Human Immune Virus (HIV) Infection among Children, Treatment and Under-5 Deaths in Nigeria: An Empirical Analysis

Theoretical Review

Considering the biological science theories, and looking at theory of epidemiology transition, Omran AR [3], is a theory which describes the changes in population patterns in terms of fertility, life expectancy, mortality and leading causes of death. Epidemiological concept is a quantitative science concerned with infectious diseases, with the circumstances under which diseases processes occur, the factors that affects their incidence and the host response to which the infectious agent, and the use of this knowledge for control and prevention.

Therefore, the theory of epidemiology transition concisely explains about the changes in population as a result of deaths caused by HIV/AIDS prevalence. It is an infectious disease, and the theory explains the process in which HIV/ AIDS occurs, the factors affecting the treatment of HIV among carriers and the control of the HIV infections. The theory of epidemiological transition explains the ideology associated with this study which is to investigate the outcome relating HIV and under-5 mortality rate in Nigeria.

Empirical Review

The connection between HIV/AIDS and under-5 mortalities has attracted fewer awareness through current research. The prevalence of HIV/AIDS that exerts influence directly on under-5 mortality has many causes and different countries have different reasons leading to the incidence of HIV/AIDS prevalence.

Eduardo V, et al. [4] on their study titled “ Child mortality in relation to HIV infection, nutritional status, and socio-economic background, examine the impact of child HIV infection on mortality and to identify nutritional and sociodemographic factors that increase the risk of child mortality independent of human immunodeficiency virus (HIV) infection” using primary data method of analysis concluded that HIV infection was associated with an adjusted 4-fold higher risk of mortality and HIV infection appeared to be a stronger predictor of mortality among children who were wasted than among those who were not.

Another study is Weldemariam SA, et al. [5], which is titled “Time to death among HIV-infected under-five children after initiation of anti-retroviral therapy and its predictors in Oromiya liyu zone, Amhara region, Ethiopia: A retrospective cohort  study”, using a primary data methods of collection and multivariable Cox-proportional hazard regression model conducted a study among 376 under-5 HIV infected children who are on antiretroviral therapy from January 2014 to December 2019, Oromia Liyu Zone Amhara region in Ethiopia. The result of this study indicated that approximately 81% of HIV infected children were alive, 11% were lost to follow up, 3.2% were transferred out while 5.6% were dead due to HIV/AIDS. The study also proved that the overall mean time to death was 19.7 months with incidence of 5.9 deaths per 100 children in a month. It concluded that poor adherence to ART were significantly associated to high mortality events and death of HIV-infected under-five children on ART is high within the first one year after enrolment.

Cuddington JT [6] study was on modelling the macro- economic effects of AIDS using the Solow framework and he focused on one country, Tanzania. This study reported that the rise of HIV/AIDS deaths had reduced labour productivity, leading to the high rate of healthcare cost and investment which reduced savings and consumption expenditure. Such a scenario is reported to be linked to reduced human capital investment at the family level due to the inability to afford the healthcare cost. Cuddington JT [6] also explained that an increase in mortality as a result of infectious diseases would lead to reduced average age and experience of the working population, leading to a reduction in average productivity and economic growth. This will likely increase the dependency ratio due to the deaths of many working- aged people. Cuddington JT [6] concludes that the presence of AIDS in Tanzania may lower the per capita income by up to 11% annually.

Empirical Model Specification

The model specification simply specifies the function that expresses the relationship between the HIV infections and under-5 mortality variables as well with the other independent variables to help this study achieve its objective. We acknowledge and emulate a simple mathematical/ economic function stated by Cobb CW, et al. [7] output (Y) is a function of inputs (K) for capital and (L) for labour and it is stated below as:

Y = KαLβ (1) In equation 1, β and α estimates the proportion of capital and labour used for the level of output (Y) achieved. Therefore, this study expresses the impact of HIV infections as an input to the outcome of under-5 mortalities in consideration with the ART exercise during the study period. The advantage of this function form is that under-5 mortalities depends on the level of HIV infections. Therefore, this study model is stated as NU5D = CLHIVβ1CNIHIVβ2 TPWLARTβ3TPEOLARTβ4 (2) Where NU5D = Number of under -5 deaths, CLHIV = Children (age 0 -14) living with HIV, CNIHIV = Children (ages 0 -14) newly infected with HIV, TPWLART = Antiretroviral therapy coverage for PMTCT (% of pregnant women living with HIV and TPEOLART = Antiretroviral therapy coverage (% of people living with HIV). β1, β2, β3 and β4 measures the rate of the independent variable incidences within the period of this research. Statistically, Equ (2) is reduced to the form NU5D = Z + β1CLHIVt + β2CNIHIVt + β3TPWLARTt + β4TPEOLARTt + ɛt (3) And equation 3 is modified and reduced to natural logarithm to help the interpretation of the coefficient estimated results of the variables in the model and its reduction into the natural logarithm is written and stated as InNU5D = Z + β1InCLHIVt + β2InCNIHIVt + β3InTPWLARTt + β4InTPEOLARTt + ɛt (4) Where Z = intercept; In = natural logarithm; t = time; ɛ = error term; β1, β2, β3 and β4 are the coefficient of the independent variables.

