between variables, and MST is then used to construct a cohesive graphical representation using only the relevant associations, which can then be used to construct a more complex global picture representing the entire pattern of variation.
We doubled the preselected clinical variables by reshaping the range of values typical of the variable from 0 to 1 and dichotomized the values in two classes, High (H) and Low (L). To do this we used a particular complement transformation, by scaling original variable values from 0 to 1, and creating a complement variable by subtracting the scaled value from 1. See Gironi et al, 2013 for further details.20
In this way the system establishes the mutual relationships among variables as defined by the disease. This is a key issue: in non-linear systems, the position of any given values (High or Low) is not necessarily symmetric. In this manner the value of the original variables represents the “high†values whereas the complementary transformed values make up the “low†values, which are accordingly demarcated in the generated map. This scaling dynamic makes a proportional comparison possible among all the variables and allows for understanding of the connections between each variable.
Application of supervised neural networks
In order to assess the predictive value of the subset of variables most closely correlated to a target diagnosis (ie, response to secukinumab) we assembled a data set with seven variables as input and two variables (fast-responder vs non-responder) as output. The evolutionary algorithm called Training with Input Selection and Testing, or TWIST, was employed to select the most representative variables based on the transformation into Low and High.
TWIST works by taking the global dataset, using it to generate the maximal distribution and processing the data into two balanced subsets, each containing a minimal amount of input data allowing for optimal pattern recognition. The TWIST algorithm approach was first described in 2013, and several promising examples of its use have been published.21-23 In most cases, the TWIST algorithm is comprised of a population of Multilayer Perceptrons.21-23
Each ANN is “taught†a subset of the larger global dataset and then tested in a blinded fashion using with another subset. Here, we re-programmed the TWIST fitness function and exchanged the population of Multilayer Perceptrons with a population of simple K Nearest Neighbor (KNN) values, using Euclidean metrics. This alteration accelerates TWIST and makes it more “focused†on discovering f explicit similarities between input attributes. Indeed, TWIST selects the most appropriate attributes from the original attributes and generates a global dataset of attributes, identifying two optimal subsets for training and testing. By applying the training testing protocol to the global data set, we can verify that the attributes selected by TWIST provide good discrimination between fast-responders and non-responders to secukinumab.
Supervised ANNs with four hidden units equipped with a back- propagation algorithm were trained and tested on this data set employing the Leave One Out protocol (LOOP, or rotational estimation), which is a comprehensive method for cross-validation and can predict all cases in a blinded manner. In this protocol, the training model includes all cases except 1, the latter being used as a rotating test case. This is also called “Leave-p- out cross-validation,†where a “p†number of observations are kept for validation while the other observations are used in the training set. Every possible combination of “p†observations and other observations are created for cross-validation.
As mentioned in the introduction, having used ANNs in combination with LOOP, the small dimension of the sample size was counterpartyed. A calculation of sample power is not applicable due to the study nature (pilot study) and the non- linear statistics (ANNs).
We doubled the preselected clinical variables by reshaping the range of values typical of the variable from 0 to 1 and dichotomized the values in two classes, High (H) and Low (L). To do this we used a particular complement transformation, by scaling original variable values from 0 to 1, and creating a complement variable by subtracting the scaled value from 1. See Gironi et al, 2013 for further details.20
In this way the system establishes the mutual relationships among variables as defined by the disease. This is a key issue: in non-linear systems, the position of any given values (High or Low) is not necessarily symmetric. In this manner the value of the original variables represents the “high†values whereas the complementary transformed values make up the “low†values, which are accordingly demarcated in the generated map. This scaling dynamic makes a proportional comparison possible among all the variables and allows for understanding of the connections between each variable.
Application of supervised neural networks
In order to assess the predictive value of the subset of variables most closely correlated to a target diagnosis (ie, response to secukinumab) we assembled a data set with seven variables as input and two variables (fast-responder vs non-responder) as output. The evolutionary algorithm called Training with Input Selection and Testing, or TWIST, was employed to select the most representative variables based on the transformation into Low and High.
TWIST works by taking the global dataset, using it to generate the maximal distribution and processing the data into two balanced subsets, each containing a minimal amount of input data allowing for optimal pattern recognition. The TWIST algorithm approach was first described in 2013, and several promising examples of its use have been published.21-23 In most cases, the TWIST algorithm is comprised of a population of Multilayer Perceptrons.21-23
Each ANN is “taught†a subset of the larger global dataset and then tested in a blinded fashion using with another subset. Here, we re-programmed the TWIST fitness function and exchanged the population of Multilayer Perceptrons with a population of simple K Nearest Neighbor (KNN) values, using Euclidean metrics. This alteration accelerates TWIST and makes it more “focused†on discovering f explicit similarities between input attributes. Indeed, TWIST selects the most appropriate attributes from the original attributes and generates a global dataset of attributes, identifying two optimal subsets for training and testing. By applying the training testing protocol to the global data set, we can verify that the attributes selected by TWIST provide good discrimination between fast-responders and non-responders to secukinumab.
Supervised ANNs with four hidden units equipped with a back- propagation algorithm were trained and tested on this data set employing the Leave One Out protocol (LOOP, or rotational estimation), which is a comprehensive method for cross-validation and can predict all cases in a blinded manner. In this protocol, the training model includes all cases except 1, the latter being used as a rotating test case. This is also called “Leave-p- out cross-validation,†where a “p†number of observations are kept for validation while the other observations are used in the training set. Every possible combination of “p†observations and other observations are created for cross-validation.
As mentioned in the introduction, having used ANNs in combination with LOOP, the small dimension of the sample size was counterpartyed. A calculation of sample power is not applicable due to the study nature (pilot study) and the non- linear statistics (ANNs).
RESULTS
Demographics
We enrolled 23 bio-naïve plaque psoriasis patients, respectively 6 females and 17 males, with a mean age of 39 [34.3–47.3] years, and a mean body mass index (BMI) of 26.7 [23.5–28.6] kg/m2. No statistical differences in BMI were detected. Scalp was involved in 20 of the patients and nail involvement was present in 11 patients. Among the participants, there were 5 ex-smokers (no
We enrolled 23 bio-naïve plaque psoriasis patients, respectively 6 females and 17 males, with a mean age of 39 [34.3–47.3] years, and a mean body mass index (BMI) of 26.7 [23.5–28.6] kg/m2. No statistical differences in BMI were detected. Scalp was involved in 20 of the patients and nail involvement was present in 11 patients. Among the participants, there were 5 ex-smokers (no
