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American Journal of  Applied 
Statistics and Economics (AJASE)

Survival Regression Model Allowing for Exposure-Mediator Interaction: Analysis of  
Kenya Demographic Health Survey (KDHS) 2014 Data

Irene Mundia1*, Hellen Waititu1, Nelson Owuor2

Volume 3 Issue 1, Year 2024
ISSN: 2992-927X (Online)

DOI: https://doi.org/10.54536/ajase.v3i1.3686
https://journals.e-palli.com/home/index.php/ajase

Article Information ABSTRACT

Received: September 11, 2024

Accepted: October 15, 2024

Published: October 17, 2024

Although infant and under-five mortality rates have decreased over the past decade, Kenya, 
like many other African nations, did not achieve the Millennium Development Goal (MDG) 
4 target. To accelerate progress towards reaching Sustainable Development Goal 3 by 2030, 
it is essential to understand the factors influencing under-five child mortality (UFCM), taking 
into account all potential confounding variables and effect modifiers. The child mortality 
rate serves as a key health indicator for any country. This study used data from the 2014 
Kenya Demographic and Health Survey (KHDS). This paper introduces the concept of  
decomposing the total effect of  an independent variable into three components: a direct 
effect, an indirect effect, and an interactive effect. We attempt to account for the direct 
effect of  an independent variable on the outcome, then proceed to check the effect of  the 
presence of  a possible mediator and, furthermore, the possible interactions between an 
exposure variable and a mediator variable. The outcome variable was UFCM, and the study 
was to determine the effect of  mother’s education on UFCM, in the presence of  mediators 
such as mother’s income and the effect via the interaction between mother’s education 
and maternal income was estimated. To capture the effect of  mediation and interactions 
in the context of  survival analysis, an Aalen additive model, including a product term for 
the exposure and mediator term, was developed. The methods were further illustrated with 
practical approach to KDHS data. KDHS has data on a broad scope of  risk factors for 
UFCM. Computations for all data sets was implemented using the freely available R-software 
package. This analysis suggests that while a significant portion of  the impact of  maternal 
education on UFCM is mediated by increasing maternal income, it is the interaction between 
maternal education and maternal income that leads to a reduction in UFCM. Interventions 
targeting an increase in income among mothers with no education level would yield a greater 
reduction in UFCM than interventions targeting mothers with a higher education level. 
The total effect was ascribed to an interaction between the mother’s education level and 
maternal income, and part of  it is attributable to pure indirect effect, and a given proportion 
is attributable to pure direct effect. The majority of  the total effect (70%)is attributed to the 
interaction between change from no education level to primary education level and maternal 
income. 22% is associated with the pure direct effect, while 8% is linked to the pure indirect 
effect. Interventions with a given increase in income among those with no education level 
would yield a greater reduction in UFCM than interventions targeting mothers with a higher 
education level.

Keywords

Aalen Additive Model, Child 
Mortality, Mediation

1 Department of  Mathematics and Actuarial Science, Catholic University of  Eastern Africa, Kenya
2 Quintiles East Africa, Kenya
* Corresponding author’s e-mail: imundiam@gmail.com

INTRODUCTION
Child mortality still remains a global problem despite 
many interventions going on, both in terms of  
health research and even at the level of  government 
interventions. Despite the global and national decline in 
infant and under-five mortality rates over the past decade, 
Kenya, like many other African countries, failed to meet 
the target for Millennium Development Goal (MDG) 4. 
The analysis was conducted using house hold data from 
Kenya Demographic and Health Survey (KDHS) data. 
To accelerate progress towards achieving the Sustainable 
Development Goals (SDGs), effective interventions 
must be implemented in order to meet Goal number 3 
by 2030. Determinants of  child health, such as Under 
Five Child Mortality (UFCM) need to be understood in 
the context of  all possible forms of  confounding and/
or effect moderation. Child mortality rate is one of  the 
major health indicators for any country. Kenya, just like 

