(l). This, of course, is the ultimate goal of the Logistic
Regression. Thus, we need a function that links the linear com-
bination of variables and the Bernoulli distribution together or
map the linear combination of variables that could result in any
value onto the Bernoulli probability distribution with a domain
from 0 to 1. This result in taking the natural log of Eq.(4), which
is the log of the odds. Thus this gives;

Logit(l) = Logodd s = ln(
p

1 − p
) = Ŷ (5)

2.1.2. The Binary Logistic Regression
The Binary logistic regression model is obtained from the

combination of Eqs. (2) and (5). So that we have,

ln(
p

1 − p
) = β̂0 + β̂1 X1 + β̂2 X2 + β̂3 X3 (6)

Taking the exponent of Eq. (6) above, we have
p

1 − p
= eβ̂0 +β̂1 X1 +β̂2 X2 +β̂3 X3 (7)

By simplification, we obtain

p̂ =
eβ̂0 +β̂1 X1 +β̂2 X2 +β̂3 X3

1 + eβ̂0 +β̂1 X1 +β̂2 X2 +β̂3 X3
(8)

Eq. (8) gives the estimate of the Logistic Regression, where
X1, X2, and X3 are as defined earlier with their respective es-
timated parameters β̂1, β̂2, and β̂3, e denotes the exponential
function.
p is the probability that the child is infected given the mother
has the disease.

2.1.3. The Odds Ratio
The odds ratio (denoted as θ) between the odds of two sets

of the predictor (say X1 X2). For a continuous independent vari-
able, the odds ratio defined as:

θ =

p
(1−p) ||X = X1

p
(1−p) ||X = X2

(9)

But the odds of success are as given in (7),

2.1.4. Wald Test
The Wald test (also called the Wald Chi-Squared Test) is

a way to find out if explanatory variables in a model are sig-
nificant. “Significant” means that they add something to the
model; variables which add nothing is removed without affect-
ing the model in any meaningful way. The test can be used for a
multitude of different models, including those with binary vari-
ables or continuous variables. The null hypothesis for the test
is: some parametesr are zero in value (not sugnificant). If the
null hypothesis is rejected, it suggests that the variables in ques-
tion can be removed without much harm to the model fit. If the
Wald test shows that the parameters of some explanatory vari-
ables are zero, you can remove the variables from the model. If
the test shows the parameters are not zero, you should include
the variables in the model. The Wald test statistic formula is:

Wald T est(W j) =
β2j

S E(β2j )
(10)

where; β2j is the square of the linear regression coefficient, S E(β
2
j )

is the square of the standard error of the regression coefficient
and is asymptotically distributed as a chi-square distribution
with 1 degree of freedom.

2.1.5. The Likelihood Function for Logistic Regression (De-
viance)

Deviance measures the discrepancy between the current model
and the full model. The full model is the model that has n pa-
rameters, one parameter per observation. The full model max-
imizes the log-likelihood function. The full model provides
a point of comparison for reduced model, that is, model with
fewer than n parameters. Comparisons to the full model use the
scaled deviance. The contribution to the scaled deviance from
each individual data point depends on the model. The likeli-
hood is given in the equation below

Λ
∗

= −2(l(β0) − l(β1)) (11)

where l(β1) is the log-likelihood of the fitted (full) model. l(β0)
is the log-likelihood of the (reduced) model specified by the
null hypothesis evaluated at the maximum likelihood estimate
of that reduced model.

3. Data Analysis and Results

R and Minitab were used in the analysis of the recorded
cases of vertically transmitted HIV/AIDS in Akwa Ibom State.

