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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/ You may leave the list at any time by sending the command SIGNOFF allstat to [log in to unmask], leaving the subject line blank.