other Sub-Saharan countries, have recorded high cases of  
UFCM. The SDG, goal number 3, target 3.2 on neonatal 
and child mortality has not been achieved in Kenya, with 
43.2 deaths per 1000 live births being reported in the year 
2019 (Rod et al., 2012) which is way above the 25 deaths 
per 1000 that is the target. Part of  the Kenya government’s 
previous mid term development plans, known as the “Big 
Four Agenda (2018-2022)” had universal healthcare as one 
of  the key pillars, to align with the SDG’s vision 2030. This 
work therefore aims at evaluating determinants of  UFCM 
using appropriate statistical models and assumptions. 
We have in this case applied regression with mediation 
and appropriate survival analysis models to conduct this 
analysis, taking into account the rarely considered aspect 
of  a possibility of  mediators and interactions among 
some useful UFCM determinants. Intervention strategies 
using statistical outcomes from regression type models, 
frequently encounter the task of  dissecting the impact 



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of  an exposure into various causal pathways that operate 
through specific intermediary variables. The primary 
objective of  conducting regression analysis is typically 
twofold: to gain insights into the underlying mechanisms 
and to then to propose potential intervention strategies. 
There is always a complex network surrounding 
decomposition of  exposure effects in the presence 
of  mediation and interactions. It’s important to note 
that implementing mediation analysis methods can be 
complex, as they rely on stringent assumptions that must 
be satisfied to obtain valid and interpretable estimates. 
Exposure-mediator interaction is a potential source of  
bias, that if  not carefully addressed, may lead to flawed 
conclusions in statistical analysis. Mediation analysis 
examines the effect of  the exposure variable and how 
changes in the mediator variable subsequently affect the 
outcome. Therefore, controlling for exposure-mediator 
confounding, if  it happens that such exist, is essential. 
Although a number of  studies where the determinants 
of  UFCM are of  interest have been done without due 
consideration of  the possible role of  mediation or 
moderation, attempts have been done in that direction. 
VanderWeele (2013) developed findings on direct and 
indirect effects for linear and logistic regressions in the 
presence of  exposure–mediator interaction. However, 
many studies have not considered the possibility that the 
exposure and mediator may interact in influencing the 
outcome. Including interaction effects in a model allows 
us to compare the relative importance of  several pathways 
mediated by interdependent variables (Hougaard, 1999). 
Recent advancements in causal inference theory have 
introduced concepts for mediation analysis and effect 
decomposition, enabling the separation of  a total effect 
into direct and indirect components. The indirect effect 
can be further broken down into a pure indirect effect 
and a mediated interactive effect, resulting in a three-part 
decomposition of  the total effect (direct, indirect, and 
interactive). This three-way decomposition offers deeper 
insight by allowing us to determine how much of  the 

total indirect effect is due to mediated interaction versus 
the pure indirect effect (VanderWeele, 2013).
This work makes use of  the concept of  decomposing 
the total effect into three components: a direct effect, an 
indirect effect, and an interactive effect. We perform this 
three-way decomposition using an additive regression 
type model. These additive hazard models have the 
potential to reveal intricate effects when examining the 
impact of  various factors on UFCM in Kenya. Three-way 
decomposition also applies to additive hazard scales. An 
additive model including a product term for the exposure 
and mediator term was developed and R codes for 
decomposition expanded. The analysis was conducted 
using household data from the Kenya Demographic 
and Health Surveillance (KDHS) data. Results of  the 
study shows that maternal education is recognised as 
a determinant of  child health. The pathways linking 
maternal education level to UFCM are constrained by 
the statistical methods commonly found in the literature. 
To observe the complex pathways between maternal 
education and UFCM, we employed a statistical model 
that was able to accommodate interactions between the 
maternal education as an exposure and maternal income 
as a possible mediator.

