Copperbelt University
Directorate of Distance Education and Open Learning
Master in Public Health
MEP 700: Introduction to Epidemiology, Data Analysis, and Interpretation
of Epidemiology Data
Assignment 4
Interpreting the fitted equation on the effects of toxemia in pregnant
mothers on the head circumference of the new born babies
By
Brian Kaonga
SIN: 22900539
14th May 2024
Lecturer: Dr Collins Otieno Odoyo
The fitted equation from a study on infant head circumference is as follows:
head circumference = 1.76 + 0.86×gestational age - 2.82 × toxemia + 0.046 × (gestational
age × toxemia)
where gestational age is measured in weeks and toxemia is an indicator variable for the
mother’s toxemia status during pregnancy (1=had toxemia).


For infants whose mothers did not have toxemia during
pregnancy, what is the effect of an extra two weeks of
gestation? What about for those whose mothers had
toxemia?
 What other information or calculations would you need to
decide whether to include this effect in the final model?
 What effect does the last term represent? How would you
interpret this effect?
Specify the regression models and interpret regression results
Scenario1
Using the equation below, we can find the relationship of a head circumference as
follows;
head circumference = 1.76 + 0.86 × gestational age - 2.82×toxemia + 0.046×
(gestational age × toxemia).
Based on the computation above, the effects are observed in the calculation on
infants born from mothers who had no toxemia during pregnancy as an increase
of two weeks of gestation on head circumference also increases to 0.86 translating
into 1.72.
This is expressed arithmetically as follows;
(I). Head circumference =1.76 + 0.86 x (gestation age + 2) - 2.82 + 0.46
(gestational age+2) 0).
(II.) Meaning that 1.76 + 0.086 gestation age +1.72 + 0, apart from the outcome
observed in this equation; 1.76 + 0.86 x gestation age + 1.72, it is further observed
that mothers that had toxemia during gestation, Had effects on the head
circumference of the babies.
Given the toxemia value as 1, the equation can be expressed therefore as 1.76 +
0.86 x gestation age - 2.82 x1+0.046x (gestational age x 1) with a negative
outcome of - 1.06+0.906 x gestation age.
This therefore means that, an elevation in the levels of toxemia results in an
increase in the head circumference as can be seen by a two-unit increase in
toxemia that increased head circumference by 0.906 x2 = 1.812 units.
Scenario 2
the statistical analysis of the model should be the additional aspect that should
involve hypothesis testing to enable the analysis of coefficients. This can be done
using statistical analysis methods like the Bayesian Criterion that can be
embedded in the model.
Additional statistically significant testing of parameters using a predetermined
threshold of 0.05. Significant testing, analysis, and interpretation result in an
accurate scientific conclusion of the relationship between the two sets of variables.
Scenario 3
The last term, 0.046 × (gestational age × toxemia) shows the effect of interaction
between gestational age and toxemia status of a mother during the pregnancy
period. This can be interpreted as the presence of toxemia in mothers during the
gestational period determining the variation of head circumference in infants. With
regards to the positive coefficient (0.046) for the equation, it denotes that the effect
of gestational age on head circumference differs depending on the levels of
toxemia. Furthermore, the interaction term indicates that the toxemia status may
change the effects on the head circumference.
Scenario 4
The regression model is specified as follows; Head circumference = 1.76 + 0.86
× gestational age - 2.82 × toxemia + 0.046 × (gestational age × toxemia).
This means that four coefficients can be interpreted as 1.76 stands for an intercept
and shows the head circumference assuming both gestational age and toxemia
have zero values. The second coefficient is 0.86 denoting that the head
circumference increases with unit increase in weeks of gestation.
Whereas the third coefficient -2.82 represents the difference in head circumference
between infants born from mothers who had toxemia who were found to have no
toxemia. Lastly, 0.046 shows that the presence of toxemia changes the association
between head circumference and gestational age.
Conclusion
The study on infant head circumference is a crucial aspect of pediatric
development and health. Understanding the patterns and variations in head
circumference can provide valuable insights into brain growth and potential
developmental abnormalities.
Therefore, this regression model shows predictive ability on study outcomes. The
model has been able to provide a way to predict infant head circumference
based on gestational age and toxemia status. The effect of an extra two weeks of
gestation on head circumference can be determined by examining the coefficient
of gestational age in the fitted equation (Hickey, 2020).
For infants whose mothers did not have toxemia during pregnancy, the effect of
an extra two weeks of gestation can be calculated by multiplying the coefficient.
In practical terms, regression modeling provides relevant information on how
predictive outcomes can be reinforced or improved in public health (Lefebvre &
Giorgi, 2021). In this specific case under study, understanding how these factors
interplay and influence head circumference can be crucial for monitoring infant
growth and development.
REFERENCES
1. Huang, F. L. (2022). Alternatives to logistic regression models in experimental
studies. Journal of Experimental Education, 90(1).
https://doi.org/10.1080/00220973.2019.1699769
2. Lefebvre, F., & Giorgi, R. (2021). A strategy for optimal fitting of multiplicative and
additive hazards regression models. BMC Medical Research Methodology, 21(1).
https://doi.org/10.1186/s12874-021-01273-2