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Skew-Normal Regression for Determination of
Risk Factors Associated with LBW
Student: Kristoffer Seem Mathematics  University of Wisconsin-Eau Claire
Faculty mentor: Dr. Aziz
Background
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Birth weight is one of the main aspects to look at when considering
infant mortality rates.
In the last 20 years there has been no real decrease in infant mortality
rate in the US(Lau, 2013).
This is due to a general increase in the proportion of LBW that have
been born in more recent years(Lau, 2013).
Birth weight follows a Skew-Normal distribution and thus should be
analyzed as such.
Birth weights were analyzed in groupings of all infant birth weights,
below 2500 g (LBW) and below 1500g (vLBW)
Risk factors associated with LBW were found and included physical and
socioeconomic factors of the parents.
Results
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Boxplots of the 3 birth groupings, full data set used for infant and
LBW plots. For vLBW the 98 observations in the group were used
for the boxplot.
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Introduction
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This research focuses on determination of risk factors that are
associated with LBW, so that we as a society and especially the health
care professionals can give better advice to future mothers so as to
reverse the trend there has been of more LBW infants being born. This
poster should give a quick look at some of the associated risk factors
that are present in the US population. Studies using other countries
populations would not work as well, since there are different gene pools
and different optimal birth weights in other countries.
Discussion
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Q-Q plot of the groupings to determine observations do not follow
a normal distribution.
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The skew normal distribution is given by:
𝑓 𝑦; ∝ = 2𝜙 𝑦 Φ 𝛼𝑦
Where α is the shape parameter of the distribution.
The multiple skew normal regression model is given by:
𝑝
𝑖=1 𝛽𝑖 𝑥𝑖𝑗
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𝑌𝑗 = 𝛽0 +
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It can be seen that as α changes so does the skewness and
direction of the distribution
+∝ 𝑧𝑗 +𝜖𝑗
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Materials and Methods
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Data was obtained from the state of Washington, the data
included all births that had occurred in the state in 2012.
Simple random sample groups were taken of 500 births from
the infant and LBW groups. From the LBW sample group
there was taken another subsection of only vLBW births.
Analyzed variables included: sex, plurality, age of parents,
race of father, education of parents, prior live births, start of
prenatal care, number of prenatal visits, weightgain during
pregnancy, weight before pregnancy, BMI before pregnancy,
genital herpes and gestational age.
Normality tests of birth groupings showed that the samples
did not follow a normal distribution.
When analyzing the different birth groupings we ended up with
different significant factors for all groupings.
Factors were determined to be significant if they had a p-value of less
than 0.05
In the infant birth weight group we found the significant factors: Sex,
twins, prior live births, marital status unknown, weight gain, weight
before pregnancy, BMI, herpes and gestational age.
In the LBW group the significant factors included: Triplets, prior live
births, start of prenatal care, prenatalcare visits, herpes and
gestational period.
In the vLBW group significant factors found were: Twins, triplets, age
of father, age of mother, education of mother, prior live births, start of
prenatalcare, prenatalcare visits, marital status unknown, weight gain,
BMI, herpes and gestational age.
In summation we found that Skew-Normal regression was more
appropriate for determination of risk factors when it comes to LBW
infants.
The risk factors that we found were associated with LBW were different
from the factors associated with a healthy birth weight and those
associated with vLBW.
Risk factors included both physical, pathological and socioeconomic
factors. This helps us appreciate exactly how many things and how
complex of a thing it is for a baby to develop correctly.
Some of the factors that are determined to be significant previously in
literature were not found to be significant in our analysis of the data.
At the same time we found significant factors that were not significant in
other articles from literature.
This knowledge on risk factors will allow people in the health care
professions to give coming mothers better advice when it comes to
carrying and giving birth to babies that are of a healthy weight.
Further work needs to be done with additional variables, bigger
geographic area and a determination of variables effects on each other.
The checking of association between variables is most important with
socioeconomic factors.
Acknowledgements
We thank the Office of Research and Sponsored Programs for supporting
this research, and Learning & Technology Services for printing this
poster.
Citations
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Above figure shows the distributions of Skew-Normal distributions
with the only different between them being the value of α.
As a means of comparison a regular linear normal regression
analysis was also performed, this showed less significant factors
than the Skew-Normal.
Lau, C.A., et al (2013) Extremely Low Birth Weight and Infant Mortality Rates
in the United States. Pediatrics, May 2013131(5):855-860