MATERIALS AND METHODS
This section describes the datasets and the structure 
of  a model with mediation and a model with possible 
exposure-mediator interaction. The mediation models 
are concerned with seeking answers to the relationship 
between two variables based on how, or why questions. 
We hypothesize M as an intervening or mediating 
variable to show the relationship between X and Y.X is 
an independent variable, and Y is a dependent variable 
or outcome. The test for statistical mediation has 
been supported by recent studies based on regression 
equation’s coefficients from two or more equations as 
follows:
Y= i1+cx+e1                 (1)

Figure  1:  X= the independent variable, Y= the dependent variable, and M= the mediating variable. c is the overall effect 
of  the independent variable on Y; c’ is the effect of  the independent variable on Y controlling for M; b is the effect of  
the mediating variable on Y; a is the effect of  the independent variable on the mediator; i1, i2, and i3 are the intercepts for 
each equation; and e1, e2, and e3 are the corresponding residuals in each equation (Fairchild & MacKinnon, 2009)



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Y= i2+c’x+bm+e2                  (2)
M= i3+ax+e3                 (3)
Mediation analysis uses a mediator to investigate the 
effect of  an exposure on an outcome through a mediator. 
A vast discussion on mediation analysis can be found 
in Martinussen (2006)The Aalen additive model being 
additive,is directly suitable to incorporating the role 
of  mediation as opposed to other forms of  survival 
regression models.

Survival Regression Model Incorporating One Mediator
The Aalen model specifies that the rate as a function of  
mediator (m), other baseline covariates (z) and exposure 
(x) is
γ(t;x,m,z)= λ0 (t)+λ1 (t)x+λ2 (t)z+λ3 (t)m             (4)
where γ(t;x,m,z) represents the rate, expressed as a 
function of  the mediator (m), other baseline covariates 
(z), and exposure (x). λj (t) denote potentially time-
dependent functions. A straightforward linear regression 
can be employed to characterize the mediator, under the 
assumption that it follows a normal distribution. Thus, 
with other covariates (z) and exposure (x), the mediator 
is determined by:
M= α0+α1 x+α2 z+e               (5)
where e is normally distributed error with zero mean and 

its variance σ2.The parameters are estimated using some 
statistical methods such as least squares method. Suppose 
the exposure is set to X and the mediator to M, then we 
can denote the counterfactual rate for the event by γ(t; x, 
m, c) in the presence of  other baseline covariates. The 
rate difference scale at time t is used to measure the total 
casual effect of  changing the exposure from x* to x is
γ(t;x, Mx)-γ(t;x*, Mx)=
γ(t;x, Mx)-γ(t;x*, Mx*)+γ(t;x*, Mx)-γ(t;x*, Mx*))
=λ1(t)(x-x*)+λ3 α1(t)(x-x*),
The equation TE(t) = DE(t) + IE(t) decomposes the 
effects into three distinct components: the natural 
indirect effect (IE), the natural direct effect (DE), and the 
total effect (TE). Each of  these terms carries a specific 
interpretation. The indirect effect quantifies the number 
of  deaths caused by mediation through the mediator, 
while the direct effect represents deaths due to the direct 
pathway (or through mediators not considered in the 
analysis). The overall effect, which accounts for the total 
deaths resulting from changes in exposure, is determined 
by combining the direct and indirect effects, as explained 
in Lange and Hansen (2011). When both the exposure 
and mediator exhibit no time-dependent effects in the 
Aalen model, with λ1 (t) and λ3 (t) remaining constant, 
Theorem 1 simplifies to:

Therefore, both the direct and indirect effects can be 
represented by a single numerical value rather than being 
functions of  time (t). The Aalen additive model offers a 
framework for directly deriving confidence intervals for 
the direct effects. The model assumes no confounding in 
the relationships between (i) exposure and mediator, (ii) 
mediator and outcome, and (iii) exposure and outcome, 
provided pre-exposure confounders are controlled for, as 
outlined in Nguyen et al. (2016). 