Methodology

The methodology used in this study depends on the outcome of the unit root test result conducted among the variables to know their stationary characteristics. The unit root test is conducted to know if the variables in the model are stationary at the level I(0), the first difference I(1) or mix mode, that is if the variables are stationary at both I(0) and I(1). If all the variables are stationary at I(0), this study will not use the ARDL model approach for its estimation, rather the Ordinary Least Square (OLS) approach will be used because variables exhibit their stationarity at I(0) suits the OLS method of analysis. Also if the variables are stationary at I(1) or mix mode, then the ARDL method suits the analysis. Moreover, the ARDL method has the advantage over other methods like the OLS in the estimation of linear relationships among variables because the lag of the dependent variable can be used as an independent variable in the estimation process. Other methods of analysis lack this characteristic.

After conducting the unit root test, it proved that the variables in the model are stationary at level I (0), therefore this study continued to adopt the OLS. Also, this study suits the use of OLS method for its analysis because the lag of the dependent variable is not included in the model. Estimation of the coefficient relationship is performed to find out the equilibrium relationship that exists between the dependent and independent variables. The formula is thus $$ \begin{array}{l} \mathrm {I n N U 5 D} _ {\mathrm {t}} = A + \sum_ {i = 1} ^ {p} \beta_ {1} \mathrm {I n N U 5 D} _ {\mathrm {t - i}} + \sum_ {i = 0} ^ {q} \beta_ {2} \mathrm {I n C L H I V} _ {\mathrm {t - i}} + \sum_ {i = 0} ^ {r} \beta_ {3} \mathrm {I n C N I H I V} _ {\mathrm {t - i}} \\ + \sum_ {i = 0} ^ {s} \beta_ {4} \mathrm {I n T P W L A R T} _ {\mathrm {t - i}} + \sum_ {i = 0} ^ {T} \beta_ {5} \mathrm {I n T P E O L A R T} _ {\mathrm {t - i}} + \varepsilon_ {\mathrm {t}} \\ \end{array} $$ (5) After the estimation of the coefficient relationship that exists among the variables in the model, the next test to be done is the diagnostics test which comprises of the serial correlation, heteroscedasticity and normality test to check if there is any serial or auto correlation problem, constant variance problem and normality distribution problems in the models used to explain the relationship between the dependent and independent variables in the model after the coefficient analysis test.

Data Sources and Justification of the Sample Size

Data sources are very important in every research mostly when the data collection is secondary. This study used secondary data collection method and all the data were collected from World Bank. The data are annual time series starting from 1990 to 2021 which is 32 years of observation Table 1.

Table 1 presents the sources and justifications of the variables used in this study. The dependent variable is NU5D. The independent variables are CLHIV, CNIHIV, TPWLART and TPEOLART.

Descriptive Statistics

The descriptive statistics value of this study is found in Table 2 below. It shows the variables and their years of observation, the mean, standard deviation, minimum and maximum values used in the study.

Note: OBS = observation; Std.Dev = Standard Deviation; Max = Maximum; Min = Minimum; NU5D = number of under-5 deaths; CLHIV = number of children living with HIV/AIDS; CNIHIV = number of children newly infected with HIV; TPWLART = total percentage number of pregnant women living with HIV that receives ART treatment and TPEOLART = the total percentage number of people living with HIV that receives ART treatment in Nigeria. Table 2: Descriptive Statistics.

The descriptive statistics values show that NU5D has the highest maximum value of 927731.0 as well has the highest minimum value, proving that NU5D is high in Nigeria.

Covariance Matrix

Table 3 below is the covariance matrix table. It shows the diagonal relationship among the variables used in this study model. For example, the relationship between NU5D and CNIHIV is positive with the value of 1.63E8 indicating that increase in CNIHIV leads to increase in NU5D, and also consider the relationship between NU5D and TPWLART which has a negative value of -337353.0 which implies that increase in the percentage number of pregnant woman receiving ART reduces NU5D.

The covariance matrix coefficient relationship does not give a complete analysis of the relationship among the variables. This study will continue with other necessary analysis needed to ascertain the objective of this study.

