Biology Reference
In-Depth Information
individuals about the mean. To characterize the elevated variability of the exposed popu-
lations and identify the most affected features, a
relative eigenanalysis
was performed. This
technique compares within-group covariance matrices, expressing dimensions of greatest
variability in one data set (here, the alcohol exposed population) as a multiple of the vari-
ance in the other data set (unexposed). When the data are shapes, the results can be used
to produce a picture that shows which regions are more variable and the direction of that
elevated variation. Because this study had more dimensions in either set of shape data
than individuals in any subject group, the analysis was restricted to a subset of dimen-
sions, the first 11 PCA axes. Relative eigenanalysis is similar to canonical variates analysis
(CVA) in some respects, but instead of computing axes of between group difference as
CVA does, relative eigenanalysis computes axes of within-group variance that are ampli-
fied in one group relative to the other.
The relative eigenalysis of the landmark data set indicated that the largest axis showing
increased variance in exposed individuals could be expressed in terms of length ratios
using only four anterior landmarks: the interior genu, the caudate, the rostrum and the
genu. This was using measurements taken from a baseline registration with the genu and
rostrum as endpoints. Scatter-plots of the relative height of the interior genu vs the height
of the caudate show a tight cluster of most unexposed individuals, within a much larger
scatter of exposed individuals (and a few unusual unexposed individuals). Relative eigen-
analysis of the corpus callosum semilandmarks revealed a similar pattern of excess vari-
ance that was not as narrowly circumscribed anatomically, but scatterplots of scores on
these eigenvectors again showed that many exposed individuals were outside the range of
variation of most unexposed individuals.
Although the results is somewhat disappointing with regards to using brain scans as
diagnostic tool for fetal alcohol exposure (the broad overlaps result in poor classification
efficiency), they are interesting for their biological significance. Based on the evidence of
elevated variation in the affected populations, the authors concluded that fetal alcohol
exposure caused disruptions in the developmental process in the maturing fetal brain.
This manifested as increased variation in structure, rather than specific defects or altera-
tions, as there was no change in the mean shapes of the examined structures. Thus these
data appear to be an example of disruption of a developmental process resulting in
increased variation, rather than a specific alteration in shape.
In a later discussion,
Bookstein and Kowell (2010)
explain how a likelihood ratio can be
constructed to express the strength of evidence that a given individual has FASD based on
geometric measurements of brain structure. In a likelihood ratio, one calculates the proba-
bility of the data
X
given two different hypotheses H
1
and H
2
, such as the two claims
made by opposing sides in a courtroom (
Lindley, 1977
):
Likelihood
P
ð
X
j
H
1
Þ
=
P
ð
X
j
H
2
Þ
(14.9)
5
The likelihood ratio approach to describing the strength of forensic evidence has seen a
rapid growth in other forensic settings as well (
Lindley, 1977; Neumann et al., 2007; Su
and Srihari, 2009, 2010
).
In the case of the brain scan data,
X
is the set of processed measurements as described
above, the classifying data. H
1
is the hypothesis that the individual suffered some level of