Survival Regression Model Allowing for Exposure-
Mediator Interaction
Even when there is interaction between the exposure 
and the mediator in its impact on the outcome, it is still 
possible to perform mediation analysis by breaking down 
the total effect into direct and indirect effects. The model 
for outcome including an exposure mediator interaction is 
E[Y|a, m, c]= θ0+θ1 a+θ2 m+θ3 am+θ4 c             (7)
We once again fit a linear regression model for the 
mediator. 
E[M|a, c]=β0+β1 a+β2 c               (8)
If  the models are accurately specified, and the assumptions 
related to confounding are met, then the estimates of  
direct and indirect effects resulting from a change in 
exposure from a level denoted as “a*” are provided as 
follows: 

DE=θ1+θ3 (β0+β1 a*+β2 a)(a-a*)              (9)
IE=(β1 θ2+β1 θ3 a)(a-a*)             (10)
Standard errors for these equations are also calculated 
(Vanderweele TJ et al., 2009). When there is no interaction 
between the exposure and mediator (i.e., when θ3=0), the 
equations simplify, with θ1 representing the direct effect 
and β1 θ2 representing the indirect effect.
As the explanatory variables are expressed on the additive 
hazards scale, product terms can be included to evaluate 
deviations from additive effects, similar to standard linear 
models. In the specified additive model, the rate is treated 
as a function of  the mediator (m), baseline covariates (z), 
and the interaction between exposure (x) and the mediator 
(xm). This method is outlined in Rod et al. (2012) work .
γ(t;x,m,z)=λ0 (t)+λ1 (t)x+λ2 (t)z+λ3 (t)m+λ4 (t)xm       (11)
whereγ(t;x,m,z) is the rate, which is written as a function 
of  mediator (m), other baseline covariates (z) , exposure 
(x) and interaction (xm). λj (t) are potentially time-
dependent functions.
Casual diagrams with exposure-mediator interaction 
representing a three-way decomposition.
The total indirect effect consists of  both the pure indirect 
effect and the mediated interaction. The difference 
between the total indirect effect and the pure indirect 
effect serves as a measure of  interaction, referred to as 
the mediated interactive effect (VanderWeele, 2013).



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Data
The research utilized data from the KDHS 2014 survey, 
collected from a random sample of  20,964 respondents. 
This data set offers comprehensive information about 
every child under five years old within households, 
including the child’s gender, survival status, birth intervals, 
birth circumstances, and birth weight. In addition, the 
data set encompasses a wide range of  information related 
to domestic and community characteristics, access to 
healthcare care, maternal and prenatal care, infant feeding 
practices, vaccination exposure, and more.
Our dependent variables include the time until a specific 
event occurs and the corresponding event status. In this 
context, the event status is coded as 1 for “dead” and 0 
for “alive.” All children still alive during data collection 
were considered right-censored, meaning their event 
status was unknown. The data used in this article was 
right-censored. Right censored data is vastly discussed 
by Hougaard (1999). Notable strengths of  the KDHS 
data set include its large sample size, which represents 
the country’s entire population, and its rigorous quality 
control measures (Manski, 2003). 

Variables
The risk factors examined in the study were selected 
based on the results of  articles already published. They 
include sex of  the child, age of  mother, mother’s level 
of  education, maternal income, and maternal health 
behavior. Maternal education is considered in this context 
as an exposure,while maternal income and health behavior 
are considered as mediators. Education is grouped in four 
categories; no education, primary education, secondary 
education, and higher education. The level of  household 
wealth was used for maternal income. The wealth level 
was derived from an index calculated using data on 

ownership. The outcome variable is mortality status and 
month of  death. Status was recorded and subsequently 
coded according to whether the child is alive or not, with 
0 for being alive while 1 for being dead within the first 
5 years. Age at death is given in months. The covariates 
included in the model were the sex of  the child and the age.
Aalen additive model was used in the presence of  
mediation and interaction. It was used to assess mediation 
and interaction on two factors that are significant 
regulators of  UFCM. Mediation analysis can still be 
conducted even when the exposure and mediator interact 
in their effect on the outcome, by dividing the total effect 
into direct and indirect components. An Aalen additive 
model was developed that incorporated a product term 
for the exposure and mediator, allowing the total effect 
to be broken down into three distinct components rather 
than just two.