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Table 1: 2018 Early Infant Diagnosis (EID) Results Summaro

Mnth No. of PW No. of + Enrolled Not Enrolled
Jan 291 23 16 7
Feb 48 15 12 3
Mar 193 12 9 3
Apr 200 13 11 2
May 89 20 13 7
Jun 36 12 10 2
Jul 132 33 16 17

Aug 96 12 10 2
Sep 143 9 7 2
Oct 92 5 0 5
Nov 250 12 11 1
Total 1570 166 115 51

Table 2: Data Count

Variable Value Count
Y 1 166 (Event)

0 1404
Total 1570

Table 3: Model Summary

Deviance Deviance

R-Sq R-Sq (adj) AIC
0.04% 0.00% 1067.35

3.1. Data Collection

Data used for this research work are secondary data ob-
tained from the Akwa Ibom State Ministry of Health (MOH).
Monthly dataset for the year 2018 was considered.

3.2. Data Presentation

Table 1 shows the dataset used for the analysis of this re-
search, PW: Pregnant Women.
+: Positive.
Mnth: Month
Enrolled: Number of pregnant women on Antiretroviral Ther-
apy (ART) intervention. Not Enrolled: Number of pregnant
women not on Antiretroviral Therapy (ART) intervention.

3.3. Results of Analyses

The data was Bernoulli (binary) coded to reflect the status
of the respondents. The data were randomly distributed with-
out any prior knowledge about the outcome The data count is
as shown in Table 2.

The outputs are given in Table 4: Binary Logistic Regres-
sion: Y(newborn HIV/AIDS status-Positive (1), Negative (0)
versus Age, Weight, Dosage (Drugs)

3.4. The Binary Logistic Regression Function or the Logit
Recall that the Logit Function is as given below.

P = eŷ

where

ŷ = β̂0 + β̂1 X1 + β̂2 X2 + β̂3 X3

Using the above, we have that

Ŷi = −2.312+0.0037Age−0.121Weight+0.314Dosage (Drugs)

The probability of the child being infected is computed as
follows

p =
eŶ

(1 + eŶ )

For i = 1, the probability of that child being positive given
that the mother is negative is given by;

p =
eŶ

1 + eŶ
=

0.108937
1 + e(−2.21699)

= 0.098235

Thus, the probability that her child will be infected is 0.098235
≈ 0.1, and this is unlikely to happen given the small probability.
This result agrees with the proportion of Event count recorded
in Table 2 as 1661570 ≈ 0.1

3.5. The Odds Ratio
The odds ratio denoted by θ and given in Eq. (10) is the

odds ratio between two sets of the predictor presented in Table
5 below.

The result above implies that a unit increase in Age in-
creases the odds of a newborn being infected by the mother
by a factor of 1.0037. In the same vein, the result shows that a
unit increase in Weight increases the odds of a newborn being
infected by the mother by a factor of 0.8862. And also, a unit
increase in Dosage of Drugs increases the odds of a newborn
being infected by the mother by a factor of 1.3691. This fol-
lows that Age and Dosage may increase the odds of a newborn
being infected by an infected mother minimally while Weight
does not yeild such increase at all.

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Table 4: Coefficients (Wgt:Weight; DD: Drug Dosage.)

Term Coef SE 95% CI Z-Val P VIF
Const -2.312 0.503 (-3.298, -1.326) -4.59 0
Age 0.004 0.011 (-0.018, 0.025) 0.34 0.733 1
Wgt -0.121 0.550 (-1.199, 0.958) -0.22 0.826 1
DD 0.314 0.651 (-0.962, 1.590) 0.48 0.629 1

Table 5: Odds ratio

Odds Ratio 95% CI
Age 1.0037 (0.9824, 1.0255)

Weight 0.8862 (0.3014, 2.6056)
Dosage (Drugs) 1.3691 (0.3821, 4.9056)

3.6. The Wald Test

The Wald test is the test of Significance for individual re-
gression coefficients in the Logistic Regression, (recall that in
the Generalized Linear Regression Analysis we use the t-test
statistics). For maximum likelihood estimates, we use Eq. (11),
and these are z − values given in Table 4.

