Subjects in the study were selected from a cohort of 117 participants in the Nun Study who had donated their brains . The Nun Study was approved by the University of Kentucky's Institutional Review Board. In order to select control subjects with normal cognitive function we excluded non-demented subjects with a MMSE score equal or less than 24 and/or the concomitant presence of mild cognitive impairment of the amnesic type .
Thirty six subjects matched these criteria. Six of them were ApoE4 positive (16.6%).
Selection criteria for pure AD patients was the presence of clinical dementia and values of NFT and NP in the neocortex and hippocampus above the following cut-off:
Neurofibrillary Tangles in Neocortex: average value of neocortical NFT per mm2 > 1.0;
Neurofibrillary Tangles in Hippocampus: average value of hippocampal NFT per mm2 > 10;
Neuritic Plaques in Neocortex: maximum number of NP in the neocortex >1.5;
Neuritic Plaques in Hippocampus: maximum number of NP in the hippocampus >1.5.
These cut-off derive from a previous mathematical validation of neuropathological values distribution observed in a previous study .
Twenty six patients fulfilled these criteria and they constitute the AD cases in this analyses. Nine of them were ApoE4 positive (34.6%).
Artificial neural networks analysis
ANNs structure and architecture
ANNs models were constructed by using non commercial programs developed by Semeion Research Center [12–17]. In this experiment several ANN architectures with different learning rules were assessed, all of them sharing the following structure: the input vector had number of nodes equal to the number of independent variables, the output vector had two nodes corresponding to the two different outcomes (AD cases vs normal controls), and a single layer of hidden units
ANNs with Back Propagation learning rule were employed sharing the following structure: the input layer had a number of nodes equal to the number of independent variables, the output layer had two nodes corresponding to the target (AD cases/normal controls), and the inner layer had four hidden units.
Results obtained with those neural networks have been compared with a linear statistical model: the Linear Discriminant Analysis (LDA) (Software SPSS®) using the same training and testing subsets.
During the training phase the input relevance of each variable was assessed. The so called "input relevance" is a parameter expressing the magnitude of the activation of a given node during the training phase. The magnitude of the activation is arbitrarily expressed with a number which ranges from zero to infinity.
In technical terms, the "Input Relevance" is the Fan-out of every input when the ANN is trained:
is the mean relevance of the i-th input variable of the dataset;
K is the number of classifiers used in the training phase;
N is the number of hidden units of the K classifiers trained;
is the trained weight of the c-th classifier, connecting the i-th input to the j-th hidden unit.
The Validation Protocol
The validation protocol is a fundamental procedure to verify the models' ability to generalize the results reached in the Testing phase of each model. The application of a fixed protocol measures the level of performance that a model can produce on data that are not present in the Testing and/or Training sample. Different types of protocol exist in the literature, each presenting advantages and disadvantages.
The protocol, from the point of view of a general procedure, consists of the following steps:
subdividing the database in a random way into two subsamples: Subsets A and B;
train an ANN on Subset A; in this phase the ANN learns to associate the input variables with those that are indicated as targets;
at the end of the training phase the weight matrix produced by the ANN is saved and frozen together with all the other parameters used for the training;
with the weight matrix saved, Subset B, which it has not seen before, is shown to the ANN, so that in each case the ANN can express an evaluation based on the previous training; this operation takes place for each input vector and every result (output vector) and is not communicated to the ANN; the ANN is in this way evaluated only in reference to the generalization ability that it has acquired during the Training phase;
a new ANN is constructed with identical architecture to the previous one and the procedure is repeated from point 1; but this time the ANN will be trained on Subset B and blindly tested on the Subset A.
This general training plan has been further articulated with the aim of increasing the level of reliability in terms of generalization of the processing models. More specifically we employed the so-called 5·2 cross-validation protocol . In this procedure the study sample is randomly divided ten times into two sub samples, always different but containing a similar distribution of cases and controls: the training one (containing the dependent variable) and the testing one. During the training phase the ANN learns a model of data distribution and then, on the basis of such a model, classifies subjects in the testing set in a blind way. The training and testing sets are then reversed and consequently 10 analyses for every model employed are conducted. To compare the ANNs performances, the same protocol was used with the same data distribution to validate the Linear Discriminant Analysis (LDA).