1. The effect due to mediator only (maternal income). 
2. The effect due to interaction (between maternal 

income and education) 
3. The effect due to the exposure only (education) 

RESULTS AND DISCUSSION
Through a model including a product term for 
the exposure and the mediator the total effect was 
decomposed into three distinct components (direct effect, 
pure indirect effect and the interactive effects). Additive 
hazard models are implemented in the software package 
R. In the present paper, we adopt the ordinary least 
squares (OLS) in approximating the parameters. This was 
achieved via R-programming using the package ‘timereg’.
The functions required for estimating and analyzing the 
additive hazards model are contained in the package.The 
model is fitted using the Aalen function.Lange and Hanssen 
(2011) discusses this technique widely. Descriptive statistics 

Figure  2:  X is the exposure,M is the mediator and X*M is the interaction between the exposure and the mediator.Y is 
the outcome and C is a set of  con founders.Red line shows each effect a.Pure direct effect b.pure indirect effect and c. 
Mediated interaction effect



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on mortality, mother’s education, maternal income and 
adjusting factors are presented in table 1. 

Descriptive Characteristics
A total of  20964 children were identified in the 2014 

Table  1: Descriptive Statistics of  Demographic Variables and other Determinants of  Under Five-Child Mortality 
in Kenya, 2014
Width=tw 
  0 ( N=20093) 1 ( N=871) Total (N=20964) 
Residence
Urban 6532(32.5%) 296(34.0%) 6828(32.6%) 
Rural 13561(67.5%) 575(66.0%) 14136(67.4%) 
Education level
No Education 4406(21.9%) 179(20.6%) 4585(21.9%) 
Primary Education 10551(52.5%) 504(57.9%) 11055(52.7%) 
Secondary Education 3857(19.2%) 146(16.8%) 4003(19.1%) 
Higher education 1279(6.4%) 42(4.8%) 1321(6.3%) 
Religion
Roman Catholic 3706(18.4%) 139(16.0%) 3845(18.3%) 
Protestant 12405(61.7%) 553(63.5%) 12958(61.8%) 
Muslim 3364(16.7%) 156(17.9%) 3520(16.8%) 
No religion 521(2.6%) 20(2.3%) 541(2.6%) 
Other 59(0.3%) 3(0.3%) 62(0.3%) 
Missing 38(0.2%) 0(0%) 38(0.2%) 
Wealth index
Poorest 6893(34.3%) 285(32.7%) 7178(34.2%) 
Poorer 4154(20.7%) 194(22.3%) 4348(20.7%) 
Middle 3334(16.6%) 163(18.7%) 3497(16.7%) 
Richer 3001(14.9%) 130(14.9%) 3131(14.9%) 
Richest 2711(13.5%) 99(11.4%) 2810(13.4%) 
Sex
Male 10157(50.6%) 476(54.6%) 10633(50.7%) 
Female 9936(49.5%) 395(45.4%) 10331(49.3%) 
Age group
15-19 1024(5.1%) 28(3.2%) 1052(5.0%) 
20-24 4773(23.8%) 210(24.1%) 4983(23.8%) 
25-29 6143(30.6%) 250(28.7%) 6393(30.5%) 
30-34 4009(20.0%) 179(20.6%) 4188(20.0%) 
35-39 2659(13.2%) 117(13.4%) 2776(13.2%) 
40-44 1164(5.8%) 69(7.9%) 1233(5.9%) 
45-49 321(1.6%) 18(2.1%) 339(1.6%) 
Birth type
Single Birth 19596(97.5%) 784(90.0%) 20380(97.2%) 
1st of  multiple 240(1.2%) 52(6.0%) 292(1.4%) 
2nd of  multiple 257(1.3%) 35(4.0%) 292(1.4%) 
No of  children
0 586(2.9%) 251(28.8%) 837(4.0%) 
1 7415(36.9%) 372(42.7%) 7787(37.1%) 
2 8314(41.4%) 198(22.7%) 8512(40.6%) 
3 3086(15.4%) 38(4.4%) 3124(14.9%) 
4 570(2.8%) 8(0.9%) 578(2.8%) 



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KDHS data. Of  these 871 had died within their first 
years of  life and 20,093 were alive. Table 1 shows the 
descriptive characteristics of  some the variables included 
in the study. Around 34 per cent of  those who died were 
living in urban areas and 66 percent in rural areas. Among 
the dead children 54.6 percent were male and 45.4 percent 
were female.There were more children born in the 

poorest households than the richest households. Almost 
53% of  the mothers had primary level of  education, 22% 
no education, 19% secondary education and 6% higher 
education.