Using the formula in Eq. (10) and the values of β′s, the
Wald test is computed and the result is as follows, 0.113 for
Age, 0.0484 for Weight and 0.233 for Drugs Dosage. The
smallness of the value of the Wald Test result for the Weight
biomarker suggests that the presence of Weight may not be nec-
essary for the model. The above indicator informs us to refit the
model without the Weight; the parameters of the reduced model
are presented in Table 6;

The Wald test results for the two biomarkers are 0.116 for
Age and 0.225 for Dosage of Drugs. These may not be as strong
as should, but it is a better model to be entertained.

3.7. The Likelihood Ratio Test or Deviance

Here, we use the likelihood-ratio test to compare two mod-
els. Specifically, we are testing H0 : βAge = βWeight = βDosage =
0 The Likelihood ratio test is used to test the null hypothesis
(H0) that any subset of the β′s = 0. Where the number of
β′s = 0 in the full model is p, while the number of the β′s = 0
in the reduced model is r. (r is the model that results when
β′s = 0 in the null hypothesis are set to 0). The result is as
given in the Analysis of Deviance in Table 7. From the result
of our Wald Test, it is observed that the value of the test for
Weight was small. At that point, it was suspected that fitting a
new model without the variable would give a better fit. Due to
this, a reduced model with Weight was fitted and the Deviance
analysis carried out.

We see that the test statistic that we had just calculated ap-
pears in the output. The very big p-value suggests that there
is no significant difference between the larger model and the
reduced one. The values of the residual deviance for the two
models also support the above claim as the two values are al-
most the same. Hence, there is need for the Weight biomarker
to be removed from the model since it may lead to overfitting.
Of course, this is also an indication that in investigating the VT

infections from positive pregnant women to the newborns, the
weight of the women is not necessarily one of the determining
factors. An overview of the two fitted models generally sug-
gests that Age, Weight, and Dosage of drugs taken by reactive
pregnant women do not imply or contribute to the vertical trans-
mission of the HIV/AIDS from the mothers to their newborns.

4. Conclusion

This paper is designed to explore the proportion of HIV/AIDS
infections attributed to VT in Akwa Ibom State. From the data
collected from the Akwa Ibom Ministry of Health on the virus
and VT related cases, the paper used the Binary Logistic Re-
gression Analysis to predict the HIV status of newborns given
the chosen biomarkers in the pregnant and breastfeeding women,
in this case, Age, Weight, and Drug (Dosage) intake. In do-
ing this, the Logit function, the Odds ratio, the Wald test, and
the Likelihood Ratio test were used to explain the adequacy of
the fitted model. The results clearly showed that given these
biomarkers (Age, Weight, and Dosage of Drugs), the rate of
spread of the HIV/AIDS is seldom through vertical transmis-
sion, that is, from an infected mother to her newborn. The im-
plication of this finding is that the prevalence rate of the disease
in Akwa Ibom State may be attributed more to other modes of
transmission and less to VT. While it is important to continue
in the interventions focusing on antiretroviral treatments for the
positive mothers, it is more advisable to intervene by creating
more awareness on the other modes of transmission.

5. Abbreviations

HIV - Human Immunodeficiency Virus.
AIDS- Acquired Immune Deficiency Syndrome.
VTIs - Vertically Transmitted Infections.
VT - Vertical Transmision.
MTCT - Mother-To-Child Transmision.
PMTCT - Prevention of Mother-to-Child Transmision.
NAIIS - Nigeria AIDS/HIV Indicator and Impact Survey.
ART - Antiretroviral Therapy.

6. Availability of data and materials

All data used for supporting the conclusions of this arti-
cle are available from the public data repository at the website
https://zenodo.org/record/4243862.

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Table 6: Coefficient of the reduced model

Estimate Std. Error t value Pr(> |t|)

(Intercept) -2.373300 0.418955 -5.665 1.75e-08
Age 0.003736 0.010968 0.341 0.733

Dosage of Drugs 0.308619 0.650987 0.474 0.636

Table 7: Analysis of deviance Table

Resid. Df Resid. Dev Df Deviance Pr(> Chi)
1 1566 1059.3
2 1567 1059.4 -1 -0.048187 0.8265

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