Early brain development in infants at high risk for autism spectrum disorder
http://www.nature.com/nature/journal/v542/n7641/full/nature21369.html
This study claims to be able to predict a diagnosis of autism (A) “with
a positive predictive value of 81% and a sensitivity of 88%”.
(Full abstract below).
But, as far as I can tell, (B) the mutual information between a
diagnosis of autism and a PREDICTED diagnosis of autism is 0.41 bits.
This means that knowing the predicted diagnosis reduces uncertainty
regarding a child's actual diagnosis (relative to guessing) by a factor
of only 1.33 (=2**0.41).
This seems like a remarkably weak result. Can anyone spot if I have
missed something here? Or is that just what we should expect when
translating from conventional measures to information-theoretic measures?
with thanks,
Jim Stone
=======================
More details ...
The hits and false alarms data are:
Hits = 30
FAs = 7
Correct rejections = 138
Misses = 4
The study comprised two groups of children, called low-risk and high risk.
The high-risk group comprised 34 children who were diagnosed as autistic
at 2 years of age.
The low-risk group comprised 145 children.
Total number of children in cohort, N = 179.
Key:
x = autism diagnosed at 24 months.
y = predicted diagnosis of autism based on measured variables (cortical
volume, etc).
The mutual information between x and y is I(x,y) = 0.41 bits (see
below). This means that knowing the predicted diagnosis reduces
uncertainty regarding a child's diagnosis by a factor of 2**0.41 = 1.33.
Notice that, within this cohort, if a child is chosen at random then the
probability that it has an autism diagnosis is 34/179=0.190, so one
background probability is quite high.
These calculations are model-free, inasmuch as they require no
assumptions regarding the underlying distributions of variables.
=======================
Appendices
=======================
MATHS CALCULATIONS
The mutual information between x and y is the difference in entropies
I(x,y) = H(x) + H(y) - H(x,y),
Where (using logs to the base 2) the entropy of the joint distribution
p(x,y) is
H(x,y) = sumi sumj p(xi,yj) log(1/p(xi,yj)),
and the entropies of the marginal distributions of p(x,y) are
H(x) = sum_i p(xi) log(1/p(xi))
H(y) = sum_j p(yj) log(1/p(yj)).
=======================
MATLAB CALCULATIONS
% Results from Nature paper.
hits=30;
FA=7; % false alarms.
miss=4;
CR=138; % correct rejections
data = [hits FA; miss CR]; % make 2D table;
n = sum(data(:)); % total cohort.
data = data/n; % convert to proportions.
px = sum(data); % marginal distribution for autism diagnosis.
py = sum(data'); % marginal distribution for PREDICTED autism diagnosis.
Hx = sum(px.*log2(1./px)); % entropy of px.
Hy = sum(py.*log2(1./py)); % entropy of py.
ppp=data(:); % Joint distribution p(x,y).
Hxy = sum(ppp.*log2(1./ppp)); % entropy of joint distribution.
I = Hx+Hy-Hxy % = 0.4099 bits. MI between predicted autism diagnosis
and autism diagnosis.
2^I % equivalent number of outcomes. = 1.3285
=======================
Paper abstract
Brain enlargement has been observed in children with autism spectrum
disorder (ASD), but the timing of this phenomenon, and the relationship
between ASD and the appearance of behavioural symptoms, are unknown.
Retrospective head circumference and longitudinal brain volume studies
of two-year olds followed up at four years of age have provided evidence
that increased brain volume may emerge early in development1, 2. Studies
of infants at high familial risk of autism can provide insight into the
early development of autism and have shown that characteristic social
deficits in ASD emerge during the latter part of the first and in the
second year of life3, 4. These observations suggest that prospective
brain-imaging studies of infants at high familial risk of ASD might
identify early postnatal changes in brain volume that occur before an
ASD diagnosis. In this prospective neuroimaging study of 106 infants at
high familial risk of ASD and 42 low-risk infants, we show that
hyperexpansion of the cortical surface area between 6 and 12 months of
age precedes brain volume overgrowth observed between 12 and 24 months
in 15 high-risk infants who were diagnosed with autism at 24 months.
Brain volume overgrowth was linked to the emergence and severity of
autistic social deficits. A deep-learning algorithm that primarily uses
surface area information from magnetic resonance imaging of the brain of
6–12-month-old individuals predicted the diagnosis of autism in
individual high-risk children at 24 months (with a positive predictive
value of 81% and a sensitivity of 88%). These findings demonstrate that
early brain changes occur during the period in which autistic behaviours
are first emerging.
=======================
--
Dr James V Stone
Psychology Department, Sheffield University.
http://www.jim-stone.staff.shef.ac.uk/
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