Bivariate Analysis between Maternal Education and 
Household Wealth Level

5 98(0.5%) 3(0.3%) 101(0.5%) 
6 19(0.1%) 1(0.1%) 20(0.1%) 
7 5(0.0%) 0(0%) 5(0.0%) 

Table 2: Bivariate analysis between maternal education and household wealth level
Highest Education Level Wealth index 
 
 
 
 
 
 
 

 Poorest Poorer Middle Richer Richest 
No Education 3690 306 186 229 174 
 80.5 % 6.7 % 4.1 % 5.0 % 3.8 % 
Secondary Education 311 718 917 1096 961 
 7.8 % 17.9 % 22.9 % 27.4 % 24.0 % 
Higher education 17 64 142 321 777 
 1.3 % 4.8 % 10.8 % 24.3 % 58.8 % 

Table 3: Parameter estimates and standard errors for the regression of  maternal income on education adjusting for 
Age and sex
Coefficients Estimate Std. Error t value Pr(>|t|) 
(Intercept) 1.281 0.048 26.565 <2e-16***
Age 0.005 0.001 3.942 8.09e-05***
Sex 0.013 0.016 0.810 0.418 
Primary education 0.987 0.021 47.064 <2e-16***
Secondary education 1.980 0.026 76.482 <2e-16***
Higher education 2.896 0.037 77.901 <2e-16***

Signif. codes: 0***,0.001**,0.01*,0.05.,0.11 

Table 4: Parameter estimates and standard errors(SE) from the Aalen additive model adjusting for maternal income, 
Education level, age and Sex
Education level Estimate(SE) x10-3

No education 0.00(0.00)
Primary education -1.45(0.057)

Mothers residing in households with higher levels 
of  wealth and affluence exhibited a greater level of  
educational attainment in comparison to mothers from 
economically disadvantaged households. Among the 
poorest families (80.5%) were at no education level. 
Among the richest households only(3.8%) were in the 

no education level. However only (1.3%) of  the poorest 
households had a higher education level compared with 
(58.8%) from the richest households. 

Regression of  Maternal Income on Education 
Adjusting for Age and Sex

Table 3 suggests that, on average, mothers at higher 
education levels have an income of  2.9 units higher than 
mothers at no education level when adjusted for age and 
sex. Mothers in secondary education have an income of  
1.98 units higher than mothers in no education level. 
Mothers in primary level have an income of  0.99 units 

higher than mothers in no education level.Mothers with 
higher education level in general have higher incomes 
compared to those with low education levels. 

Aalen Additive Model Adjusting for Maternal 
Income, Education Level, Age and Sex



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Secondary education -2.30(0.812)
Higher education -2.75(0.26)
Maternal income -2.16(0.728)

Table 4 shows that children born of  mother’s in higher 
education level have a mortality rate that is 2.75X10-3 
units lower than those of  mothers in no education level 
adjusted for age and sex. Children born of  mothers in 
secondary education level have a mortality rate that 
is 2.30X10-3 units lower than those of  mothers in no 
education level. Children born of  mothers in primary 

education level have a mortality rate that is 1.45X10-3 
units lower than those of  mothers in no education level. 
The higher the education level for the mothers,the lower 
the mortality rate for their under-five children. 