Note: NU5D = number of under-5 deaths; CLHIV = number of children living with HIV/AIDS; CNIHIV = number of children newly infected with HIV; TPWLART = total percentage number of pregnant women living with HIV that receives ART treatment and TPEOLART = the total percentage number of people living with HIV that receives ART treatment in Nigeria. Table 3: Covariance Matrix of coefficient of NU5D model.

Unit Root Test

The unit root test of this study was performed using the Augmented Dickey Fuller (ADF) test to find the stationary properties of the variables used in this study. The Philip Perron (PP) unit root test was also conducted in conformity with the ADF test result.

Table 4 is the unit root test results of the variables in the model for this study. It shows that for the ADF, all the variables are significantly stationary at the level I(0). Also for the PP unit root test, only CLHIV and TPEOLART were significantly stationary at level I(0). Therefore, the result of the unit test is in agreement with the OLS model testing approach.

Note: Significant level *10%, 5%, and *1% respectively. NOTE: Obs = observation; Std.Dev = Standard Deviation; Max = Maximum; Min = Minimum; NU5D = number of under-5 deaths; CLHIV = number of children living with HIV/AIDS; CNIHIV = number of children newly infected with HIV; TPWLART = total percentage number of pregnant women living with HIV that receives ART treatment and TPEOLART = the total percentage number of people living with HIV that receives ART treatment in Nigeria. Table 4: Unit Root Test Result.

OLS Estimated Long-Run Coefficient Test

The long-run coefficient test is important to run in the OLS model. It is performed to determine the connection and behavioural relationship between the dependent and independent variable in the long-run. The results are tabulated in Table 5 below.

Note: *, and * means significant at 10%, 5% and 1% respectively. LCLHIV = Log of number of children living with HIV/AIDS; LCNIHIV = Log of number of children newly infected with HIV; LTPWLART = Log of total percentage number of pregnant women living with HIV that receives ART treatment; LTPEOLART = Log of the total percentage number of people living with HIV that receives ART treatment in Nigeria Table 5: Coefficient Estimation-NU5D Model.

The long-run coefficient test was done to achieve the objective of this study which was to investigate the impact of HIV infections among children on under-5 deaths in Nigeria. The result in table 5 shows that NU5D has a negative relationship with CLHIV, which means increase in the number of under-5 deaths leads to decrease in the number of children living with HIV/AIDS. This simply means that children living with HIV/AIDS constitutes among the number of under-5 deaths in Nigeria. Also the coefficient value of CLHIV is -0.2183, that means for every 21% increase of NU5D, there is 1% decrease of CLHIV and it is significant at 1%.

Also, CNIHIV which is the number of children newly infected with HIV has a positive relationship with NU5D. That means increase in CNIHIV leads to increase in NU5D. This result is true because when the number of children newly infected with HIV increases, there is tendency for the number of under-5 deaths to increase. The coefficient of CNIHIV is 0.0114, which means any 1% increase of CNIHIV will lead to 1% increase of NU5D but not significant.

Additionally, TPWLART is the total percentage number of pregnant women living with HIV that receives ART treatment. The coefficient of TPWLART is 0.0396 which indicates a positive relationship with NU5D. It means increase in TPWLART brings increase to NU5D. And any 3% increase of TPWLART leads to 1% increase of NU5D. Finally, TPEOLART is the total percentage number of people living with HIV that receives ART treatment in Nigeria. The coefficient of TPEOLART is -0.0407 indicating a negative relationship between TPEOLART and NU5D. It means increase in total percentage of people living with HIV that receives ART treatment (TPEOLART) leads to decrease in number of under-5 deaths (NU5D), and any 4% increase of TPEOLART leads to 1% decrease of NU5D at 1% significant level.

Diagnostic Test

The diagnostic test for this study are the serial correlations test which helps to check if there is any serial correlation among the variables in the model of this study. Also the next is the heteroscedasticity test which is conducted to check if there is any constant variance in the regression model, and the normality test is to confirm that all the variables in the model are normally distributed and placed. Table 6 shows the summary of the diagnostic test results for this study.

As tabulated in Table 6 the NU5D Model, serial correlation LM test showed that the Obs*R-square was 1.1375 which is higher than the probability value of 0.5662, and its percentage value of 56.6% is above the 10% significance level. It implies that at 56.6%, this study proves there is no serial correlation in the study model. Also the Heteroscedasticity test has its Obs*R-square to be 5.7851 which is above the probability value of 0.2158, having its percentage value as 21.5% which is above the 10% significant level. It means that at 21.5% there is no constant variance in the model used for this study. Finally, the normality test which has its Obs*R-square value as 1.8942 which is higher than the probability value of 0.3878 proves that at 38.7% there is no problem of normality in the model. Therefore, the variables in the model are normally distributed.