Mediation Analysis of  Maternal Income on Mothers 
Education Level for Under Five Child Mortality

Table 5: Mediation analysis of  maternal income on mothers education level for Under Five Child Mortality
Education level Total effect Direct effect Indirect effect 
0-I -1.9 -1.4 -0.5 
0-II -2.5 -2.3 -0.2 
0-III -3.5 -2.8 -0.7 

As in the findings of  He et al. (2020) , high education 
level leads to a lower rate of  child mortality.The effect of  
mothers education level has two components,direct effect 
without maternal income and mediation effect of  maternal 
income. Change from no education level to higher 
education level would reduce the number of  deaths by 3.5 
per 1000 childrenβ=-3.5 of  this decrease 0.7 fewer deaths 
(β=-0.7) resulted from maternal income pathway(natural 
indirect effect)representing 20 percent of  the total effect. 
This implies that if  an intervention were able to increase 
the maternal income of  individuals with no education to 
that of  those with higher education, while leaving other 
aspects of  social deprivation unchanged, then 20% of  the 
effect associated with education level could be mitigated.

A transition from having no education to attaining a 
secondary level of  education is associated with a reduction 
of  2.5 deaths per 1000 children (β=-2.5). Among this 
decrease, 0.2 fewer deaths (β=-0.2) can be attributed to 
the maternal income pathway, considered the natural 
indirect effect. This represents 8% of  the total effect. If  
an intervention were to elevate the maternal income of  
individuals with no education to the level of  those with 
secondary education while keeping all other aspects of  
social deprivation constant, it could potentially eliminate 
8% of  the educational level’s impact. 

Estimation of  the Interaction between Maternal 
Education and Maternal Income

Table 6: Mediation analysis of  maternal income on mothers education level for Under Five Child Mortality
Education level Total effect Direct effect Indirect effect Interaction effect 
0-1 -111.8 -25.1 -8.1 -77.8 
0-II -131,6 -119.7 18.5 -30.4 
0-III -345.6 -366.4 -26.8 47.6 

The majority of  the total effect 70%is attributed to the 
interaction between change from no education level to 
primary education level and maternal income. 22% is 
associated with the pure direct effect, while 8% is linked to 
the pure indirect effect. This analysis suggests that while 
a significant portion of  the impact of  maternal education 
on under-five child mortality (UFCM) is mediated by 
increasing maternal income, it is the interaction between 
maternal education and maternal income in most cases of  
mediation that leads to a reduction in UFCM.

Discussion
While conducting regression analysis, it is an important 
subject to attempt to decompose exposure effects in 
the presence of  mediation and interactions. Evaluation 
of  mediators and interactions is vital in guiding public 
health interventions, clinical judgment, and healthcare 

planning policies. By attempting to use varied techniques 
in analysis, more insights into the data becomes clearer 
leading to improved inference. This study used the 
Aalen’s additive model which differs slightly from the Cox 
regression model. The latter approach involves modeling 
the hazard rate and assumes a proportional hazard 
structure, while the former employs an additive model, 
assuming a linear parametric structure for the hazard 
rate. Additive hazard models allow for the decomposition 
of  effects into total, direct, and indirect components. 
The analysis utilized KHDS 2014 data to identify the 
determinants of  UFCM. Kenya is one of  the countries 
in the African region with high UFCM rates. Identifying 
factors leading to mortality among children under 5 years 
is crucial problem that needs consideration. This could 
help inform more appropriate health and intervention 
strategies. Using the Aalen additive models, we identified 



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the total effects, direct effects, indirect effects and 
interactive effects between children’s survival time, 
mother’s education, maternal income and maternal health 
behaviour. We evaluated the effect of  maternal income 
in mediating the impact of  maternal education on child 
mortality among children under the age of  five in Kenya. 
Our results confirm what has generally been found. In 
the analysis, the selection of  covariates is linked to the 
findings in Nguyen et al. (2016). To assess interaction, 
we adopted a pragmatic approach grounded in the idea 
that interventions and preventive measures should target 
patients or specific subgroups of  the population where 
most cases can be prevented. Interactions are typically 
evaluated by incorporating a product term into the 
regression model, a method that relies on the model’s 
underlying scale (Martinussen, 2006). We evaluated 
interaction by calculating the deviation from the additivity 
of  effects using a model incorporating a product term to 
account for the interaction between maternal education 
level and maternal income. The findings were as follows: 
UFCM was higher amongst mothers with no education 
level. Some of  the differential effect of  maternal income 
is most likely due to varying incomes across educational 
groups. A large percentage of  the total effect (70%)was 
attributed to the interaction between change from no 
education level to primary education level and maternal 
income. Suppose we consider the observed relationships 
to be causal, that would imply that a specific intervention 
aimed at increasing income among uneducated individuals 
would result in a more significant reduction in UFCM 
than interventions directed toward mothers with a higher 
education level. Similarly, a universal intervention such as 
educating the mothers with the same increase in income 
in both groups would be expected to have a stronger 
effect on the reduction of  UFCM in the no-education 
level group. Results from other researches concur with 
our findings. For example, Imbo et al. (2021) highlighted 
that mothers without any education had significantly 
higher odds of  neonatal deaths, with an adjusted Odds 
Ratio (aOR) of  2.201, 95% CI: 1.43-4.15, p=0.049, when 
compared to mothers with higher levels of  education. 
However, this study employed logistic regression, only 
adjusting for some specific covariates of  interest. A similar 
study based on DHS data, conducted in Ethiopia showed 
that neonates born to fathers with secondary and higher 
education level (AOR=0.51; 95%CI: 0.22-0.88) had lower 
odds of  neonatal mortality in Ethiopia. The analysis was 
conducted using multiple logistic regression and missed 
out on the possible role of  mediation, moderation or 
interactions in directing the role of  some of  the defined 
exposure effects (Basha et al., 2020). Another study in 
Ethiopia also made the following findings. Neonatal 
mortality was significantly associated with being born to a 
mother without formal education (AOR = 1.79, 95% CI: 
1.12-2.88), a mother who did not participate in healthcare 
decision-making (AOR = 1.25, 95% CI: 1.14-1.79), 
and being part of  a twin birth (AOR = 6.85, 95% CI: 
3.69-12.70). The model used was a multivariable logistic 

regression model without any additional assumptions 
on covariate interactions or role of  mediation, as is 
commonly done for such cross-sectional studies using 
DHS datasets. The main limitation of  this study is that 
only a select few select variables were included in the final 
model, being the outcome variable (UFCM), the exposure 
variable (maternal education) and the mediator variables 
(maternal income and health characteristics). A more 
parsimonious model could be useful to illuminate even 
more realistic effect of  the exposure variable on UFCM.

CONCLUSION
The study involves quantification of  mediation in a 
survival context. We applied an easier and interpretable 
measure of  natural direct, indirect effects, and interactive 
effects in addition to their confidence intervals. The 
additive hazard scale is used to calculate the effects. 
This helps in direct translation of  expected no of  
extra cases. This study offers a simple and intuitive 
approach to evaluating deviations from additive effects 
in survival analysis by utilizing additive models in the 
context of  mediation and interaction. In the absence of  
bias, deviations from risk additivity suggest that certain 
subgroups may experience greater absolute risk reduction 
than others. Additionally, a researcher might be interested 
in determining the extent to which a mediated effect 
depends on the combined influence of  the exposure 
and the mediator. The method is illustrated by analysis 
of  the linkage among education, maternal income and 
under-five mortality previously examined in the study of  
Soe et al. (2019). This paper contributes to the literature 
on mediation analysthe is as well as literature on the 
importance of  education on UFCM. The influence of  
education on UFCM had different pathways in this study. 
Interventions with a given increase in income among 
those with no education level would yield a greater 
reduction in UFCM than interventions targeting mothers 
with a higher education level. The results of  this study 
may contribute to improve relevant interventions for 
UFCM among children in Kenya. It will assist the Kenyan 
government, non-governmental organizations, and other 
health sector partners in identifying key focus areas and 
relevant statistical tools needed to formulate policies and 
implement projects aimed at reducing UFCM, which 
aligns with the Sustainable Development Goals (SDGs).
Future experimental studies are then necessary to provide 
more information on the implementation of  mediation 
analysis methods in cases where the strong assumptions 
that need to be met are violated. Studies on statistical 
power to detect interactions and to incorporate additive 
hazard models into other conventional software package 
are required.

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